Comprehensive Analysis of Silkworm Phenotypic Traits in the Phillipines
Jeshurun Asher Tarun
2024-08-07
INTRODUCTION
Unraveling the Genetic Tapestry of Silkworm Phenotypes: Silkworms (Bombyx mori), have been integral to human civilization for millennia, primarily for their silk production. However, beyond their economic significance, silkworms represent a fascinating model organism for genetic and evolutionary studies. Understanding the phenotypic diversity within and across silkworm strains is crucial for both fundamental biological research and applied breeding programs aimed at improving silk yield, quality, and other desirable traits.
This R Markdown document presents a comprehensive analysis of silkworm phenotypic traits, employing a robust statistical and multivariate framework. Our investigation encompasses the following key objectives:
1. Data Exploration & Assumption Validation: Thorough examination of the distributional properties of each phenotypic trait across different strains. Rigorous assessment of the assumptions of normality and homogeneity of variance, fundamental to the validity of subsequent statistical tests. Visual representation of trait distributions using boxplots, highlighting potential outliers that might influence the analysis. Generation of density plots to gain deeper insights into the shape and spread of trait distributions within and across strains.
2. ANOVA & Non-Parametric Testing: Application of Analysis of Variance (ANOVA) to discern statistically significant differences in trait means among silkworm strains, contingent upon the fulfillment of normality and homogeneity assumptions. Strategic employment of log transformations to rectify deviations from normality or homoscedasticity. Adoption of the non-parametric Kruskal-Wallis test when ANOVA assumptions remain unmet even after transformation. Implementation of post-hoc tests (Tukey’s HSD for ANOVA, Dunn’s test for Kruskal-Wallis) to pinpoint specific strain pairs exhibiting significant differences.
3. Multivariate Analysis: Utilization of Principal Component Analysis (PCA) to unveil the underlying structure of phenotypic variation, reducing dimensionality and identifying key patterns. Scrutiny of scree plots and biplots to ascertain the contribution of each trait to the principal components and visualize the relationships between individuals (silkworms) and variables (traits). Application of hierarchical clustering and k-means clustering on principal component scores to classify silkworms into distinct groups based on their phenotypic similarities.
4. Correlation Analysis: Computation and visualization of Pearson and Spearman correlation matrices to quantify and depict the linear and monotonic relationships between traits, respectively. Scrutiny of correlograms to discern clusters of highly correlated traits and potential multicollinearity. Execution of individual correlation tests (Pearson and Spearman) to assess the strength and significance of associations between specific trait pairs. Generation of scatterplot matrices to visualize all pairwise relationships between traits, aiding in the identification of patterns, outliers, and potential non-linear associations. Exploration of trait correlations within the context of strain variation using mixed-effects models, enabling us to discern whether correlations are consistent or differ across strains.
By integrating these diverse analytical approaches, this study aims to provide a comprehensive portrait of the phenotypic landscape in silkworms. The insights gleaned from this investigation will not only deepen our understanding of the genetic architecture underlying silkworm traits but also furnish valuable information for targeted breeding efforts to enhance silk production and other economically important characteristics. Moreover, this study contributes to the broader field of evolutionary biology by shedding light on the interplay between genetic variation and phenotypic diversity in a model organism with significant implications for both science and industry.
Data Loading and Pre-processing
# Read the data
data <- read_excel("Hatching_percentage.xls")
# Pre-process the 'Strain' column
data$Strain <- as.factor(data$Strain)
data$Strain <- unlist(lapply(strsplit(as.character(data$Strain), " - "), function(x) x[2]))
data$Strain <- as.factor(data$Strain)
# List of traits to analyze
traits <- c("Hatching_Percentage", "Larval_Weight", "Single_Cocoon_Weight",
"Cocoon_Shell_Weight", "Cocoon_Shell_Percentage", "Live_Pupa_Percentage")
# Traits for transformation and potential non-parametric tests
non_parametric_traits <- c("Hatching_Percentage", "Cocoon_Shell_Percentage", "Live_Pupa_Percentage")
# Reshape data for heatmap (use the original 'data' dataframe and keep rows with missing values)
heatmap_data <- data %>%
pivot_longer(cols = traits, names_to = "Trait", values_to = "Value", values_drop_na = FALSE)
# Convert 'Strain' and 'Trait' to factors to ensure all levels are included
heatmap_data$Strain <- factor(heatmap_data$Strain, levels = levels(data$Strain))
heatmap_data$Trait <- factor(heatmap_data$Trait, levels = traits)Data Exploration and Assumption Checking
We begin by exploring the distributions of each trait and checking the assumptions of normality and homogeneity of variance, crucial for subsequent analyses.
# Function to visualize model diagnostics
check_model <- function(model) {
# Create a layout with 2 rows and 2 columns
par(mfrow = c(2, 2))
# Plot model diagnostics
plot(model, which = 1, caption = "Residuals vs Fitted")
plot(model, which = 2, caption = "Normal Q-Q")
plot(model, which = 3, caption = "Scale-Location")
plot(model, which = 5, caption = "Residuals vs Leverage")
# Reset the plot layout
par(mfrow = c(1, 1))
}
# Loop through each trait
for (trait in traits) {
cat("\n\n--- Analyzing", trait, "---\n")
# Fit a temporary linear model to check assumptions (not assigned to global environment)
temp_model <- lm(as.formula(paste(trait, "~ Strain")), data = data)
# Boxplot with outliers (using tidy evaluation and vertical labels)
cat("\nBoxplot for", trait, ":\n")
boxplot_outliers <- ggplot(data, aes(x = Strain, y = .data[[trait]])) +
geom_boxplot(outlier.shape = 16, outlier.size = 2) +
labs(title = paste("Boxplot of", trait, "by Strain"),
x = "Strain", y = trait) +
theme_bw() +
theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1))
print(boxplot_outliers)
# Outlier Detection and Treatment (using Tukey's fences)
Q1 <- quantile(data[[trait]], 0.25)
Q3 <- quantile(data[[trait]], 0.75)
IQR <- Q3 - Q1
lower_bound <- Q1 - 1.5 * IQR
upper_bound <- Q3 + 1.5 * IQR
outliers <- data[data[[trait]] < lower_bound | data[[trait]] > upper_bound, c("Strain", trait)]
if (nrow(outliers) > 0) {
cat("\nOutliers for", trait, ":\n")
print(outliers)
} else {
cat("\nNo outliers found for", trait, "\n")
}
# Normality test (Shapiro-Wilk)
normality_test <- shapiro.test(residuals(temp_model))
cat("\nNormality Test (Shapiro-Wilk):\n")
print(normality_test)
# Homogeneity of variance test (Levene's)
variance_test <- leveneTest(residuals(temp_model) ~ data$Strain)
cat("\nHomogeneity of Variance Test (Levene's):\n")
print(variance_test)
# Distribution plots with strain labels on individual plots
cat("\nDistribution Plots for", trait, ":\n")
# Combined distribution plot
p1 <- ggplot(data, aes_string(x = trait)) +
geom_density(fill = "lightblue", alpha = 0.5) +
labs(title = paste("Distribution of", trait, "(All Strains)"),
x = trait, y = "Density") +
theme_bw()
# Distribution plots by strain (one plot per strain)
p2 <- ggplot(data, aes_string(x = trait)) +
geom_density(fill = "lightblue", alpha = 0.5) +
labs(x = trait, y = "Density") +
facet_wrap(~Strain, ncol = 6) +
theme_bw() +
theme(strip.text = element_text(size = 6))
# Arrange and print the plots (without coord_fixed)
print(ggarrange(p1, p2, nrow = 2, heights = c(1, 3)))
}##
##
## --- Analyzing Hatching_Percentage ---
##
## Boxplot for Hatching_Percentage :
##
## Outliers for Hatching_Percentage :
## # A tibble: 13 × 2
## Strain Hatching_Percentage
## <fct> <dbl>
## 1 MO204 75.4
## 2 MO224 81.7
## 3 MO237 76.1
## 4 MO240 80.1
## 5 MO240 63.8
## 6 MO240 66.0
## 7 MO241 70.3
## 8 MO255 62.6
## 9 MO261 69.7
## 10 MO261 80.7
## 11 MO267 79.8
## 12 MO269 84.6
## 13 MO279 83.8
##
## Normality Test (Shapiro-Wilk):
##
## Shapiro-Wilk normality test
##
## data: residuals(temp_model)
## W = 0.87684, p-value = 4.279e-07
##
##
## Homogeneity of Variance Test (Levene's):
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 29 1.0611 0.4121
## 60
##
## Distribution Plots for Hatching_Percentage :
##
##
## --- Analyzing Larval_Weight ---
##
## Boxplot for Larval_Weight :
##
## Outliers for Larval_Weight :
## # A tibble: 3 × 2
## Strain Larval_Weight
## <fct> <dbl>
## 1 MO257 1.32
## 2 MO261 1.35
## 3 MO288 1.47
##
## Normality Test (Shapiro-Wilk):
##
## Shapiro-Wilk normality test
##
## data: residuals(temp_model)
## W = 0.98251, p-value = 0.2686
##
##
## Homogeneity of Variance Test (Levene's):
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 29 0.7282 0.8236
## 60
##
## Distribution Plots for Larval_Weight :
##
##
## --- Analyzing Single_Cocoon_Weight ---
##
## Boxplot for Single_Cocoon_Weight :
##
## Outliers for Single_Cocoon_Weight :
## # A tibble: 5 × 2
## Strain Single_Cocoon_Weight
## <fct> <dbl>
## 1 MO224 0.9
## 2 MO234 1.66
## 3 MO239 0.83
## 4 MO241 1.58
## 5 MO261 0.49
##
## Normality Test (Shapiro-Wilk):
##
## Shapiro-Wilk normality test
##
## data: residuals(temp_model)
## W = 0.95741, p-value = 0.004935
##
##
## Homogeneity of Variance Test (Levene's):
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 29 0.5511 0.9593
## 60
##
## Distribution Plots for Single_Cocoon_Weight :
##
##
## --- Analyzing Cocoon_Shell_Weight ---
##
## Boxplot for Cocoon_Shell_Weight :
##
## Outliers for Cocoon_Shell_Weight :
## # A tibble: 3 × 2
## Strain Cocoon_Shell_Weight
## <fct> <dbl>
## 1 MO239 0.15
## 2 MO241 0.34
## 3 MO257 0.16
##
## Normality Test (Shapiro-Wilk):
##
## Shapiro-Wilk normality test
##
## data: residuals(temp_model)
## W = 0.98258, p-value = 0.2715
##
##
## Homogeneity of Variance Test (Levene's):
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 29 0.4007 0.9957
## 60
##
## Distribution Plots for Cocoon_Shell_Weight :
##
##
## --- Analyzing Cocoon_Shell_Percentage ---
##
## Boxplot for Cocoon_Shell_Percentage :
##
## Outliers for Cocoon_Shell_Percentage :
## # A tibble: 4 × 2
## Strain Cocoon_Shell_Percentage
## <fct> <dbl>
## 1 MO204 26.6
## 2 MO240 26.0
## 3 MO259 13.4
## 4 MO261 36.7
##
## Normality Test (Shapiro-Wilk):
##
## Shapiro-Wilk normality test
##
## data: residuals(temp_model)
## W = 0.86688, p-value = 1.756e-07
##
##
## Homogeneity of Variance Test (Levene's):
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 29 0.9515 0.5464
## 60
##
## Distribution Plots for Cocoon_Shell_Percentage :
##
##
## --- Analyzing Live_Pupa_Percentage ---
##
## Boxplot for Live_Pupa_Percentage :
##
## No outliers found for Live_Pupa_Percentage
##
## Normality Test (Shapiro-Wilk):
##
## Shapiro-Wilk normality test
##
## data: residuals(temp_model)
## W = 0.97768, p-value = 0.124
##
##
## Homogeneity of Variance Test (Levene's):
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 29 0.4747 0.9847
## 60
##
## Distribution Plots for Live_Pupa_Percentage :
Technical Discussion Points and Considerations:
Boxplots: 1. Central Tendency and Spread: Examine the medians (horizontal lines within the boxes) to compare the typical values of each trait across strains. Observe the interquartile ranges (IQR, the height of the boxes) to gauge the spread of the data within each strain. 2. Outliers: Identify any points plotted individually outside the whiskers. These outliers might indicate unusual observations or potential errors in data collection. Consider their impact on 3. subsequent analyses and whether they should be handled (e.g., removal, winsorization) if they are deemed to be influential. 4. Strain Differences: Visually compare the boxplots across strains to get a preliminary sense of which traits might show significant differences between strains.
Normality Tests (Shapiro-Wilk): 1. P-values: Assess the p-values for each trait. If p < 0.05, it suggests a significant departure from normality. This might necessitate data transformation or the use of non-parametric tests. 2. Visual Inspection of Q-Q Plots: Complement the p-values by examining the Q-Q plots generated by the check_model function. If the points deviate substantially from the straight line, it further supports the evidence of non-normality.
Homogeneity of Variance Tests (Levene’s): 1. P-values: Evaluate the p-values for each trait. If p < 0.05, it suggests significant heterogeneity of variance (unequal variances) across strains. This might also necessitate data transformation or the use of alternative statistical tests. 2. Visual Inspection of Residuals vs. Fitted Plots: Examine the Residuals vs. Fitted plots from check_model. If the spread of the residuals is not roughly constant across the range of fitted values, it further supports the evidence of heteroscedasticity.
Distribution Plots: 1. Shape of Distributions: Observe the shape of the density curves for each trait, both for all strains combined and for individual strains. Look for deviations from a normal bell-shaped curve (e.g., skewness, multiple peaks). 2. Strain Comparisons: Compare the density curves across strains to visually assess differences in central tendency (mean or median) and spread (variance or interquartile range).
ANOVA, Transformation, and Non-Parametric Testing
Based on the assumption checks, we’ll perform either ANOVA (if assumptions are met) or Kruskal-Wallis test (if assumptions are violated), along with appropriate post-hoc analyses. We’ll attempt a log transformation if needed to address non-normality or heteroscedasticity.
We’ll check the assumptions of normality and homogeneity of variance for all traits. If both `assumptions are met for a trait, we’ll perform ANOVA directly on the original data, followed by Tukey’s HSD for post-hoc comparisons if the ANOVA is significant. If any trait violates at least one assumption, we’ll attempt a log transformation and re-check the assumptions. If the transformed data meets both assumptions, we’ll perform ANOVA on the transformed data, again followed by Tukey’s HSD if significant. If the transformed data still violates at least one assumption, we’ll resort to the non-parametric Kruskal-Wallis test, and if that’s significant, we’ll conduct Dunn’s test for post-hoc comparisons.
# Subset the data for multivariate and correlation analyses (excluding "Replicate")
analysis_data <- data[, sapply(data, is.numeric)] # Select numeric columns
analysis_data$Replicate <- NULL # Remove "Replicate" column
# Loop through each trait
for (trait in traits) {
cat("\n\n--- Analyzing", trait, "---\n")
model <- lm(as.formula(paste(trait, "~ Strain")), data = data)
check_model(model)
# Check for non-normality or heteroscedasticity
normality_p_value <- shapiro.test(residuals(model))$p.value
levene_result <- leveneTest(residuals(model) ~ data$Strain)
homogeneity_p_value <- levene_result$"Pr(>F)"[1]
if (normality_p_value >= 0.05 & homogeneity_p_value >= 0.05) {
# Perform ANOVA directly on original data if both assumptions are met
cat("\n**Performing ANOVA on original data:**\n")
anova_result <- anova(model)
print(anova_result)
# Calculate and print eta-squared
eta_squared <- anova_result$`Sum Sq`[1] / sum(anova_result$`Sum Sq`)
cat("Eta-squared:", eta_squared, "\n")
# Tukey's HSD if ANOVA is significant
if (anova_result$`Pr(>F)`[1] < 0.05) {
tukey_result <- HSD.test(model, "Strain", group = TRUE)
print(tukey_result)
} else {
cat("\nANOVA not significant. No post-hoc test needed.\n")
}
} else {
# Attempt log transformation if at least one assumption is not met
cat("\n**Attempting log transformation...**\n")
transformed_data <- data
transformed_data[[trait]] <- log1p(transformed_data[[trait]])
transformed_model <- lm(as.formula(paste(trait, "~ Strain")), data = transformed_data)
check_model(transformed_model)
# Re-check assumptions after transformation
normality_p_value <- shapiro.test(residuals(transformed_model))$p.value
levene_result <- leveneTest(residuals(transformed_model) ~ transformed_data$Strain)
homogeneity_p_value <- levene_result$"Pr(>F)"[1]
# Print the results of assumption checks after transformation
cat("\nAssumption Checks after Transformation:\n")
cat(" Normality (Shapiro-Wilk) p-value:", normality_p_value, "\n")
cat(" Homogeneity of Variance (Levene's) p-value:", homogeneity_p_value, "\n")
if (normality_p_value >= 0.05 & homogeneity_p_value >= 0.05) {
# Use ANOVA on transformed data if both assumptions are now met
cat("\n**Performing ANOVA on transformed data:**\n")
anova_result <- anova(transformed_model)
print(anova_result)
# Tukey's HSD if ANOVA is significant
if (anova_result$`Pr(>F)`[1] < 0.05) {
tukey_result <- HSD.test(transformed_model, "Strain", group = TRUE)
print(tukey_result)
} else {
cat("\nANOVA not significant. No post-hoc test needed.\n")
}
} else {
# Use Kruskal-Wallis if at least one assumption is still violated after transformation
cat("\n**Performing Kruskal-Wallis test:**\n")
kruskal_result <- kruskal.test(as.formula(paste(trait, "~ Strain")), data = data)
print(kruskal_result)
# Calculate and print epsilon-squared (effect size for Kruskal-Wallis)
k <- length(unique(data$Strain)) # Number of groups
n <- nrow(data) # Total number of observations
epsilon_squared <- (kruskal_result$statistic - (k - 1)) / (n - k)
cat("Epsilon-squared:", epsilon_squared, "\n")
# Dunn's Test if Kruskal-Wallis is significant
if (kruskal_result$p.value < 0.05) {
cat("\n**Dunn's Test (Post-hoc with Benjamini-Hochberg correction):**\n")
dunn_result <- dunnTest(as.formula(paste(trait, "~ Strain")), data = data, method="bh")
print(dunn_result)
cat("\n**Dunn's Test (Post-hoc with Bonferroni correction):**\n")
dunn_result_bonferroni <- dunnTest(as.formula(paste(trait, "~ Strain")), data = data, method="bonferroni")
print(dunn_result_bonferroni)
}
}
}
}##
##
## --- Analyzing Hatching_Percentage ---
##
## **Attempting log transformation...**##
## Assumption Checks after Transformation:
## Normality (Shapiro-Wilk) p-value: 9.440512e-08
## Homogeneity of Variance (Levene's) p-value: 0.38741
##
## **Performing Kruskal-Wallis test:**
##
## Kruskal-Wallis rank sum test
##
## data: Hatching_Percentage by Strain
## Kruskal-Wallis chi-squared = 55.926, df = 29, p-value = 0.001928
##
## Epsilon-squared: 0.4487734
##
## **Dunn's Test (Post-hoc with Benjamini-Hochberg correction):**## Dunn (1964) Kruskal-Wallis multiple comparison## p-values adjusted with the Benjamini-Hochberg method.## Comparison Z P.unadj P.adj
## 1 MO201 - MO202 1.41430500 0.1572723698 0.46539783
## 2 MO201 - MO203 1.73467243 0.0827988423 0.35660888
## 3 MO202 - MO203 0.32036743 0.7486898120 0.90718682
## 4 MO201 - MO204 2.25819969 0.0239332123 0.25392554
## 5 MO202 - MO204 0.84389470 0.3987282525 0.69378716
## 6 MO203 - MO204 0.52352726 0.6006073826 0.83470994
## 7 MO201 - MO221 0.96110229 0.3365007372 0.65640278
## 8 MO202 - MO221 -0.45320271 0.6504027834 0.86257686
## 9 MO203 - MO221 -0.77357014 0.4391850372 0.74336767
## 10 MO204 - MO221 -1.29709740 0.1945976751 0.50386898
## 11 MO201 - MO222 -0.17190448 0.8635126284 0.95337054
## 12 MO202 - MO222 -1.58620947 0.1126917993 0.40181092
## 13 MO203 - MO222 -1.90657691 0.0565753981 0.31961426
## 14 MO204 - MO222 -2.43010417 0.0150944838 0.20519064
## 15 MO221 - MO222 -1.13300677 0.2572114114 0.59199452
## 16 MO201 - MO223 1.04705453 0.2950744291 0.61710277
## 17 MO202 - MO223 -0.36725047 0.7134321962 0.89694510
## 18 MO203 - MO223 -0.68761790 0.4916934329 0.77776961
## 19 MO204 - MO223 -1.21114517 0.2258397742 0.55191181
## 20 MO221 - MO223 0.08595224 0.9315043856 0.96938854
## 21 MO222 - MO223 1.21895900 0.2228597525 0.54770617
## 22 MO201 - MO224 2.89893456 0.0037443304 0.09581081
## 23 MO202 - MO224 1.48462956 0.1376419813 0.44025193
## 24 MO203 - MO224 1.16426213 0.2443178000 0.57138840
## 25 MO204 - MO224 0.64073486 0.5216949603 0.78797676
## 26 MO221 - MO224 1.93783226 0.0526436901 0.30945953
## 27 MO222 - MO224 3.07083903 0.0021345819 0.07142640
## 28 MO223 - MO224 1.85188003 0.0640430527 0.33165152
## 29 MO201 - MO230 2.36759345 0.0179041978 0.22252360
## 30 MO202 - MO230 0.95328845 0.3404439406 0.65819162
## 31 MO203 - MO230 0.63292102 0.5267852192 0.79291201
## 32 MO204 - MO230 0.10939376 0.9128901853 0.96855422
## 33 MO221 - MO230 1.40649116 0.1595783279 0.46903090
## 34 MO222 - MO230 2.53949793 0.0111011703 0.17885219
## 35 MO223 - MO230 1.32053892 0.1866551499 0.49509140
## 36 MO224 - MO230 -0.53134110 0.5951824260 0.82982165
## 37 MO201 - MO232 0.88296389 0.3772557795 0.68952212
## 38 MO202 - MO232 -0.53134110 0.5951824260 0.83517534
## 39 MO203 - MO232 -0.85170854 0.3943758821 0.69174802
## 40 MO204 - MO232 -1.37523580 0.1690583527 0.47753496
## 41 MO221 - MO232 -0.07813840 0.9377179636 0.96890098
## 42 MO222 - MO232 1.05486837 0.2914855302 0.61551556
## 43 MO223 - MO232 -0.16409064 0.8696597939 0.95290179
## 44 MO224 - MO232 -2.01597066 0.0438030437 0.31236597
## 45 MO230 - MO232 -1.48462956 0.1376419813 0.44351305
## 46 MO201 - MO234 1.00798533 0.3134615045 0.62836753
## 47 MO202 - MO234 -0.40631967 0.6845077357 0.88356340
## 48 MO203 - MO234 -0.72668710 0.4674176582 0.75306178
## 49 MO204 - MO234 -1.25021436 0.2112212511 0.53731722
## 50 MO221 - MO234 0.04688304 0.9626064464 0.98064123
## 51 MO222 - MO234 1.17988981 0.2380440448 0.55972519
## 52 MO223 - MO234 -0.03906920 0.9688352179 0.98238536
## 53 MO224 - MO234 -1.89094923 0.0586311224 0.31880673
## 54 MO230 - MO234 -1.35960812 0.1739539669 0.48197437
## 55 MO232 - MO234 0.12502144 0.9005065797 0.96245789
## 56 MO201 - MO236 -0.17971831 0.8573737144 0.95630145
## 57 MO202 - MO236 -1.59402331 0.1109308132 0.40550339
## 58 MO203 - MO236 -1.91439074 0.0555702472 0.31806655
## 59 MO204 - MO236 -2.43791801 0.0147721241 0.20728626
## 60 MO221 - MO236 -1.14082061 0.2539445833 0.58758454
## 61 MO222 - MO236 -0.00781384 0.9937655213 0.99376552
## 62 MO223 - MO236 -1.22677284 0.2199079800 0.54662841
## 63 MO224 - MO236 -3.07865287 0.0020793882 0.07537782
## 64 MO230 - MO236 -2.54731177 0.0108556401 0.18162321
## 65 MO232 - MO236 -1.06268221 0.2879260914 0.62003886
## 66 MO234 - MO236 -1.18770365 0.2349501869 0.56465929
## 67 MO201 - MO237 3.13334975 0.0017282337 0.08353130
## 68 MO202 - MO237 1.71904475 0.0856062238 0.36154085
## 69 MO203 - MO237 1.39867732 0.1619097684 0.46642880
## 70 MO204 - MO237 0.87515005 0.3814922648 0.69145473
## 71 MO221 - MO237 2.17224746 0.0298370028 0.27039784
## 72 MO222 - MO237 3.30525422 0.0009489029 0.05896754
## 73 MO223 - MO237 2.08629522 0.0369518894 0.30911677
## 74 MO224 - MO237 0.23441519 0.8146626647 0.93257437
## 75 MO230 - MO237 0.76575630 0.4438213220 0.74254721
## 76 MO232 - MO237 2.25038586 0.0244244621 0.25296764
## 77 MO234 - MO237 2.12536442 0.0335562169 0.29193909
## 78 MO236 - MO237 3.31306806 0.0009227852 0.06690193
## 79 MO201 - MO238 2.83642384 0.0045621858 0.10445004
## 80 MO202 - MO238 1.42211884 0.1549917546 0.46820426
## 81 MO203 - MO238 1.10175141 0.2705697607 0.60357870
## 82 MO204 - MO238 0.57822414 0.5631128006 0.81924438
## 83 MO221 - MO238 1.87532155 0.0607485010 0.32226339
## 84 MO222 - MO238 3.00832831 0.0026268918 0.07617986
## 85 MO223 - MO238 1.78936931 0.0735553588 0.34778892
## 86 MO224 - MO238 -0.06251072 0.9501561267 0.97711091
## 87 MO230 - MO238 0.46883039 0.6391908782 0.85817294
## 88 MO232 - MO238 1.95345994 0.0507651193 0.31102573
## 89 MO234 - MO238 1.82843851 0.0674837666 0.34134231
## 90 MO236 - MO238 3.01614215 0.0025601321 0.07954696
## 91 MO237 - MO238 -0.29692591 0.7665230733 0.91103152
## 92 MO201 - MO239 1.24240052 0.2140888223 0.54144557
## 93 MO202 - MO239 -0.17190448 0.8635126284 0.95579642
## 94 MO203 - MO239 -0.49227191 0.6225271380 0.85425648
## 95 MO204 - MO239 -1.01579917 0.3097250310 0.63253704
## 96 MO221 - MO239 0.28129823 0.7784816663 0.91277500
## 97 MO222 - MO239 1.41430500 0.1572723698 0.46858549
## 98 MO223 - MO239 0.19534599 0.8451220923 0.94994344
## 99 MO224 - MO239 -1.65653403 0.0976137190 0.38254025
## 100 MO230 - MO239 -1.12519293 0.2605072895 0.59330194
## 101 MO232 - MO239 0.35943663 0.7192684766 0.88886871
## 102 MO234 - MO239 0.23441519 0.8146626647 0.93503498
## 103 MO236 - MO239 1.42211884 0.1549917546 0.47147841
## 104 MO237 - MO239 -1.89094923 0.0586311224 0.32284226
## 105 MO238 - MO239 -1.59402331 0.1109308132 0.39880086
## 106 MO201 - MO240 3.57092478 0.0003557231 0.05157984
## 107 MO202 - MO240 2.15661978 0.0310353022 0.27551748
## 108 MO203 - MO240 1.83625235 0.0663203439 0.33940411
## 109 MO204 - MO240 1.31272508 0.1892756026 0.49302328
## 110 MO221 - MO240 2.60982248 0.0090589217 0.16419296
## 111 MO222 - MO240 3.74282925 0.0001819599 0.03957627
## 112 MO223 - MO240 2.52387025 0.0116070761 0.18032422
## 113 MO224 - MO240 0.67199022 0.5015899221 0.78486193
## 114 MO230 - MO240 1.20333133 0.2288481316 0.55613931
## 115 MO232 - MO240 2.68796088 0.0071889818 0.14891462
## 116 MO234 - MO240 2.56293945 0.0103790149 0.18059486
## 117 MO236 - MO240 3.75064309 0.0001763816 0.07672600
## 118 MO237 - MO240 0.43757503 0.6616943773 0.86697908
## 119 MO238 - MO240 0.73450094 0.4626434882 0.75093253
## 120 MO239 - MO240 2.32852425 0.0198842830 0.22762271
## 121 MO201 - MO241 1.61746483 0.1057779807 0.39666743
## 122 MO202 - MO241 0.20315983 0.8390101058 0.94551657
## 123 MO203 - MO241 -0.11720760 0.9066955472 0.96669746
## 124 MO204 - MO241 -0.64073486 0.5216949603 0.79627126
## 125 MO221 - MO241 0.65636254 0.5115908862 0.78915615
## 126 MO222 - MO241 1.78936931 0.0735553588 0.34404926
## 127 MO223 - MO241 0.57041030 0.5683994428 0.82417919
## 128 MO224 - MO241 -1.28146972 0.2000287279 0.51183822
## 129 MO230 - MO241 -0.75012862 0.4531772449 0.75241260
## 130 MO232 - MO241 0.73450094 0.4626434882 0.75374501
## 131 MO234 - MO241 0.60947950 0.5422066552 0.80224454
## 132 MO236 - MO241 1.79718315 0.0723065489 0.34564120
## 133 MO237 - MO241 -1.51588492 0.1295484550 0.43684944
## 134 MO238 - MO241 -1.21895900 0.2228597525 0.55081814
## 135 MO239 - MO241 0.37506431 0.7076126398 0.89220724
## 136 MO240 - MO241 -1.95345994 0.0507651193 0.31546896
## 137 MO201 - MO242 1.82062467 0.0686639305 0.34331965
## 138 MO202 - MO242 0.40631967 0.6845077357 0.87576725
## 139 MO203 - MO242 0.08595224 0.9315043856 0.97171321
## 140 MO204 - MO242 -0.43757503 0.6616943773 0.86959835
## 141 MO221 - MO242 0.85952238 0.3900523808 0.69254198
## 142 MO222 - MO242 1.99252914 0.0463130309 0.31978045
## 143 MO223 - MO242 0.77357014 0.4391850372 0.74627145
## 144 MO224 - MO242 -1.07830989 0.2808954854 0.60790814
## 145 MO230 - MO242 -0.54696878 0.5844001781 0.82805888
## 146 MO232 - MO242 0.93766077 0.3484187689 0.66184351
## 147 MO234 - MO242 0.81263934 0.4164248714 0.71882865
## 148 MO236 - MO242 2.00034298 0.0454632407 0.31897596
## 149 MO237 - MO242 -1.31272508 0.1892756026 0.49599330
## 150 MO238 - MO242 -1.01579917 0.3097250310 0.62958125
## 151 MO239 - MO242 0.57822414 0.5631128006 0.82199352
## 152 MO240 - MO242 -1.75030011 0.0800665420 0.35180753
## 153 MO241 - MO242 0.20315983 0.8390101058 0.95044114
## 154 MO201 - MO243 0.86733622 0.3857578194 0.69340765
## 155 MO202 - MO243 -0.54696878 0.5844001781 0.83076496
## 156 MO203 - MO243 -0.86733622 0.3857578194 0.69628486
## 157 MO204 - MO243 -1.39086348 0.1642668290 0.47010573
## 158 MO221 - MO243 -0.09376608 0.9252949793 0.96755605
## 159 MO222 - MO243 1.03924069 0.2986928108 0.62168121
## 160 MO223 - MO243 -0.17971831 0.8573737144 0.95385567
## 161 MO224 - MO243 -2.03159834 0.0421943347 0.30590893
## 162 MO230 - MO243 -1.50025724 0.1335477820 0.44010065
## 163 MO232 - MO243 -0.01562768 0.9875314233 0.98980684
## 164 MO234 - MO243 -0.14064912 0.8881471450 0.96345139
## 165 MO236 - MO243 1.04705453 0.2950744291 0.62008395
## 166 MO237 - MO243 -2.26601353 0.0234505546 0.25502478
## 167 MO238 - MO243 -1.96908762 0.0489430299 0.31309144
## 168 MO239 - MO243 -0.37506431 0.7076126398 0.89480087
## 169 MO240 - MO243 -2.70358856 0.0068595166 0.14919449
## 170 MO241 - MO243 -0.75012862 0.4531772449 0.74671251
## 171 MO242 - MO243 -0.95328845 0.3404439406 0.66112997
## 172 MO201 - MO253 1.51588492 0.1295484550 0.43017998
## 173 MO202 - MO253 0.10157992 0.9190901208 0.97039855
## 174 MO203 - MO253 -0.21878751 0.8268155739 0.93907252
## 175 MO204 - MO253 -0.74231478 0.4578966398 0.74881593
## 176 MO221 - MO253 0.55478262 0.5790433536 0.82856533
## 177 MO222 - MO253 1.68778939 0.0914516648 0.37178948
## 178 MO223 - MO253 0.46883039 0.6391908782 0.86082982
## 179 MO224 - MO253 -1.38304964 0.1666496456 0.47380782
## 180 MO230 - MO253 -0.85170854 0.3943758821 0.69737199
## 181 MO232 - MO253 0.63292102 0.5267852192 0.79017783
## 182 MO234 - MO253 0.50789959 0.6115237655 0.84448520
## 183 MO236 - MO253 1.69560323 0.0899610455 0.37269576
## 184 MO237 - MO253 -1.61746483 0.1057779807 0.40011671
## 185 MO238 - MO253 -1.32053892 0.1866551499 0.49812877
## 186 MO239 - MO253 0.27348439 0.7844808885 0.91733652
## 187 MO240 - MO253 -2.05503986 0.0398751548 0.30431039
## 188 MO241 - MO253 -0.10157992 0.9190901208 0.97275962
## 189 MO242 - MO253 -0.30473975 0.7605643716 0.91142011
## 190 MO243 - MO253 0.64854870 0.5166301223 0.79131726
## 191 MO201 - MO255 2.93018992 0.0033875490 0.09209899
## 192 MO202 - MO255 1.51588492 0.1295484550 0.43348906
## 193 MO203 - MO255 1.19551749 0.2318849087 0.56038853
## 194 MO204 - MO255 0.67199022 0.5015899221 0.78769536
## 195 MO221 - MO255 1.96908762 0.0489430299 0.31776445
## 196 MO222 - MO255 3.10209439 0.0019215668 0.07598923
## 197 MO223 - MO255 1.88313539 0.0596820228 0.32051457
## 198 MO224 - MO255 0.03125536 0.9750658913 0.98640387
## 199 MO230 - MO255 0.56259646 0.5737097005 0.82364264
## 200 MO232 - MO255 2.04722602 0.0406358977 0.30476923
## 201 MO234 - MO255 1.92220458 0.0545800202 0.31656412
## 202 MO236 - MO255 3.10990823 0.0018714548 0.08140828
## 203 MO237 - MO255 -0.20315983 0.8390101058 0.94797246
## 204 MO238 - MO255 0.09376608 0.9252949793 0.96988751
## 205 MO239 - MO255 1.68778939 0.0914516648 0.37529693
## 206 MO240 - MO255 -0.64073486 0.5216949603 0.79072233
## 207 MO241 - MO255 1.31272508 0.1892756026 0.49899932
## 208 MO242 - MO255 1.10956525 0.2671864134 0.60220772
## 209 MO243 - MO255 2.06285370 0.0391265302 0.30392930
## 210 MO253 - MO255 1.41430500 0.1572723698 0.47181711
## 211 MO201 - MO257 1.80499699 0.0710751534 0.34738979
## 212 MO202 - MO257 0.39069199 0.6960249212 0.88529486
## 213 MO203 - MO257 0.07032456 0.9439353365 0.97301391
## 214 MO204 - MO257 -0.45320271 0.6504027834 0.86521471
## 215 MO221 - MO257 0.84389470 0.3987282525 0.69657345
## 216 MO222 - MO257 1.97690146 0.0480527694 0.31671143
## 217 MO223 - MO257 0.75794246 0.4484854311 0.74747572
## 218 MO224 - MO257 -1.09393757 0.2739823605 0.60498643
## 219 MO230 - MO257 -0.56259646 0.5737097005 0.82911535
## 220 MO232 - MO257 0.92203309 0.3565113140 0.67427140
## 221 MO234 - MO257 0.79701166 0.4254442613 0.72861517
## 222 MO236 - MO257 1.98471530 0.0471761553 0.31571735
## 223 MO237 - MO257 -1.32835276 0.1840615971 0.49423947
## 224 MO238 - MO257 -1.03142685 0.3023406950 0.62330902
## 225 MO239 - MO257 0.56259646 0.5737097005 0.82636993
## 226 MO240 - MO257 -1.76592779 0.0774079644 0.35444699
## 227 MO241 - MO257 0.18753215 0.8512434151 0.95190459
## 228 MO242 - MO257 -0.01562768 0.9875314233 0.99209277
## 229 MO243 - MO257 0.93766077 0.3484187689 0.66474634
## 230 MO253 - MO257 0.28911207 0.7724956160 0.91314020
## 231 MO255 - MO257 -1.12519293 0.2605072895 0.59642458
## 232 MO201 - MO259 1.36742196 0.1714930828 0.48128704
## 233 MO202 - MO259 -0.04688304 0.9626064464 0.98294320
## 234 MO203 - MO259 -0.36725047 0.7134321962 0.89436025
## 235 MO204 - MO259 -0.89077773 0.3730484224 0.68470913
## 236 MO221 - MO259 0.40631967 0.6845077357 0.88619305
## 237 MO222 - MO259 1.53932644 0.1237246233 0.42714453
## 238 MO223 - MO259 0.32036743 0.7486898120 0.90972086
## 239 MO224 - MO259 -1.53151260 0.1256427558 0.43035117
## 240 MO230 - MO259 -1.00017149 0.3172275233 0.63010946
## 241 MO232 - MO259 0.48445807 0.6280608178 0.85377017
## 242 MO234 - MO259 0.35943663 0.7192684766 0.89394796
## 243 MO236 - MO259 1.54714028 0.1218294239 0.42738548
## 244 MO237 - MO259 -1.76592779 0.0774079644 0.35075484
## 245 MO238 - MO259 -1.46900188 0.1418322799 0.44708001
## 246 MO239 - MO259 0.12502144 0.9005065797 0.97201082
## 247 MO240 - MO259 -2.20350282 0.0275593287 0.26640684
## 248 MO241 - MO259 -0.25004287 0.8025541937 0.93096286
## 249 MO242 - MO259 -0.45320271 0.6504027834 0.85995505
## 250 MO243 - MO259 0.50008575 0.6170147027 0.84937151
## 251 MO253 - MO259 -0.14846296 0.8819774190 0.95915044
## 252 MO255 - MO259 -1.56276795 0.1181071841 0.41769614
## 253 MO257 - MO259 -0.43757503 0.6616943773 0.86178759
## 254 MO201 - MO261 3.22711583 0.0012504483 0.06799313
## 255 MO202 - MO261 1.81281083 0.0698610034 0.34533564
## 256 MO203 - MO261 1.49244340 0.1355829455 0.44344798
## 257 MO204 - MO261 0.96891613 0.3325870358 0.65463964
## 258 MO221 - MO261 2.26601353 0.0234505546 0.26156388
## 259 MO222 - MO261 3.39902030 0.0006762770 0.05883610
## 260 MO223 - MO261 2.18006130 0.0292529182 0.27074509
## 261 MO224 - MO261 0.32818127 0.7427746083 0.90506150
## 262 MO230 - MO261 0.85952238 0.3900523808 0.69538027
## 263 MO232 - MO261 2.34415193 0.0190704012 0.22420607
## 264 MO234 - MO261 2.21913050 0.0264778479 0.26785730
## 265 MO236 - MO261 3.40683414 0.0006572105 0.07147164
## 266 MO237 - MO261 0.09376608 0.9252949793 0.97223023
## 267 MO238 - MO261 0.39069199 0.6960249212 0.88789103
## 268 MO239 - MO261 1.98471530 0.0471761553 0.32065043
## 269 MO240 - MO261 -0.34380895 0.7309899689 0.90079500
## 270 MO241 - MO261 1.60965099 0.1074740691 0.39619678
## 271 MO242 - MO261 1.40649116 0.1595783279 0.46277715
## 272 MO243 - MO261 2.35977961 0.0182857948 0.22095335
## 273 MO253 - MO261 1.71123091 0.0870384946 0.36405524
## 274 MO255 - MO261 0.29692591 0.7665230733 0.91352750
## 275 MO257 - MO261 1.42211884 0.1549917546 0.47479869
## 276 MO259 - MO261 1.85969387 0.0629288503 0.32980783
## 277 MO201 - MO263 1.89876307 0.0575956354 0.32120643
## 278 MO202 - MO263 0.48445807 0.6280608178 0.85111045
## 279 MO203 - MO263 0.16409064 0.8696597939 0.95530811
## 280 MO204 - MO263 -0.35943663 0.7192684766 0.89650942
## 281 MO221 - MO263 0.93766077 0.3484187689 0.66767473
## 282 MO222 - MO263 2.07066754 0.0383898756 0.30362902
## 283 MO223 - MO263 0.85170854 0.3943758821 0.69454862
## 284 MO224 - MO263 -1.00017149 0.3172275233 0.63299987
## 285 MO230 - MO263 -0.46883039 0.6391908782 0.86350321
## 286 MO232 - MO263 1.01579917 0.3097250310 0.62375180
## 287 MO234 - MO263 0.89077773 0.3730484224 0.68761044
## 288 MO236 - MO263 2.07848138 0.0376650441 0.30341286
## 289 MO237 - MO263 -1.23458668 0.2169843672 0.54246092
## 290 MO238 - MO263 -0.93766077 0.3484187689 0.67062905
## 291 MO239 - MO263 0.65636254 0.5115908862 0.79196454
## 292 MO240 - MO263 -1.67216171 0.0944924383 0.37710285
## 293 MO241 - MO263 0.28129823 0.7784816663 0.91524196
## 294 MO242 - MO263 0.07813840 0.9377179636 0.97120789
## 295 MO243 - MO263 1.03142685 0.3023406950 0.62036888
## 296 MO253 - MO263 0.38287815 0.7018101137 0.89005073
## 297 MO255 - MO263 -1.03142685 0.3023406950 0.62627715
## 298 MO257 - MO263 0.09376608 0.9252949793 0.97458430
## 299 MO259 - MO263 0.53134110 0.5951824260 0.83248989
## 300 MO261 - MO263 -1.32835276 0.1840615971 0.49730928
## 301 MO201 - MO267 1.17988981 0.2380440448 0.56276717
## 302 MO202 - MO267 -0.23441519 0.8146626647 0.93750862
## 303 MO203 - MO267 -0.55478262 0.5790433536 0.82584872
## 304 MO204 - MO267 -1.07830989 0.2808954854 0.61094768
## 305 MO221 - MO267 0.21878751 0.8268155739 0.94400203
## 306 MO222 - MO267 1.35179428 0.1764411342 0.48271631
## 307 MO223 - MO267 0.13283528 0.8943236552 0.96773828
## 308 MO224 - MO267 -1.71904475 0.0856062238 0.36508537
## 309 MO230 - MO267 -1.18770365 0.2349501869 0.56155677
## 310 MO232 - MO267 0.29692591 0.7665230733 0.91603719
## 311 MO234 - MO267 0.17190448 0.8635126284 0.95823468
## 312 MO236 - MO267 1.35960812 0.1739539669 0.48506395
## 313 MO237 - MO267 -1.95345994 0.0507651193 0.30670593
## 314 MO238 - MO267 -1.65653403 0.0976137190 0.37912471
## 315 MO239 - MO267 -0.06251072 0.9501561267 0.97480640
## 316 MO240 - MO267 -2.39103497 0.0168009525 0.21495336
## 317 MO241 - MO267 -0.43757503 0.6616943773 0.86437554
## 318 MO242 - MO267 -0.64073486 0.5216949603 0.79348709
## 319 MO243 - MO267 0.31255359 0.7546198417 0.91183231
## 320 MO253 - MO267 -0.33599511 0.7368745538 0.90548144
## 321 MO255 - MO267 -1.75030011 0.0800665420 0.35539741
## 322 MO257 - MO267 -0.62510718 0.5319007146 0.79238634
## 323 MO259 - MO267 -0.18753215 0.8512434151 0.95435795
## 324 MO261 - MO267 -2.04722602 0.0406358977 0.29960365
## 325 MO263 - MO267 -0.71887326 0.4722190140 0.75520320
## 326 MO201 - MO269 1.49244340 0.1355829455 0.44013867
## 327 MO202 - MO269 0.07813840 0.9377179636 0.97352581
## 328 MO203 - MO269 -0.24222903 0.8086026997 0.93300312
## 329 MO204 - MO269 -0.76575630 0.4438213220 0.74541419
## 330 MO221 - MO269 0.53134110 0.5951824260 0.83787817
## 331 MO222 - MO269 1.66434787 0.0960429308 0.37980614
## 332 MO223 - MO269 0.44538887 0.6560387562 0.86477836
## 333 MO224 - MO269 -1.40649116 0.1595783279 0.46588304
## 334 MO230 - MO269 -0.87515005 0.3814922648 0.69434785
## 335 MO232 - MO269 0.60947950 0.5422066552 0.80498258
## 336 MO234 - MO269 0.48445807 0.6280608178 0.85644657
## 337 MO236 - MO269 1.67216171 0.0944924383 0.38059454
## 338 MO237 - MO269 -1.64090635 0.1008168561 0.38469590
## 339 MO238 - MO269 -1.34398044 0.1789547117 0.48653312
## 340 MO239 - MO269 0.25004287 0.8025541937 0.93345207
## 341 MO240 - MO269 -2.07848138 0.0376650441 0.30913763
## 342 MO241 - MO269 -0.12502144 0.9005065797 0.96482848
## 343 MO242 - MO269 -0.32818127 0.7427746083 0.90760381
## 344 MO243 - MO269 0.62510718 0.5319007146 0.79510932
## 345 MO253 - MO269 -0.02344152 0.9812980865 0.98811266
## 346 MO255 - MO269 -1.43774652 0.1505059889 0.46764361
## 347 MO257 - MO269 -0.31255359 0.7546198417 0.90679456
## 348 MO259 - MO269 0.12502144 0.9005065797 0.96721077
## 349 MO261 - MO269 -1.73467243 0.0827988423 0.36017496
## 350 MO263 - MO269 -0.40631967 0.6845077357 0.87835063
## 351 MO267 - MO269 0.31255359 0.7546198417 0.90930646
## 352 MO201 - MO273 0.71887326 0.4722190140 0.75798993
## 353 MO202 - MO273 -0.69543174 0.4867847752 0.77281525
## 354 MO203 - MO273 -1.01579917 0.3097250310 0.62665297
## 355 MO204 - MO273 -1.53932644 0.1237246233 0.43056169
## 356 MO221 - MO273 -0.24222903 0.8086026997 0.93548451
## 357 MO222 - MO273 0.89077773 0.3730484224 0.69053644
## 358 MO223 - MO273 -0.32818127 0.7427746083 0.91016044
## 359 MO224 - MO273 -2.18006130 0.0292529182 0.27663086
## 360 MO230 - MO273 -1.64872019 0.0992049714 0.38189524
## 361 MO232 - MO273 -0.16409064 0.8696597939 0.95772661
## 362 MO234 - MO273 -0.28911207 0.7724956160 0.91562832
## 363 MO236 - MO273 0.89859157 0.3688702484 0.69163172
## 364 MO237 - MO273 -2.41447649 0.0157578399 0.20771698
## 365 MO238 - MO273 -2.11755058 0.0342131474 0.29181802
## 366 MO239 - MO273 -0.52352726 0.6006073826 0.83205163
## 367 MO240 - MO273 -2.85205152 0.0043438060 0.10497531
## 368 MO241 - MO273 -0.89859157 0.3688702484 0.68866334
## 369 MO242 - MO273 -1.10175141 0.2705697607 0.60049921
## 370 MO243 - MO273 -0.14846296 0.8819774190 0.96155433
## 371 MO253 - MO273 -0.79701166 0.4254442613 0.73149507
## 372 MO255 - MO273 -2.21131666 0.0270139167 0.26706940
## 373 MO257 - MO273 -1.08612373 0.2774242555 0.60642991
## 374 MO259 - MO273 -0.64854870 0.5166301223 0.79411344
## 375 MO261 - MO273 -2.50824257 0.0121333343 0.18200001
## 376 MO263 - MO273 -1.17988981 0.2380440448 0.56584240
## 377 MO267 - MO273 -0.46101655 0.6447867337 0.86302224
## 378 MO269 - MO273 -0.77357014 0.4391850372 0.74919800
## 379 MO201 - MO279 2.47698721 0.0132496650 0.19212014
## 380 MO202 - MO279 1.06268221 0.2879260914 0.61396005
## 381 MO203 - MO279 0.74231478 0.4578966398 0.75164165
## 382 MO204 - MO279 0.21878751 0.8268155739 0.94153082
## 383 MO221 - MO279 1.51588492 0.1295484550 0.44026233
## 384 MO222 - MO279 2.64889168 0.0080756210 0.15273457
## 385 MO223 - MO279 1.42993268 0.1527363418 0.47120786
## 386 MO224 - MO279 -0.42194735 0.6730634492 0.87397791
## 387 MO230 - MO279 0.10939376 0.9128901853 0.97092232
## 388 MO232 - MO279 1.59402331 0.1109308132 0.40212420
## 389 MO234 - MO279 1.46900188 0.1418322799 0.45034337
## 390 MO236 - MO279 2.65670552 0.0078908336 0.15602330
## 391 MO237 - MO279 -0.65636254 0.5115908862 0.79479298
## 392 MO238 - MO279 -0.35943663 0.7192684766 0.89908560
## 393 MO239 - MO279 1.23458668 0.2169843672 0.54559653
## 394 MO240 - MO279 -1.09393757 0.2739823605 0.60193094
## 395 MO241 - MO279 0.85952238 0.3900523808 0.69824192
## 396 MO242 - MO279 0.65636254 0.5115908862 0.79764170
## 397 MO243 - MO279 1.60965099 0.1074740691 0.39958308
## 398 MO253 - MO279 0.96110229 0.3365007372 0.65935955
## 399 MO255 - MO279 -0.45320271 0.6504027834 0.86786874
## 400 MO257 - MO279 0.67199022 0.5015899221 0.79054933
## 401 MO259 - MO279 1.10956525 0.2671864134 0.59910356
## 402 MO261 - MO279 -0.75012862 0.4531772449 0.74955172
## 403 MO263 - MO279 0.57822414 0.5631128006 0.82476117
## 404 MO267 - MO279 1.29709740 0.1945976751 0.50088751
## 405 MO269 - MO279 0.98454381 0.3248482011 0.64231349
## 406 MO273 - MO279 1.75811395 0.0787281228 0.35305911
## 407 MO201 - MO288 1.77374163 0.0761058972 0.35219218
## 408 MO202 - MO288 0.35943663 0.7192684766 0.89140110
## 409 MO203 - MO288 0.03906920 0.9688352179 0.98468065
## 410 MO204 - MO288 -0.48445807 0.6280608178 0.85913980
## 411 MO221 - MO288 0.81263934 0.4164248714 0.72169251
## 412 MO222 - MO288 1.94564610 0.0516972649 0.30805904
## 413 MO223 - MO288 0.72668710 0.4674176582 0.75586127
## 414 MO224 - MO288 -1.12519293 0.2605072895 0.59021183
## 415 MO230 - MO288 -0.59385182 0.5526112242 0.81486740
## 416 MO232 - MO288 0.89077773 0.3730484224 0.69348745
## 417 MO234 - MO288 0.76575630 0.4438213220 0.74830339
## 418 MO236 - MO288 1.95345994 0.0507651193 0.32004097
## 419 MO237 - MO288 -1.35960812 0.1739539669 0.47892390
## 420 MO238 - MO288 -1.06268221 0.2879260914 0.61698448
## 421 MO239 - MO288 0.53134110 0.5951824260 0.84059856
## 422 MO240 - MO288 -1.79718315 0.0723065489 0.34948165
## 423 MO241 - MO288 0.15627680 0.8758148461 0.95723482
## 424 MO242 - MO288 -0.04688304 0.9626064464 0.98525601
## 425 MO243 - MO288 0.90640541 0.3647213083 0.68681285
## 426 MO253 - MO288 0.25785671 0.7965174937 0.92891450
## 427 MO255 - MO288 -1.15644829 0.2474978404 0.57573027
## 428 MO257 - MO288 -0.03125536 0.9750658913 0.98411523
## 429 MO259 - MO288 0.40631967 0.6845077357 0.88094930
## 430 MO261 - MO288 -1.45337420 0.1461198863 0.45728166
## 431 MO263 - MO288 -0.12502144 0.9005065797 0.96960486
## 432 MO267 - MO288 0.59385182 0.5526112242 0.81211447
## 433 MO269 - MO288 0.28129823 0.7784816663 0.91772229
## 434 MO273 - MO288 1.05486837 0.2914855302 0.61851808
## 435 MO279 - MO288 -0.70324558 0.4819027186 0.76786697
##
## **Dunn's Test (Post-hoc with Bonferroni correction):**## Dunn (1964) Kruskal-Wallis multiple comparison## p-values adjusted with the Bonferroni method.
## Comparison Z P.unadj P.adj
## 1 MO201 - MO202 1.41430500 0.1572723698 1.00000000
## 2 MO201 - MO203 1.73467243 0.0827988423 1.00000000
## 3 MO202 - MO203 0.32036743 0.7486898120 1.00000000
## 4 MO201 - MO204 2.25819969 0.0239332123 1.00000000
## 5 MO202 - MO204 0.84389470 0.3987282525 1.00000000
## 6 MO203 - MO204 0.52352726 0.6006073826 1.00000000
## 7 MO201 - MO221 0.96110229 0.3365007372 1.00000000
## 8 MO202 - MO221 -0.45320271 0.6504027834 1.00000000
## 9 MO203 - MO221 -0.77357014 0.4391850372 1.00000000
## 10 MO204 - MO221 -1.29709740 0.1945976751 1.00000000
## 11 MO201 - MO222 -0.17190448 0.8635126284 1.00000000
## 12 MO202 - MO222 -1.58620947 0.1126917993 1.00000000
## 13 MO203 - MO222 -1.90657691 0.0565753981 1.00000000
## 14 MO204 - MO222 -2.43010417 0.0150944838 1.00000000
## 15 MO221 - MO222 -1.13300677 0.2572114114 1.00000000
## 16 MO201 - MO223 1.04705453 0.2950744291 1.00000000
## 17 MO202 - MO223 -0.36725047 0.7134321962 1.00000000
## 18 MO203 - MO223 -0.68761790 0.4916934329 1.00000000
## 19 MO204 - MO223 -1.21114517 0.2258397742 1.00000000
## 20 MO221 - MO223 0.08595224 0.9315043856 1.00000000
## 21 MO222 - MO223 1.21895900 0.2228597525 1.00000000
## 22 MO201 - MO224 2.89893456 0.0037443304 1.00000000
## 23 MO202 - MO224 1.48462956 0.1376419813 1.00000000
## 24 MO203 - MO224 1.16426213 0.2443178000 1.00000000
## 25 MO204 - MO224 0.64073486 0.5216949603 1.00000000
## 26 MO221 - MO224 1.93783226 0.0526436901 1.00000000
## 27 MO222 - MO224 3.07083903 0.0021345819 0.92854315
## 28 MO223 - MO224 1.85188003 0.0640430527 1.00000000
## 29 MO201 - MO230 2.36759345 0.0179041978 1.00000000
## 30 MO202 - MO230 0.95328845 0.3404439406 1.00000000
## 31 MO203 - MO230 0.63292102 0.5267852192 1.00000000
## 32 MO204 - MO230 0.10939376 0.9128901853 1.00000000
## 33 MO221 - MO230 1.40649116 0.1595783279 1.00000000
## 34 MO222 - MO230 2.53949793 0.0111011703 1.00000000
## 35 MO223 - MO230 1.32053892 0.1866551499 1.00000000
## 36 MO224 - MO230 -0.53134110 0.5951824260 1.00000000
## 37 MO201 - MO232 0.88296389 0.3772557795 1.00000000
## 38 MO202 - MO232 -0.53134110 0.5951824260 1.00000000
## 39 MO203 - MO232 -0.85170854 0.3943758821 1.00000000
## 40 MO204 - MO232 -1.37523580 0.1690583527 1.00000000
## 41 MO221 - MO232 -0.07813840 0.9377179636 1.00000000
## 42 MO222 - MO232 1.05486837 0.2914855302 1.00000000
## 43 MO223 - MO232 -0.16409064 0.8696597939 1.00000000
## 44 MO224 - MO232 -2.01597066 0.0438030437 1.00000000
## 45 MO230 - MO232 -1.48462956 0.1376419813 1.00000000
## 46 MO201 - MO234 1.00798533 0.3134615045 1.00000000
## 47 MO202 - MO234 -0.40631967 0.6845077357 1.00000000
## 48 MO203 - MO234 -0.72668710 0.4674176582 1.00000000
## 49 MO204 - MO234 -1.25021436 0.2112212511 1.00000000
## 50 MO221 - MO234 0.04688304 0.9626064464 1.00000000
## 51 MO222 - MO234 1.17988981 0.2380440448 1.00000000
## 52 MO223 - MO234 -0.03906920 0.9688352179 1.00000000
## 53 MO224 - MO234 -1.89094923 0.0586311224 1.00000000
## 54 MO230 - MO234 -1.35960812 0.1739539669 1.00000000
## 55 MO232 - MO234 0.12502144 0.9005065797 1.00000000
## 56 MO201 - MO236 -0.17971831 0.8573737144 1.00000000
## 57 MO202 - MO236 -1.59402331 0.1109308132 1.00000000
## 58 MO203 - MO236 -1.91439074 0.0555702472 1.00000000
## 59 MO204 - MO236 -2.43791801 0.0147721241 1.00000000
## 60 MO221 - MO236 -1.14082061 0.2539445833 1.00000000
## 61 MO222 - MO236 -0.00781384 0.9937655213 1.00000000
## 62 MO223 - MO236 -1.22677284 0.2199079800 1.00000000
## 63 MO224 - MO236 -3.07865287 0.0020793882 0.90453385
## 64 MO230 - MO236 -2.54731177 0.0108556401 1.00000000
## 65 MO232 - MO236 -1.06268221 0.2879260914 1.00000000
## 66 MO234 - MO236 -1.18770365 0.2349501869 1.00000000
## 67 MO201 - MO237 3.13334975 0.0017282337 0.75178168
## 68 MO202 - MO237 1.71904475 0.0856062238 1.00000000
## 69 MO203 - MO237 1.39867732 0.1619097684 1.00000000
## 70 MO204 - MO237 0.87515005 0.3814922648 1.00000000
## 71 MO221 - MO237 2.17224746 0.0298370028 1.00000000
## 72 MO222 - MO237 3.30525422 0.0009489029 0.41277275
## 73 MO223 - MO237 2.08629522 0.0369518894 1.00000000
## 74 MO224 - MO237 0.23441519 0.8146626647 1.00000000
## 75 MO230 - MO237 0.76575630 0.4438213220 1.00000000
## 76 MO232 - MO237 2.25038586 0.0244244621 1.00000000
## 77 MO234 - MO237 2.12536442 0.0335562169 1.00000000
## 78 MO236 - MO237 3.31306806 0.0009227852 0.40141156
## 79 MO201 - MO238 2.83642384 0.0045621858 1.00000000
## 80 MO202 - MO238 1.42211884 0.1549917546 1.00000000
## 81 MO203 - MO238 1.10175141 0.2705697607 1.00000000
## 82 MO204 - MO238 0.57822414 0.5631128006 1.00000000
## 83 MO221 - MO238 1.87532155 0.0607485010 1.00000000
## 84 MO222 - MO238 3.00832831 0.0026268918 1.00000000
## 85 MO223 - MO238 1.78936931 0.0735553588 1.00000000
## 86 MO224 - MO238 -0.06251072 0.9501561267 1.00000000
## 87 MO230 - MO238 0.46883039 0.6391908782 1.00000000
## 88 MO232 - MO238 1.95345994 0.0507651193 1.00000000
## 89 MO234 - MO238 1.82843851 0.0674837666 1.00000000
## 90 MO236 - MO238 3.01614215 0.0025601321 1.00000000
## 91 MO237 - MO238 -0.29692591 0.7665230733 1.00000000
## 92 MO201 - MO239 1.24240052 0.2140888223 1.00000000
## 93 MO202 - MO239 -0.17190448 0.8635126284 1.00000000
## 94 MO203 - MO239 -0.49227191 0.6225271380 1.00000000
## 95 MO204 - MO239 -1.01579917 0.3097250310 1.00000000
## 96 MO221 - MO239 0.28129823 0.7784816663 1.00000000
## 97 MO222 - MO239 1.41430500 0.1572723698 1.00000000
## 98 MO223 - MO239 0.19534599 0.8451220923 1.00000000
## 99 MO224 - MO239 -1.65653403 0.0976137190 1.00000000
## 100 MO230 - MO239 -1.12519293 0.2605072895 1.00000000
## 101 MO232 - MO239 0.35943663 0.7192684766 1.00000000
## 102 MO234 - MO239 0.23441519 0.8146626647 1.00000000
## 103 MO236 - MO239 1.42211884 0.1549917546 1.00000000
## 104 MO237 - MO239 -1.89094923 0.0586311224 1.00000000
## 105 MO238 - MO239 -1.59402331 0.1109308132 1.00000000
## 106 MO201 - MO240 3.57092478 0.0003557231 0.15473953
## 107 MO202 - MO240 2.15661978 0.0310353022 1.00000000
## 108 MO203 - MO240 1.83625235 0.0663203439 1.00000000
## 109 MO204 - MO240 1.31272508 0.1892756026 1.00000000
## 110 MO221 - MO240 2.60982248 0.0090589217 1.00000000
## 111 MO222 - MO240 3.74282925 0.0001819599 0.07915255
## 112 MO223 - MO240 2.52387025 0.0116070761 1.00000000
## 113 MO224 - MO240 0.67199022 0.5015899221 1.00000000
## 114 MO230 - MO240 1.20333133 0.2288481316 1.00000000
## 115 MO232 - MO240 2.68796088 0.0071889818 1.00000000
## 116 MO234 - MO240 2.56293945 0.0103790149 1.00000000
## 117 MO236 - MO240 3.75064309 0.0001763816 0.07672600
## 118 MO237 - MO240 0.43757503 0.6616943773 1.00000000
## 119 MO238 - MO240 0.73450094 0.4626434882 1.00000000
## 120 MO239 - MO240 2.32852425 0.0198842830 1.00000000
## 121 MO201 - MO241 1.61746483 0.1057779807 1.00000000
## 122 MO202 - MO241 0.20315983 0.8390101058 1.00000000
## 123 MO203 - MO241 -0.11720760 0.9066955472 1.00000000
## 124 MO204 - MO241 -0.64073486 0.5216949603 1.00000000
## 125 MO221 - MO241 0.65636254 0.5115908862 1.00000000
## 126 MO222 - MO241 1.78936931 0.0735553588 1.00000000
## 127 MO223 - MO241 0.57041030 0.5683994428 1.00000000
## 128 MO224 - MO241 -1.28146972 0.2000287279 1.00000000
## 129 MO230 - MO241 -0.75012862 0.4531772449 1.00000000
## 130 MO232 - MO241 0.73450094 0.4626434882 1.00000000
## 131 MO234 - MO241 0.60947950 0.5422066552 1.00000000
## 132 MO236 - MO241 1.79718315 0.0723065489 1.00000000
## 133 MO237 - MO241 -1.51588492 0.1295484550 1.00000000
## 134 MO238 - MO241 -1.21895900 0.2228597525 1.00000000
## 135 MO239 - MO241 0.37506431 0.7076126398 1.00000000
## 136 MO240 - MO241 -1.95345994 0.0507651193 1.00000000
## 137 MO201 - MO242 1.82062467 0.0686639305 1.00000000
## 138 MO202 - MO242 0.40631967 0.6845077357 1.00000000
## 139 MO203 - MO242 0.08595224 0.9315043856 1.00000000
## 140 MO204 - MO242 -0.43757503 0.6616943773 1.00000000
## 141 MO221 - MO242 0.85952238 0.3900523808 1.00000000
## 142 MO222 - MO242 1.99252914 0.0463130309 1.00000000
## 143 MO223 - MO242 0.77357014 0.4391850372 1.00000000
## 144 MO224 - MO242 -1.07830989 0.2808954854 1.00000000
## 145 MO230 - MO242 -0.54696878 0.5844001781 1.00000000
## 146 MO232 - MO242 0.93766077 0.3484187689 1.00000000
## 147 MO234 - MO242 0.81263934 0.4164248714 1.00000000
## 148 MO236 - MO242 2.00034298 0.0454632407 1.00000000
## 149 MO237 - MO242 -1.31272508 0.1892756026 1.00000000
## 150 MO238 - MO242 -1.01579917 0.3097250310 1.00000000
## 151 MO239 - MO242 0.57822414 0.5631128006 1.00000000
## 152 MO240 - MO242 -1.75030011 0.0800665420 1.00000000
## 153 MO241 - MO242 0.20315983 0.8390101058 1.00000000
## 154 MO201 - MO243 0.86733622 0.3857578194 1.00000000
## 155 MO202 - MO243 -0.54696878 0.5844001781 1.00000000
## 156 MO203 - MO243 -0.86733622 0.3857578194 1.00000000
## 157 MO204 - MO243 -1.39086348 0.1642668290 1.00000000
## 158 MO221 - MO243 -0.09376608 0.9252949793 1.00000000
## 159 MO222 - MO243 1.03924069 0.2986928108 1.00000000
## 160 MO223 - MO243 -0.17971831 0.8573737144 1.00000000
## 161 MO224 - MO243 -2.03159834 0.0421943347 1.00000000
## 162 MO230 - MO243 -1.50025724 0.1335477820 1.00000000
## 163 MO232 - MO243 -0.01562768 0.9875314233 1.00000000
## 164 MO234 - MO243 -0.14064912 0.8881471450 1.00000000
## 165 MO236 - MO243 1.04705453 0.2950744291 1.00000000
## 166 MO237 - MO243 -2.26601353 0.0234505546 1.00000000
## 167 MO238 - MO243 -1.96908762 0.0489430299 1.00000000
## 168 MO239 - MO243 -0.37506431 0.7076126398 1.00000000
## 169 MO240 - MO243 -2.70358856 0.0068595166 1.00000000
## 170 MO241 - MO243 -0.75012862 0.4531772449 1.00000000
## 171 MO242 - MO243 -0.95328845 0.3404439406 1.00000000
## 172 MO201 - MO253 1.51588492 0.1295484550 1.00000000
## 173 MO202 - MO253 0.10157992 0.9190901208 1.00000000
## 174 MO203 - MO253 -0.21878751 0.8268155739 1.00000000
## 175 MO204 - MO253 -0.74231478 0.4578966398 1.00000000
## 176 MO221 - MO253 0.55478262 0.5790433536 1.00000000
## 177 MO222 - MO253 1.68778939 0.0914516648 1.00000000
## 178 MO223 - MO253 0.46883039 0.6391908782 1.00000000
## 179 MO224 - MO253 -1.38304964 0.1666496456 1.00000000
## 180 MO230 - MO253 -0.85170854 0.3943758821 1.00000000
## 181 MO232 - MO253 0.63292102 0.5267852192 1.00000000
## 182 MO234 - MO253 0.50789959 0.6115237655 1.00000000
## 183 MO236 - MO253 1.69560323 0.0899610455 1.00000000
## 184 MO237 - MO253 -1.61746483 0.1057779807 1.00000000
## 185 MO238 - MO253 -1.32053892 0.1866551499 1.00000000
## 186 MO239 - MO253 0.27348439 0.7844808885 1.00000000
## 187 MO240 - MO253 -2.05503986 0.0398751548 1.00000000
## 188 MO241 - MO253 -0.10157992 0.9190901208 1.00000000
## 189 MO242 - MO253 -0.30473975 0.7605643716 1.00000000
## 190 MO243 - MO253 0.64854870 0.5166301223 1.00000000
## 191 MO201 - MO255 2.93018992 0.0033875490 1.00000000
## 192 MO202 - MO255 1.51588492 0.1295484550 1.00000000
## 193 MO203 - MO255 1.19551749 0.2318849087 1.00000000
## 194 MO204 - MO255 0.67199022 0.5015899221 1.00000000
## 195 MO221 - MO255 1.96908762 0.0489430299 1.00000000
## 196 MO222 - MO255 3.10209439 0.0019215668 0.83588155
## 197 MO223 - MO255 1.88313539 0.0596820228 1.00000000
## 198 MO224 - MO255 0.03125536 0.9750658913 1.00000000
## 199 MO230 - MO255 0.56259646 0.5737097005 1.00000000
## 200 MO232 - MO255 2.04722602 0.0406358977 1.00000000
## 201 MO234 - MO255 1.92220458 0.0545800202 1.00000000
## 202 MO236 - MO255 3.10990823 0.0018714548 0.81408283
## 203 MO237 - MO255 -0.20315983 0.8390101058 1.00000000
## 204 MO238 - MO255 0.09376608 0.9252949793 1.00000000
## 205 MO239 - MO255 1.68778939 0.0914516648 1.00000000
## 206 MO240 - MO255 -0.64073486 0.5216949603 1.00000000
## 207 MO241 - MO255 1.31272508 0.1892756026 1.00000000
## 208 MO242 - MO255 1.10956525 0.2671864134 1.00000000
## 209 MO243 - MO255 2.06285370 0.0391265302 1.00000000
## 210 MO253 - MO255 1.41430500 0.1572723698 1.00000000
## 211 MO201 - MO257 1.80499699 0.0710751534 1.00000000
## 212 MO202 - MO257 0.39069199 0.6960249212 1.00000000
## 213 MO203 - MO257 0.07032456 0.9439353365 1.00000000
## 214 MO204 - MO257 -0.45320271 0.6504027834 1.00000000
## 215 MO221 - MO257 0.84389470 0.3987282525 1.00000000
## 216 MO222 - MO257 1.97690146 0.0480527694 1.00000000
## 217 MO223 - MO257 0.75794246 0.4484854311 1.00000000
## 218 MO224 - MO257 -1.09393757 0.2739823605 1.00000000
## 219 MO230 - MO257 -0.56259646 0.5737097005 1.00000000
## 220 MO232 - MO257 0.92203309 0.3565113140 1.00000000
## 221 MO234 - MO257 0.79701166 0.4254442613 1.00000000
## 222 MO236 - MO257 1.98471530 0.0471761553 1.00000000
## 223 MO237 - MO257 -1.32835276 0.1840615971 1.00000000
## 224 MO238 - MO257 -1.03142685 0.3023406950 1.00000000
## 225 MO239 - MO257 0.56259646 0.5737097005 1.00000000
## 226 MO240 - MO257 -1.76592779 0.0774079644 1.00000000
## 227 MO241 - MO257 0.18753215 0.8512434151 1.00000000
## 228 MO242 - MO257 -0.01562768 0.9875314233 1.00000000
## 229 MO243 - MO257 0.93766077 0.3484187689 1.00000000
## 230 MO253 - MO257 0.28911207 0.7724956160 1.00000000
## 231 MO255 - MO257 -1.12519293 0.2605072895 1.00000000
## 232 MO201 - MO259 1.36742196 0.1714930828 1.00000000
## 233 MO202 - MO259 -0.04688304 0.9626064464 1.00000000
## 234 MO203 - MO259 -0.36725047 0.7134321962 1.00000000
## 235 MO204 - MO259 -0.89077773 0.3730484224 1.00000000
## 236 MO221 - MO259 0.40631967 0.6845077357 1.00000000
## 237 MO222 - MO259 1.53932644 0.1237246233 1.00000000
## 238 MO223 - MO259 0.32036743 0.7486898120 1.00000000
## 239 MO224 - MO259 -1.53151260 0.1256427558 1.00000000
## 240 MO230 - MO259 -1.00017149 0.3172275233 1.00000000
## 241 MO232 - MO259 0.48445807 0.6280608178 1.00000000
## 242 MO234 - MO259 0.35943663 0.7192684766 1.00000000
## 243 MO236 - MO259 1.54714028 0.1218294239 1.00000000
## 244 MO237 - MO259 -1.76592779 0.0774079644 1.00000000
## 245 MO238 - MO259 -1.46900188 0.1418322799 1.00000000
## 246 MO239 - MO259 0.12502144 0.9005065797 1.00000000
## 247 MO240 - MO259 -2.20350282 0.0275593287 1.00000000
## 248 MO241 - MO259 -0.25004287 0.8025541937 1.00000000
## 249 MO242 - MO259 -0.45320271 0.6504027834 1.00000000
## 250 MO243 - MO259 0.50008575 0.6170147027 1.00000000
## 251 MO253 - MO259 -0.14846296 0.8819774190 1.00000000
## 252 MO255 - MO259 -1.56276795 0.1181071841 1.00000000
## 253 MO257 - MO259 -0.43757503 0.6616943773 1.00000000
## 254 MO201 - MO261 3.22711583 0.0012504483 0.54394502
## 255 MO202 - MO261 1.81281083 0.0698610034 1.00000000
## 256 MO203 - MO261 1.49244340 0.1355829455 1.00000000
## 257 MO204 - MO261 0.96891613 0.3325870358 1.00000000
## 258 MO221 - MO261 2.26601353 0.0234505546 1.00000000
## 259 MO222 - MO261 3.39902030 0.0006762770 0.29418048
## 260 MO223 - MO261 2.18006130 0.0292529182 1.00000000
## 261 MO224 - MO261 0.32818127 0.7427746083 1.00000000
## 262 MO230 - MO261 0.85952238 0.3900523808 1.00000000
## 263 MO232 - MO261 2.34415193 0.0190704012 1.00000000
## 264 MO234 - MO261 2.21913050 0.0264778479 1.00000000
## 265 MO236 - MO261 3.40683414 0.0006572105 0.28588657
## 266 MO237 - MO261 0.09376608 0.9252949793 1.00000000
## 267 MO238 - MO261 0.39069199 0.6960249212 1.00000000
## 268 MO239 - MO261 1.98471530 0.0471761553 1.00000000
## 269 MO240 - MO261 -0.34380895 0.7309899689 1.00000000
## 270 MO241 - MO261 1.60965099 0.1074740691 1.00000000
## 271 MO242 - MO261 1.40649116 0.1595783279 1.00000000
## 272 MO243 - MO261 2.35977961 0.0182857948 1.00000000
## 273 MO253 - MO261 1.71123091 0.0870384946 1.00000000
## 274 MO255 - MO261 0.29692591 0.7665230733 1.00000000
## 275 MO257 - MO261 1.42211884 0.1549917546 1.00000000
## 276 MO259 - MO261 1.85969387 0.0629288503 1.00000000
## 277 MO201 - MO263 1.89876307 0.0575956354 1.00000000
## 278 MO202 - MO263 0.48445807 0.6280608178 1.00000000
## 279 MO203 - MO263 0.16409064 0.8696597939 1.00000000
## 280 MO204 - MO263 -0.35943663 0.7192684766 1.00000000
## 281 MO221 - MO263 0.93766077 0.3484187689 1.00000000
## 282 MO222 - MO263 2.07066754 0.0383898756 1.00000000
## 283 MO223 - MO263 0.85170854 0.3943758821 1.00000000
## 284 MO224 - MO263 -1.00017149 0.3172275233 1.00000000
## 285 MO230 - MO263 -0.46883039 0.6391908782 1.00000000
## 286 MO232 - MO263 1.01579917 0.3097250310 1.00000000
## 287 MO234 - MO263 0.89077773 0.3730484224 1.00000000
## 288 MO236 - MO263 2.07848138 0.0376650441 1.00000000
## 289 MO237 - MO263 -1.23458668 0.2169843672 1.00000000
## 290 MO238 - MO263 -0.93766077 0.3484187689 1.00000000
## 291 MO239 - MO263 0.65636254 0.5115908862 1.00000000
## 292 MO240 - MO263 -1.67216171 0.0944924383 1.00000000
## 293 MO241 - MO263 0.28129823 0.7784816663 1.00000000
## 294 MO242 - MO263 0.07813840 0.9377179636 1.00000000
## 295 MO243 - MO263 1.03142685 0.3023406950 1.00000000
## 296 MO253 - MO263 0.38287815 0.7018101137 1.00000000
## 297 MO255 - MO263 -1.03142685 0.3023406950 1.00000000
## 298 MO257 - MO263 0.09376608 0.9252949793 1.00000000
## 299 MO259 - MO263 0.53134110 0.5951824260 1.00000000
## 300 MO261 - MO263 -1.32835276 0.1840615971 1.00000000
## 301 MO201 - MO267 1.17988981 0.2380440448 1.00000000
## 302 MO202 - MO267 -0.23441519 0.8146626647 1.00000000
## 303 MO203 - MO267 -0.55478262 0.5790433536 1.00000000
## 304 MO204 - MO267 -1.07830989 0.2808954854 1.00000000
## 305 MO221 - MO267 0.21878751 0.8268155739 1.00000000
## 306 MO222 - MO267 1.35179428 0.1764411342 1.00000000
## 307 MO223 - MO267 0.13283528 0.8943236552 1.00000000
## 308 MO224 - MO267 -1.71904475 0.0856062238 1.00000000
## 309 MO230 - MO267 -1.18770365 0.2349501869 1.00000000
## 310 MO232 - MO267 0.29692591 0.7665230733 1.00000000
## 311 MO234 - MO267 0.17190448 0.8635126284 1.00000000
## 312 MO236 - MO267 1.35960812 0.1739539669 1.00000000
## 313 MO237 - MO267 -1.95345994 0.0507651193 1.00000000
## 314 MO238 - MO267 -1.65653403 0.0976137190 1.00000000
## 315 MO239 - MO267 -0.06251072 0.9501561267 1.00000000
## 316 MO240 - MO267 -2.39103497 0.0168009525 1.00000000
## 317 MO241 - MO267 -0.43757503 0.6616943773 1.00000000
## 318 MO242 - MO267 -0.64073486 0.5216949603 1.00000000
## 319 MO243 - MO267 0.31255359 0.7546198417 1.00000000
## 320 MO253 - MO267 -0.33599511 0.7368745538 1.00000000
## 321 MO255 - MO267 -1.75030011 0.0800665420 1.00000000
## 322 MO257 - MO267 -0.62510718 0.5319007146 1.00000000
## 323 MO259 - MO267 -0.18753215 0.8512434151 1.00000000
## 324 MO261 - MO267 -2.04722602 0.0406358977 1.00000000
## 325 MO263 - MO267 -0.71887326 0.4722190140 1.00000000
## 326 MO201 - MO269 1.49244340 0.1355829455 1.00000000
## 327 MO202 - MO269 0.07813840 0.9377179636 1.00000000
## 328 MO203 - MO269 -0.24222903 0.8086026997 1.00000000
## 329 MO204 - MO269 -0.76575630 0.4438213220 1.00000000
## 330 MO221 - MO269 0.53134110 0.5951824260 1.00000000
## 331 MO222 - MO269 1.66434787 0.0960429308 1.00000000
## 332 MO223 - MO269 0.44538887 0.6560387562 1.00000000
## 333 MO224 - MO269 -1.40649116 0.1595783279 1.00000000
## 334 MO230 - MO269 -0.87515005 0.3814922648 1.00000000
## 335 MO232 - MO269 0.60947950 0.5422066552 1.00000000
## 336 MO234 - MO269 0.48445807 0.6280608178 1.00000000
## 337 MO236 - MO269 1.67216171 0.0944924383 1.00000000
## 338 MO237 - MO269 -1.64090635 0.1008168561 1.00000000
## 339 MO238 - MO269 -1.34398044 0.1789547117 1.00000000
## 340 MO239 - MO269 0.25004287 0.8025541937 1.00000000
## 341 MO240 - MO269 -2.07848138 0.0376650441 1.00000000
## 342 MO241 - MO269 -0.12502144 0.9005065797 1.00000000
## 343 MO242 - MO269 -0.32818127 0.7427746083 1.00000000
## 344 MO243 - MO269 0.62510718 0.5319007146 1.00000000
## 345 MO253 - MO269 -0.02344152 0.9812980865 1.00000000
## 346 MO255 - MO269 -1.43774652 0.1505059889 1.00000000
## 347 MO257 - MO269 -0.31255359 0.7546198417 1.00000000
## 348 MO259 - MO269 0.12502144 0.9005065797 1.00000000
## 349 MO261 - MO269 -1.73467243 0.0827988423 1.00000000
## 350 MO263 - MO269 -0.40631967 0.6845077357 1.00000000
## 351 MO267 - MO269 0.31255359 0.7546198417 1.00000000
## 352 MO201 - MO273 0.71887326 0.4722190140 1.00000000
## 353 MO202 - MO273 -0.69543174 0.4867847752 1.00000000
## 354 MO203 - MO273 -1.01579917 0.3097250310 1.00000000
## 355 MO204 - MO273 -1.53932644 0.1237246233 1.00000000
## 356 MO221 - MO273 -0.24222903 0.8086026997 1.00000000
## 357 MO222 - MO273 0.89077773 0.3730484224 1.00000000
## 358 MO223 - MO273 -0.32818127 0.7427746083 1.00000000
## 359 MO224 - MO273 -2.18006130 0.0292529182 1.00000000
## 360 MO230 - MO273 -1.64872019 0.0992049714 1.00000000
## 361 MO232 - MO273 -0.16409064 0.8696597939 1.00000000
## 362 MO234 - MO273 -0.28911207 0.7724956160 1.00000000
## 363 MO236 - MO273 0.89859157 0.3688702484 1.00000000
## 364 MO237 - MO273 -2.41447649 0.0157578399 1.00000000
## 365 MO238 - MO273 -2.11755058 0.0342131474 1.00000000
## 366 MO239 - MO273 -0.52352726 0.6006073826 1.00000000
## 367 MO240 - MO273 -2.85205152 0.0043438060 1.00000000
## 368 MO241 - MO273 -0.89859157 0.3688702484 1.00000000
## 369 MO242 - MO273 -1.10175141 0.2705697607 1.00000000
## 370 MO243 - MO273 -0.14846296 0.8819774190 1.00000000
## 371 MO253 - MO273 -0.79701166 0.4254442613 1.00000000
## 372 MO255 - MO273 -2.21131666 0.0270139167 1.00000000
## 373 MO257 - MO273 -1.08612373 0.2774242555 1.00000000
## 374 MO259 - MO273 -0.64854870 0.5166301223 1.00000000
## 375 MO261 - MO273 -2.50824257 0.0121333343 1.00000000
## 376 MO263 - MO273 -1.17988981 0.2380440448 1.00000000
## 377 MO267 - MO273 -0.46101655 0.6447867337 1.00000000
## 378 MO269 - MO273 -0.77357014 0.4391850372 1.00000000
## 379 MO201 - MO279 2.47698721 0.0132496650 1.00000000
## 380 MO202 - MO279 1.06268221 0.2879260914 1.00000000
## 381 MO203 - MO279 0.74231478 0.4578966398 1.00000000
## 382 MO204 - MO279 0.21878751 0.8268155739 1.00000000
## 383 MO221 - MO279 1.51588492 0.1295484550 1.00000000
## 384 MO222 - MO279 2.64889168 0.0080756210 1.00000000
## 385 MO223 - MO279 1.42993268 0.1527363418 1.00000000
## 386 MO224 - MO279 -0.42194735 0.6730634492 1.00000000
## 387 MO230 - MO279 0.10939376 0.9128901853 1.00000000
## 388 MO232 - MO279 1.59402331 0.1109308132 1.00000000
## 389 MO234 - MO279 1.46900188 0.1418322799 1.00000000
## 390 MO236 - MO279 2.65670552 0.0078908336 1.00000000
## 391 MO237 - MO279 -0.65636254 0.5115908862 1.00000000
## 392 MO238 - MO279 -0.35943663 0.7192684766 1.00000000
## 393 MO239 - MO279 1.23458668 0.2169843672 1.00000000
## 394 MO240 - MO279 -1.09393757 0.2739823605 1.00000000
## 395 MO241 - MO279 0.85952238 0.3900523808 1.00000000
## 396 MO242 - MO279 0.65636254 0.5115908862 1.00000000
## 397 MO243 - MO279 1.60965099 0.1074740691 1.00000000
## 398 MO253 - MO279 0.96110229 0.3365007372 1.00000000
## 399 MO255 - MO279 -0.45320271 0.6504027834 1.00000000
## 400 MO257 - MO279 0.67199022 0.5015899221 1.00000000
## 401 MO259 - MO279 1.10956525 0.2671864134 1.00000000
## 402 MO261 - MO279 -0.75012862 0.4531772449 1.00000000
## 403 MO263 - MO279 0.57822414 0.5631128006 1.00000000
## 404 MO267 - MO279 1.29709740 0.1945976751 1.00000000
## 405 MO269 - MO279 0.98454381 0.3248482011 1.00000000
## 406 MO273 - MO279 1.75811395 0.0787281228 1.00000000
## 407 MO201 - MO288 1.77374163 0.0761058972 1.00000000
## 408 MO202 - MO288 0.35943663 0.7192684766 1.00000000
## 409 MO203 - MO288 0.03906920 0.9688352179 1.00000000
## 410 MO204 - MO288 -0.48445807 0.6280608178 1.00000000
## 411 MO221 - MO288 0.81263934 0.4164248714 1.00000000
## 412 MO222 - MO288 1.94564610 0.0516972649 1.00000000
## 413 MO223 - MO288 0.72668710 0.4674176582 1.00000000
## 414 MO224 - MO288 -1.12519293 0.2605072895 1.00000000
## 415 MO230 - MO288 -0.59385182 0.5526112242 1.00000000
## 416 MO232 - MO288 0.89077773 0.3730484224 1.00000000
## 417 MO234 - MO288 0.76575630 0.4438213220 1.00000000
## 418 MO236 - MO288 1.95345994 0.0507651193 1.00000000
## 419 MO237 - MO288 -1.35960812 0.1739539669 1.00000000
## 420 MO238 - MO288 -1.06268221 0.2879260914 1.00000000
## 421 MO239 - MO288 0.53134110 0.5951824260 1.00000000
## 422 MO240 - MO288 -1.79718315 0.0723065489 1.00000000
## 423 MO241 - MO288 0.15627680 0.8758148461 1.00000000
## 424 MO242 - MO288 -0.04688304 0.9626064464 1.00000000
## 425 MO243 - MO288 0.90640541 0.3647213083 1.00000000
## 426 MO253 - MO288 0.25785671 0.7965174937 1.00000000
## 427 MO255 - MO288 -1.15644829 0.2474978404 1.00000000
## 428 MO257 - MO288 -0.03125536 0.9750658913 1.00000000
## 429 MO259 - MO288 0.40631967 0.6845077357 1.00000000
## 430 MO261 - MO288 -1.45337420 0.1461198863 1.00000000
## 431 MO263 - MO288 -0.12502144 0.9005065797 1.00000000
## 432 MO267 - MO288 0.59385182 0.5526112242 1.00000000
## 433 MO269 - MO288 0.28129823 0.7784816663 1.00000000
## 434 MO273 - MO288 1.05486837 0.2914855302 1.00000000
## 435 MO279 - MO288 -0.70324558 0.4819027186 1.00000000
##
##
## --- Analyzing Larval_Weight ---
##
## **Performing ANOVA on original data:**
## Analysis of Variance Table
##
## Response: Larval_Weight
## Df Sum Sq Mean Sq F value Pr(>F)
## Strain 29 4.5519 0.156964 2.2045 0.004944 **
## Residuals 60 4.2721 0.071201
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Eta-squared: 0.5158588
## $statistics
## MSerror Df Mean CV MSD
## 0.07120111 60 2.222333 12.00699 0.8575344
##
## $parameters
## test name.t ntr StudentizedRange alpha
## Tukey Strain 30 5.566328 0.05
##
## $means
## Larval_Weight std r se Min Max Q25 Q50 Q75
## MO201 2.326667 0.08386497 3 0.1540575 2.23 2.38 2.300 2.37 2.375
## MO202 2.083333 0.15307950 3 0.1540575 1.91 2.20 2.025 2.14 2.170
## MO203 2.290000 0.10583005 3 0.1540575 2.17 2.37 2.250 2.33 2.350
## MO204 2.296667 0.16072751 3 0.1540575 2.18 2.48 2.205 2.23 2.355
## MO221 2.323333 0.17473790 3 0.1540575 2.13 2.47 2.250 2.37 2.420
## MO222 2.510000 0.25514702 3 0.1540575 2.25 2.76 2.385 2.52 2.640
## MO223 2.526667 0.09609024 3 0.1540575 2.44 2.63 2.475 2.51 2.570
## MO224 2.060000 0.26000000 3 0.1540575 1.76 2.22 1.980 2.20 2.210
## MO230 2.020000 0.39736633 3 0.1540575 1.60 2.39 1.835 2.07 2.230
## MO232 2.073333 0.22744963 3 0.1540575 1.82 2.26 1.980 2.14 2.200
## MO234 2.506667 0.38004386 3 0.1540575 2.13 2.89 2.315 2.50 2.695
## MO236 2.433333 0.09712535 3 0.1540575 2.35 2.54 2.380 2.41 2.475
## MO237 2.256667 0.08962886 3 0.1540575 2.20 2.36 2.205 2.21 2.285
## MO238 2.316667 0.07371115 3 0.1540575 2.26 2.40 2.275 2.29 2.345
## MO239 1.933333 0.38888730 3 0.1540575 1.67 2.38 1.710 1.75 2.065
## MO240 2.080000 0.11357817 3 0.1540575 1.95 2.16 2.040 2.13 2.145
## MO241 2.566667 0.31628047 3 0.1540575 2.31 2.92 2.390 2.47 2.695
## MO242 2.173333 0.09504385 3 0.1540575 2.08 2.27 2.125 2.17 2.220
## MO243 2.330000 0.44192760 3 0.1540575 2.06 2.84 2.075 2.09 2.465
## MO253 2.466667 0.07371115 3 0.1540575 2.41 2.55 2.425 2.44 2.495
## MO255 1.966667 0.05033223 3 0.1540575 1.92 2.02 1.940 1.96 1.990
## MO257 1.753333 0.37740341 3 0.1540575 1.32 2.01 1.625 1.93 1.970
## MO259 2.050000 0.23515952 3 0.1540575 1.82 2.29 1.930 2.04 2.165
## MO261 1.700000 0.35510562 3 0.1540575 1.35 2.06 1.520 1.69 1.875
## MO263 2.270000 0.42142615 3 0.1540575 1.87 2.71 2.050 2.23 2.470
## MO267 2.046667 0.11015141 3 0.1540575 1.94 2.16 1.990 2.04 2.100
## MO269 2.190000 0.21931712 3 0.1540575 1.94 2.35 2.110 2.28 2.315
## MO273 2.470000 0.27838822 3 0.1540575 2.22 2.77 2.320 2.42 2.595
## MO279 2.506667 0.07637626 3 0.1540575 2.44 2.59 2.465 2.49 2.540
## MO288 2.143333 0.63058174 3 0.1540575 1.47 2.72 1.855 2.24 2.480
##
## $comparison
## NULL
##
## $groups
## Larval_Weight groups
## MO241 2.566667 a
## MO223 2.526667 ab
## MO222 2.510000 ab
## MO234 2.506667 ab
## MO279 2.506667 ab
## MO273 2.470000 ab
## MO253 2.466667 ab
## MO236 2.433333 ab
## MO243 2.330000 ab
## MO201 2.326667 ab
## MO221 2.323333 ab
## MO238 2.316667 ab
## MO204 2.296667 ab
## MO203 2.290000 ab
## MO263 2.270000 ab
## MO237 2.256667 ab
## MO269 2.190000 ab
## MO242 2.173333 ab
## MO288 2.143333 ab
## MO202 2.083333 ab
## MO240 2.080000 ab
## MO232 2.073333 ab
## MO224 2.060000 ab
## MO259 2.050000 ab
## MO267 2.046667 ab
## MO230 2.020000 ab
## MO255 1.966667 ab
## MO239 1.933333 ab
## MO257 1.753333 ab
## MO261 1.700000 b
##
## attr(,"class")
## [1] "group"
##
##
## --- Analyzing Single_Cocoon_Weight ---
##
## **Attempting log transformation...**
##
## Assumption Checks after Transformation:
## Normality (Shapiro-Wilk) p-value: 9.197164e-05
## Homogeneity of Variance (Levene's) p-value: 0.9438139
##
## **Performing Kruskal-Wallis test:**
##
## Kruskal-Wallis rank sum test
##
## data: Single_Cocoon_Weight by Strain
## Kruskal-Wallis chi-squared = 41.645, df = 29, p-value = 0.06042
##
## Epsilon-squared: 0.2107454
##
##
## --- Analyzing Cocoon_Shell_Weight ---
##
## **Performing ANOVA on original data:**
## Analysis of Variance Table
##
## Response: Cocoon_Shell_Weight
## Df Sum Sq Mean Sq F value Pr(>F)
## Strain 29 0.081366 0.0028057 3.6917 9.58e-06 ***
## Residuals 60 0.045600 0.0007600
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Eta-squared: 0.6408475
## $statistics
## MSerror Df Mean CV MSD
## 0.00076 60 0.2467778 11.17122 0.08859617
##
## $parameters
## test name.t ntr StudentizedRange alpha
## Tukey Strain 30 5.566328 0.05
##
## $means
## Cocoon_Shell_Weight std r se Min Max Q25 Q50 Q75
## MO201 0.2833333 0.005773503 3 0.01591645 0.28 0.29 0.280 0.28 0.285
## MO202 0.2333333 0.025166115 3 0.01591645 0.21 0.26 0.220 0.23 0.245
## MO203 0.2633333 0.030550505 3 0.01591645 0.23 0.29 0.250 0.27 0.280
## MO204 0.2766667 0.032145503 3 0.01591645 0.24 0.30 0.265 0.29 0.295
## MO221 0.2533333 0.015275252 3 0.01591645 0.24 0.27 0.245 0.25 0.260
## MO222 0.2433333 0.028867513 3 0.01591645 0.21 0.26 0.235 0.26 0.260
## MO223 0.2533333 0.020816660 3 0.01591645 0.23 0.27 0.245 0.26 0.265
## MO224 0.2066667 0.032145503 3 0.01591645 0.17 0.23 0.195 0.22 0.225
## MO230 0.2333333 0.011547005 3 0.01591645 0.22 0.24 0.230 0.24 0.240
## MO232 0.2500000 0.020000000 3 0.01591645 0.23 0.27 0.240 0.25 0.260
## MO234 0.2800000 0.026457513 3 0.01591645 0.26 0.31 0.265 0.27 0.290
## MO236 0.2733333 0.020816660 3 0.01591645 0.25 0.29 0.265 0.28 0.285
## MO237 0.2566667 0.015275252 3 0.01591645 0.24 0.27 0.250 0.26 0.265
## MO238 0.2433333 0.005773503 3 0.01591645 0.24 0.25 0.240 0.24 0.245
## MO239 0.2266667 0.066583281 3 0.01591645 0.15 0.27 0.205 0.26 0.265
## MO240 0.2466667 0.025166115 3 0.01591645 0.22 0.27 0.235 0.25 0.260
## MO241 0.3166667 0.025166115 3 0.01591645 0.29 0.34 0.305 0.32 0.330
## MO242 0.2400000 0.030000000 3 0.01591645 0.21 0.27 0.225 0.24 0.255
## MO243 0.2633333 0.015275252 3 0.01591645 0.25 0.28 0.255 0.26 0.270
## MO253 0.2466667 0.015275252 3 0.01591645 0.23 0.26 0.240 0.25 0.255
## MO255 0.1933333 0.015275252 3 0.01591645 0.18 0.21 0.185 0.19 0.200
## MO257 0.1866667 0.030550505 3 0.01591645 0.16 0.22 0.170 0.18 0.200
## MO259 0.1766667 0.005773503 3 0.01591645 0.17 0.18 0.175 0.18 0.180
## MO261 0.2133333 0.041633320 3 0.01591645 0.18 0.26 0.190 0.20 0.230
## MO263 0.2300000 0.043588989 3 0.01591645 0.20 0.28 0.205 0.21 0.245
## MO267 0.2400000 0.010000000 3 0.01591645 0.23 0.25 0.235 0.24 0.245
## MO269 0.2666667 0.025166115 3 0.01591645 0.24 0.29 0.255 0.27 0.280
## MO273 0.2833333 0.037859389 3 0.01591645 0.24 0.31 0.270 0.30 0.305
## MO279 0.2633333 0.030550505 3 0.01591645 0.23 0.29 0.250 0.27 0.280
## MO288 0.2600000 0.026457513 3 0.01591645 0.24 0.29 0.245 0.25 0.270
##
## $comparison
## NULL
##
## $groups
## Cocoon_Shell_Weight groups
## MO241 0.3166667 a
## MO201 0.2833333 ab
## MO273 0.2833333 ab
## MO234 0.2800000 abc
## MO204 0.2766667 abc
## MO236 0.2733333 abcd
## MO269 0.2666667 abcd
## MO203 0.2633333 abcde
## MO243 0.2633333 abcde
## MO279 0.2633333 abcde
## MO288 0.2600000 abcde
## MO237 0.2566667 abcde
## MO221 0.2533333 abcde
## MO223 0.2533333 abcde
## MO232 0.2500000 abcde
## MO240 0.2466667 abcde
## MO253 0.2466667 abcde
## MO222 0.2433333 abcde
## MO238 0.2433333 abcde
## MO242 0.2400000 abcde
## MO267 0.2400000 abcde
## MO202 0.2333333 abcde
## MO230 0.2333333 abcde
## MO263 0.2300000 abcde
## MO239 0.2266667 bcde
## MO261 0.2133333 bcde
## MO224 0.2066667 bcde
## MO255 0.1933333 cde
## MO257 0.1866667 de
## MO259 0.1766667 e
##
## attr(,"class")
## [1] "group"
##
##
## --- Analyzing Cocoon_Shell_Percentage ---
##
## **Attempting log transformation...**##
## Assumption Checks after Transformation:
## Normality (Shapiro-Wilk) p-value: 3.336526e-05
## Homogeneity of Variance (Levene's) p-value: 0.6181337
##
## **Performing Kruskal-Wallis test:**
##
## Kruskal-Wallis rank sum test
##
## data: Cocoon_Shell_Percentage by Strain
## Kruskal-Wallis chi-squared = 45.745, df = 29, p-value = 0.02487
##
## Epsilon-squared: 0.2790885
##
## **Dunn's Test (Post-hoc with Benjamini-Hochberg correction):**## Dunn (1964) Kruskal-Wallis multiple comparison## p-values adjusted with the Benjamini-Hochberg method.## Comparison Z P.unadj P.adj
## 1 MO201 - MO202 1.78156280 0.074820555 0.4520409
## 2 MO201 - MO203 0.37506585 0.707611492 0.9106834
## 3 MO202 - MO203 -1.40649695 0.159576610 0.5423111
## 4 MO201 - MO204 0.68762073 0.491691650 0.7863451
## 5 MO202 - MO204 -1.09394207 0.273980385 0.7136615
## 6 MO203 - MO204 0.31255488 0.754618864 0.9325546
## 7 MO201 - MO221 1.81281829 0.069859852 0.4535677
## 8 MO202 - MO221 0.03125549 0.975065789 0.9841151
## 9 MO203 - MO221 1.43775244 0.150504309 0.5410692
## 10 MO204 - MO221 1.12519756 0.260505327 0.6995050
## 11 MO201 - MO222 2.14881478 0.031649085 0.3128944
## 12 MO202 - MO222 0.36725198 0.713431069 0.9074343
## 13 MO203 - MO222 1.77374893 0.076104689 0.4535005
## 14 MO204 - MO222 1.46119405 0.143962195 0.5307081
## 15 MO221 - MO222 0.33599649 0.736873511 0.9291014
## 16 MO201 - MO223 1.05487271 0.291483544 0.7204281
## 17 MO202 - MO223 -0.72669009 0.467415825 0.7760530
## 18 MO203 - MO223 0.67980686 0.496626763 0.7855732
## 19 MO204 - MO223 0.36725198 0.713431069 0.9100954
## 20 MO221 - MO223 -0.75794558 0.448483563 0.7680722
## 21 MO222 - MO223 -1.09394207 0.273980385 0.7052158
## 22 MO201 - MO224 1.96909573 0.048942099 0.4174473
## 23 MO202 - MO224 0.18753293 0.851242810 0.9668162
## 24 MO203 - MO224 1.59402988 0.110929344 0.5079396
## 25 MO204 - MO224 1.28147500 0.200026876 0.6215121
## 26 MO221 - MO224 0.15627744 0.875814339 0.9743715
## 27 MO222 - MO224 -0.17971905 0.857373134 0.9662107
## 28 MO223 - MO224 0.91422302 0.360599672 0.7577819
## 29 MO201 - MO230 2.75048292 0.005950749 0.2876196
## 30 MO202 - MO230 0.96892012 0.332585046 0.7535130
## 31 MO203 - MO230 2.37541707 0.017529131 0.2723276
## 32 MO204 - MO230 2.06286219 0.039125723 0.3545769
## 33 MO221 - MO230 0.93766463 0.348416785 0.7578065
## 34 MO222 - MO230 0.60166814 0.547395062 0.8044488
## 35 MO223 - MO230 1.69561021 0.089959723 0.4831170
## 36 MO224 - MO230 0.78138719 0.434574801 0.7622582
## 37 MO201 - MO232 0.89078140 0.373046455 0.7512741
## 38 MO202 - MO232 -0.89078140 0.373046455 0.7547684
## 39 MO203 - MO232 0.51571555 0.606053094 0.8422783
## 40 MO204 - MO232 0.20316067 0.839009452 0.9706625
## 41 MO221 - MO232 -0.92203689 0.356509334 0.7677305
## 42 MO222 - MO232 -1.25803338 0.208379684 0.6294803
## 43 MO223 - MO232 -0.16409131 0.869659262 0.9724981
## 44 MO224 - MO232 -1.07831433 0.280893505 0.7187569
## 45 MO230 - MO232 -1.85970152 0.062927767 0.4639590
## 46 MO201 - MO234 1.10956982 0.267184444 0.7043954
## 47 MO202 - MO234 -0.67199299 0.501588161 0.7876926
## 48 MO203 - MO234 0.73450396 0.462641646 0.7800353
## 49 MO204 - MO234 0.42194908 0.673062182 0.8872183
## 50 MO221 - MO234 -0.70324847 0.481900915 0.7851195
## 51 MO222 - MO234 -1.03924497 0.298690822 0.7258688
## 52 MO223 - MO234 0.05469710 0.956379777 0.9788828
## 53 MO224 - MO234 -0.85952591 0.390050430 0.7574640
## 54 MO230 - MO234 -1.64091311 0.100815454 0.4983491
## 55 MO232 - MO234 0.21878841 0.826814872 0.9616697
## 56 MO201 - MO236 1.35961372 0.173952195 0.5605126
## 57 MO202 - MO236 -0.42194908 0.673062182 0.8899150
## 58 MO203 - MO236 0.98454786 0.324846210 0.7516388
## 59 MO204 - MO236 0.67199299 0.501588161 0.7905466
## 60 MO221 - MO236 -0.45320457 0.650401440 0.8705373
## 61 MO222 - MO236 -0.78920107 0.429994499 0.7572778
## 62 MO223 - MO236 0.30474101 0.760563416 0.9345906
## 63 MO224 - MO236 -0.60948201 0.542204993 0.8022421
## 64 MO230 - MO236 -1.39086920 0.164265093 0.5496563
## 65 MO232 - MO236 0.46883232 0.639189499 0.8661914
## 66 MO234 - MO236 0.25004390 0.802553398 0.9512554
## 67 MO201 - MO237 1.23459177 0.216982475 0.6377525
## 68 MO202 - MO237 -0.54697104 0.584398631 0.8307628
## 69 MO203 - MO237 0.85952591 0.390050430 0.7608607
## 70 MO204 - MO237 0.54697104 0.584398631 0.8334866
## 71 MO221 - MO237 -0.57822652 0.563111194 0.8165112
## 72 MO222 - MO237 -0.91422302 0.360599672 0.7689258
## 73 MO223 - MO237 0.17971905 0.857373134 0.9687203
## 74 MO224 - MO237 -0.73450396 0.462641646 0.7830705
## 75 MO230 - MO237 -1.51589116 0.129546877 0.5122990
## 76 MO232 - MO237 0.34381037 0.730988905 0.9243610
## 77 MO234 - MO237 0.12502195 0.900506172 0.9744283
## 78 MO236 - MO237 -0.12502195 0.900506172 0.9696044
## 79 MO201 - MO238 1.59402988 0.110929344 0.5133432
## 80 MO202 - MO238 -0.18753293 0.851242810 0.9693472
## 81 MO203 - MO238 1.21896402 0.222857848 0.6462878
## 82 MO204 - MO238 0.90640914 0.364719334 0.7554900
## 83 MO221 - MO238 -0.21878841 0.826814872 0.9642479
## 84 MO222 - MO238 -0.55478491 0.579041791 0.8285631
## 85 MO223 - MO238 0.53915716 0.589778415 0.8329663
## 86 MO224 - MO238 -0.37506585 0.707611492 0.9133858
## 87 MO230 - MO238 -1.15645305 0.247495894 0.6771114
## 88 MO232 - MO238 0.70324847 0.481900915 0.7880710
## 89 MO234 - MO238 0.48446006 0.628059403 0.8591379
## 90 MO236 - MO238 0.23441616 0.814661916 0.9603738
## 91 MO237 - MO238 0.35943811 0.719267370 0.9121904
## 92 MO201 - MO239 1.17208079 0.241164621 0.6681950
## 93 MO202 - MO239 -0.60948201 0.542204993 0.8049801
## 94 MO203 - MO239 0.79701494 0.425442356 0.7615943
## 95 MO204 - MO239 0.48446006 0.628059403 0.8618481
## 96 MO221 - MO239 -0.64073750 0.521693246 0.7907197
## 97 MO222 - MO239 -0.97673399 0.328700862 0.7486119
## 98 MO223 - MO239 0.11720808 0.906695165 0.9643335
## 99 MO224 - MO239 -0.79701494 0.425442356 0.7647414
## 100 MO230 - MO239 -1.57840213 0.114473256 0.5081211
## 101 MO232 - MO239 0.28129939 0.778480778 0.9485690
## 102 MO234 - MO239 0.06251098 0.950155922 0.9840901
## 103 MO236 - MO239 -0.18753293 0.851242810 0.9718914
## 104 MO237 - MO239 -0.06251098 0.950155922 0.9864387
## 105 MO238 - MO239 -0.42194908 0.673062182 0.8926282
## 106 MO201 - MO240 1.20333628 0.228846216 0.6549217
## 107 MO202 - MO240 -0.57822652 0.563111194 0.8192420
## 108 MO203 - MO240 0.82827043 0.407517368 0.7640951
## 109 MO204 - MO240 0.51571555 0.606053094 0.8449779
## 110 MO221 - MO240 -0.60948201 0.542204993 0.8077369
## 111 MO222 - MO240 -0.94547850 0.344414640 0.7605095
## 112 MO223 - MO240 0.14846357 0.881976937 0.9639698
## 113 MO224 - MO240 -0.76575945 0.443819446 0.7691692
## 114 MO230 - MO240 -1.54714664 0.121827889 0.4999541
## 115 MO232 - MO240 0.31255488 0.754618864 0.9352114
## 116 MO234 - MO240 0.09376646 0.925294673 0.9698872
## 117 MO236 - MO240 -0.15627744 0.875814339 0.9768698
## 118 MO237 - MO240 -0.03125549 0.975065789 0.9887031
## 119 MO238 - MO240 -0.39069360 0.696023732 0.9064980
## 120 MO239 - MO240 0.03125549 0.975065789 0.9864038
## 121 MO201 - MO241 0.18753293 0.851242810 0.9744490
## 122 MO202 - MO241 -1.59402988 0.110929344 0.5188631
## 123 MO203 - MO241 -0.18753293 0.851242810 0.9770201
## 124 MO204 - MO241 -0.50008780 0.617013253 0.8520659
## 125 MO221 - MO241 -1.62528536 0.104101769 0.5031585
## 126 MO222 - MO241 -1.96128186 0.049846153 0.4091146
## 127 MO223 - MO241 -0.86733979 0.385755864 0.7558730
## 128 MO224 - MO241 -1.78156280 0.074820555 0.4584076
## 129 MO230 - MO241 -2.56295000 0.010378700 0.3009823
## 130 MO232 - MO241 -0.70324847 0.481900915 0.7910449
## 131 MO234 - MO241 -0.92203689 0.356509334 0.7715501
## 132 MO236 - MO241 -1.17208079 0.241164621 0.6724783
## 133 MO237 - MO241 -1.04705884 0.295072441 0.7251780
## 134 MO238 - MO241 -1.40649695 0.159576610 0.5465813
## 135 MO239 - MO241 -0.98454786 0.324846210 0.7556583
## 136 MO240 - MO241 -1.01580335 0.309723040 0.7322257
## 137 MO201 - MO242 0.90640914 0.364719334 0.7591048
## 138 MO202 - MO242 -0.87515366 0.381490305 0.7543104
## 139 MO203 - MO242 0.53134329 0.595180911 0.8324878
## 140 MO204 - MO242 0.21878841 0.826814872 0.9668400
## 141 MO221 - MO242 -0.90640914 0.364719334 0.7519095
## 142 MO222 - MO242 -1.24240564 0.214086936 0.6378618
## 143 MO223 - MO242 -0.14846357 0.881976937 0.9663979
## 144 MO224 - MO242 -1.06268658 0.287924107 0.7281802
## 145 MO230 - MO242 -1.84407378 0.065172389 0.4572579
## 146 MO232 - MO242 0.01562774 0.987531372 0.9943892
## 147 MO234 - MO242 -0.20316067 0.839009452 0.9680878
## 148 MO236 - MO242 -0.45320457 0.650401440 0.8732242
## 149 MO237 - MO242 -0.32818262 0.742773587 0.9338338
## 150 MO238 - MO242 -0.68762073 0.491691650 0.7892467
## 151 MO239 - MO242 -0.26567165 0.790492102 0.9472839
## 152 MO240 - MO242 -0.29692713 0.766522140 0.9366212
## 153 MO241 - MO242 0.71887622 0.472217191 0.7810436
## 154 MO201 - MO243 0.78920107 0.429994499 0.7603561
## 155 MO202 - MO243 -0.99236174 0.321021098 0.7507751
## 156 MO203 - MO243 0.41413521 0.678775086 0.8920458
## 157 MO204 - MO243 0.10158034 0.919089789 0.9751318
## 158 MO221 - MO243 -1.02361722 0.306016107 0.7354531
## 159 MO222 - MO243 -1.35961372 0.173952195 0.5563912
## 160 MO223 - MO243 -0.26567165 0.790492102 0.9499007
## 161 MO224 - MO243 -1.17989466 0.238042113 0.6723917
## 162 MO230 - MO243 -1.96128186 0.049846153 0.4169822
## 163 MO232 - MO243 -0.10158034 0.919089789 0.9727593
## 164 MO234 - MO243 -0.32036875 0.748688812 0.9305132
## 165 MO236 - MO243 -0.57041265 0.568397851 0.8160167
## 166 MO237 - MO243 -0.44539070 0.656037432 0.8753874
## 167 MO238 - MO243 -0.80482881 0.420918474 0.7758455
## 168 MO239 - MO243 -0.38287972 0.701808945 0.9113042
## 169 MO240 - MO243 -0.41413521 0.678775086 0.8893589
## 170 MO241 - MO243 0.60166814 0.547395062 0.8071758
## 171 MO242 - MO243 -0.11720808 0.906695165 0.9666971
## 172 MO201 - MO253 2.60983323 0.009058637 0.3031159
## 173 MO202 - MO253 0.82827043 0.407517368 0.7674028
## 174 MO203 - MO253 2.23476737 0.025432625 0.2990052
## 175 MO204 - MO253 1.92221250 0.054579025 0.4165241
## 176 MO221 - MO253 0.79701494 0.425442356 0.7808752
## 177 MO222 - MO253 0.46101844 0.644785372 0.8683642
## 178 MO223 - MO253 1.55496052 0.119955473 0.5017368
## 179 MO224 - MO253 0.64073750 0.521693246 0.7934845
## 180 MO230 - MO253 -0.14064969 0.888146688 0.9658595
## 181 MO232 - MO253 1.71905183 0.085604935 0.4899756
## 182 MO234 - MO253 1.50026341 0.133546183 0.5140937
## 183 MO236 - MO253 1.25021951 0.211219372 0.6336581
## 184 MO237 - MO253 1.37524146 0.169056598 0.5571183
## 185 MO238 - MO253 1.01580335 0.309723040 0.7402721
## 186 MO239 - MO253 1.43775244 0.150504309 0.5455781
## 187 MO240 - MO253 1.40649695 0.159576610 0.5509192
## 188 MO241 - MO253 2.42230030 0.015422600 0.2916883
## 189 MO242 - MO253 1.70342408 0.088488734 0.4872481
## 190 MO243 - MO253 1.82063216 0.068662791 0.4595125
## 191 MO201 - MO255 2.46918353 0.013542174 0.2945423
## 192 MO202 - MO255 0.68762073 0.491691650 0.7921699
## 193 MO203 - MO255 2.09411768 0.036249499 0.3427942
## 194 MO204 - MO255 1.78156280 0.074820555 0.4649563
## 195 MO221 - MO255 0.65636524 0.511589148 0.7891535
## 196 MO222 - MO255 0.32036875 0.748688812 0.9385580
## 197 MO223 - MO255 1.41431082 0.157270661 0.5473019
## 198 MO224 - MO255 0.50008780 0.617013253 0.8547795
## 199 MO230 - MO255 -0.28129939 0.778480778 0.9459194
## 200 MO232 - MO255 1.57840213 0.114473256 0.5133594
## 201 MO234 - MO255 1.35961372 0.173952195 0.5646956
## 202 MO236 - MO255 1.10956982 0.267184444 0.7130382
## 203 MO237 - MO255 1.23459177 0.216982475 0.6334723
## 204 MO238 - MO255 0.87515366 0.381490305 0.7577547
## 205 MO239 - MO255 1.29710274 0.194595838 0.6089870
## 206 MO240 - MO255 1.26584725 0.205567774 0.6253285
## 207 MO241 - MO255 2.28165061 0.022509976 0.2879953
## 208 MO242 - MO255 1.56277439 0.118105671 0.5036859
## 209 MO243 - MO255 1.67998247 0.092960727 0.4872038
## 210 MO253 - MO255 -0.14064969 0.888146688 0.9682802
## 211 MO201 - MO257 2.62546097 0.008653173 0.3421937
## 212 MO202 - MO257 0.84389817 0.398726311 0.7607278
## 213 MO203 - MO257 2.25039512 0.024423875 0.2951218
## 214 MO204 - MO257 1.93784024 0.052642717 0.4240663
## 215 MO221 - MO257 0.81264268 0.416422953 0.7741196
## 216 MO222 - MO257 0.47664619 0.633614088 0.8640192
## 217 MO223 - MO257 1.57058826 0.116278319 0.5058107
## 218 MO224 - MO257 0.65636524 0.511589148 0.7919618
## 219 MO230 - MO257 -0.12502195 0.900506172 0.9720104
## 220 MO232 - MO257 1.73467957 0.082797577 0.4802259
## 221 MO234 - MO257 1.51589116 0.129546877 0.5169990
## 222 MO236 - MO257 1.26584725 0.205567774 0.6297323
## 223 MO237 - MO257 1.39086920 0.164265093 0.5539172
## 224 MO238 - MO257 1.03143110 0.302338705 0.7306519
## 225 MO239 - MO257 1.45338018 0.146118226 0.5341297
## 226 MO240 - MO257 1.42212469 0.154990056 0.5481356
## 227 MO241 - MO257 2.43792804 0.014771714 0.3059855
## 228 MO242 - MO257 1.71905183 0.085604935 0.4836123
## 229 MO243 - MO257 1.83625991 0.066319227 0.4579185
## 230 MO253 - MO257 0.01562774 0.987531372 0.9920927
## 231 MO255 - MO257 0.15627744 0.875814339 0.9718858
## 232 MO201 - MO259 3.28182621 0.001031371 0.2243233
## 233 MO202 - MO259 1.50026341 0.133546183 0.5186838
## 234 MO203 - MO259 2.90676036 0.003651928 0.2269413
## 235 MO204 - MO259 2.59420548 0.009480980 0.2945876
## 236 MO221 - MO259 1.46900792 0.141830640 0.5318649
## 237 MO222 - MO259 1.13301143 0.257209453 0.6949448
## 238 MO223 - MO259 2.22695350 0.025950382 0.2894466
## 239 MO224 - MO259 1.31273049 0.189273781 0.5966239
## 240 MO230 - MO259 0.53134329 0.595180911 0.8351732
## 241 MO232 - MO259 2.39104481 0.016800502 0.2810853
## 242 MO234 - MO259 2.17225640 0.029836329 0.3165562
## 243 MO236 - MO259 1.92221250 0.054579025 0.4239621
## 244 MO237 - MO259 2.04723445 0.040635071 0.3607399
## 245 MO238 - MO259 1.68779634 0.091450331 0.4851329
## 246 MO239 - MO259 2.10974542 0.034880290 0.3371761
## 247 MO240 - MO259 2.07848994 0.037664257 0.3485947
## 248 MO241 - MO259 3.09429329 0.001972824 0.2860594
## 249 MO242 - MO259 2.37541707 0.017529131 0.2824138
## 250 MO243 - MO259 2.49262515 0.012680264 0.3064397
## 251 MO253 - MO259 0.67199299 0.501588161 0.7820461
## 252 MO255 - MO259 0.81264268 0.416422953 0.7708255
## 253 MO257 - MO259 0.65636524 0.511589148 0.7947903
## 254 MO201 - MO261 0.96110625 0.336498748 0.7506511
## 255 MO202 - MO261 -0.82045655 0.411955887 0.7691022
## 256 MO203 - MO261 0.58604040 0.557848369 0.8143089
## 257 MO204 - MO261 0.27348552 0.784480023 0.9479134
## 258 MO221 - MO261 -0.85171204 0.394373936 0.7557386
## 259 MO222 - MO261 -1.18770853 0.234948260 0.6679902
## 260 MO223 - MO261 -0.09376646 0.925294673 0.9722299
## 261 MO224 - MO261 -1.00798948 0.313459513 0.7370534
## 262 MO230 - MO261 -1.78937667 0.073554173 0.4705304
## 263 MO232 - MO261 0.07032485 0.943935106 0.9823248
## 264 MO234 - MO261 -0.14846357 0.881976937 0.9688383
## 265 MO236 - MO261 -0.39850747 0.690256154 0.9016860
## 266 MO237 - MO261 -0.27348552 0.784480023 0.9505538
## 267 MO238 - MO261 -0.63292363 0.526783518 0.7929094
## 268 MO239 - MO261 -0.21097454 0.832907137 0.9661723
## 269 MO240 - MO261 -0.24223003 0.808601927 0.9558202
## 270 MO241 - MO261 0.77357332 0.439183154 0.7641787
## 271 MO242 - MO261 0.05469710 0.956379777 0.9811915
## 272 MO243 - MO261 0.17190518 0.863512072 0.9706143
## 273 MO253 - MO261 -1.64872698 0.099203580 0.4960179
## 274 MO255 - MO261 -1.50807728 0.131534748 0.5154740
## 275 MO257 - MO261 -1.66435472 0.096041563 0.4915068
## 276 MO259 - MO261 -2.32071997 0.020301962 0.2848824
## 277 MO201 - MO263 1.85188765 0.064041958 0.4566927
## 278 MO202 - MO263 0.07032485 0.943935106 0.9846805
## 279 MO203 - MO263 1.47682180 0.139723412 0.5285190
## 280 MO204 - MO263 1.16426692 0.244315858 0.6726418
## 281 MO221 - MO263 0.03906936 0.968835090 0.9893034
## 282 MO222 - MO263 -0.29692713 0.766522140 0.9392595
## 283 MO223 - MO263 0.79701494 0.425442356 0.7679146
## 284 MO224 - MO263 -0.11720808 0.906695165 0.9690722
## 285 MO230 - MO263 -0.89859527 0.368868278 0.7568759
## 286 MO232 - MO263 0.96110625 0.336498748 0.7545204
## 287 MO234 - MO263 0.74231783 0.457894789 0.7811146
## 288 MO236 - MO263 0.49227393 0.622525706 0.8569579
## 289 MO237 - MO263 0.61729588 0.537039582 0.8027911
## 290 MO238 - MO263 0.25785777 0.796516675 0.9466797
## 291 MO239 - MO263 0.67980686 0.496626763 0.7884403
## 292 MO240 - MO263 0.64855137 0.516628396 0.7913146
## 293 MO241 - MO263 1.66435472 0.096041563 0.4973581
## 294 MO242 - MO263 0.94547850 0.344414640 0.7528662
## 295 MO243 - MO263 1.06268658 0.287924107 0.7324385
## 296 MO253 - MO263 -0.75794558 0.448483563 0.7741681
## 297 MO255 - MO263 -0.61729588 0.537039582 0.8055594
## 298 MO257 - MO263 -0.77357332 0.439183154 0.7672477
## 299 MO259 - MO263 -1.42993856 0.152734652 0.5445867
## 300 MO261 - MO263 0.89078140 0.373046455 0.7582954
## 301 MO201 - MO267 0.32036875 0.748688812 0.9331795
## 302 MO202 - MO267 -1.46119405 0.143962195 0.5352441
## 303 MO203 - MO267 -0.05469710 0.956379777 0.9858417
## 304 MO204 - MO267 -0.36725198 0.713431069 0.9127721
## 305 MO221 - MO267 -1.49244954 0.135581336 0.5173498
## 306 MO222 - MO267 -1.82844603 0.067482638 0.4586711
## 307 MO223 - MO267 -0.73450396 0.462641646 0.7740351
## 308 MO224 - MO267 -1.64872698 0.099203580 0.5017856
## 309 MO230 - MO267 -2.43011417 0.015094067 0.2984509
## 310 MO232 - MO267 -0.57041265 0.568397851 0.8214388
## 311 MO234 - MO267 -0.78920107 0.429994499 0.7634596
## 312 MO236 - MO267 -1.03924497 0.298690822 0.7299467
## 313 MO237 - MO267 -0.91422302 0.360599672 0.7727136
## 314 MO238 - MO267 -1.27366113 0.202783539 0.6256088
## 315 MO239 - MO267 -0.85171204 0.394373936 0.7624563
## 316 MO240 - MO267 -0.88296753 0.377253816 0.7527771
## 317 MO241 - MO267 0.13283582 0.894323223 0.9701511
## 318 MO242 - MO267 -0.58604040 0.557848369 0.8170506
## 319 MO243 - MO267 -0.46883232 0.639189499 0.8688982
## 320 MO253 - MO267 -2.28946448 0.022052380 0.2906905
## 321 MO255 - MO267 -2.14881478 0.031649085 0.3277941
## 322 MO257 - MO267 -2.30509222 0.021161409 0.2876629
## 323 MO259 - MO267 -2.96145746 0.003061868 0.2219854
## 324 MO261 - MO267 -0.64073750 0.521693246 0.7962686
## 325 MO263 - MO267 -1.53151890 0.125641199 0.5107843
## 326 MO201 - MO269 0.21878841 0.826814872 0.9694460
## 327 MO202 - MO269 -1.56277439 0.118105671 0.5086729
## 328 MO203 - MO269 -0.15627744 0.875814339 0.9694128
## 329 MO204 - MO269 -0.46883232 0.639189499 0.8635013
## 330 MO221 - MO269 -1.59402988 0.110929344 0.5026486
## 331 MO222 - MO269 -1.93002637 0.053603571 0.4239555
## 332 MO223 - MO269 -0.83608430 0.403107482 0.7623989
## 333 MO224 - MO269 -1.75030731 0.080065300 0.4706541
## 334 MO230 - MO269 -2.53169451 0.011351284 0.3086130
## 335 MO232 - MO269 -0.67199299 0.501588161 0.7848592
## 336 MO234 - MO269 -0.89078140 0.373046455 0.7478120
## 337 MO236 - MO269 -1.14082530 0.253942629 0.6904065
## 338 MO237 - MO269 -1.01580335 0.309723040 0.7362269
## 339 MO238 - MO269 -1.37524146 0.169056598 0.5613711
## 340 MO239 - MO269 -0.95329238 0.340441953 0.7555727
## 341 MO240 - MO269 -0.98454786 0.324846210 0.7476619
## 342 MO241 - MO269 0.03125549 0.975065789 0.9910131
## 343 MO242 - MO269 -0.68762073 0.491691650 0.7951148
## 344 MO243 - MO269 -0.57041265 0.568397851 0.8187188
## 345 MO253 - MO269 -2.39104481 0.016800502 0.2923287
## 346 MO255 - MO269 -2.25039512 0.024423875 0.3035539
## 347 MO257 - MO269 -2.40667256 0.016098597 0.2917871
## 348 MO259 - MO269 -3.06303780 0.002191024 0.2382738
## 349 MO261 - MO269 -0.74231783 0.457894789 0.7780634
## 350 MO263 - MO269 -1.63309924 0.102448127 0.5007296
## 351 MO267 - MO269 -0.10158034 0.919089789 0.9703982
## 352 MO201 - MO273 0.25785777 0.796516675 0.9492733
## 353 MO202 - MO273 -1.52370503 0.127582413 0.5138736
## 354 MO203 - MO273 -0.11720808 0.906695165 0.9714591
## 355 MO204 - MO273 -0.42976296 0.667368082 0.8877832
## 356 MO221 - MO273 -1.55496052 0.119955473 0.4969584
## 357 MO222 - MO273 -1.89095701 0.058630083 0.4397256
## 358 MO223 - MO273 -0.79701494 0.425442356 0.7711143
## 359 MO224 - MO273 -1.71123795 0.087037195 0.4853997
## 360 MO230 - MO273 -2.49262515 0.012680264 0.3244656
## 361 MO232 - MO273 -0.63292363 0.526783518 0.7956626
## 362 MO234 - MO273 -0.85171204 0.394373936 0.7590826
## 363 MO236 - MO273 -1.10175594 0.270567789 0.7090180
## 364 MO237 - MO273 -0.97673399 0.328700862 0.7525520
## 365 MO238 - MO273 -1.33617210 0.181493028 0.5762735
## 366 MO239 - MO273 -0.91422302 0.360599672 0.7614605
## 367 MO240 - MO273 -0.94547850 0.344414640 0.7566685
## 368 MO241 - MO273 0.07032485 0.943935106 0.9870475
## 369 MO242 - MO273 -0.64855137 0.516628396 0.7941108
## 370 MO243 - MO273 -0.53134329 0.595180911 0.8378760
## 371 MO253 - MO273 -2.35197545 0.018674007 0.2707731
## 372 MO255 - MO273 -2.21132576 0.027013287 0.2937695
## 373 MO257 - MO273 -2.36760320 0.017903726 0.2685559
## 374 MO259 - MO273 -3.02396844 0.002494825 0.2170497
## 375 MO261 - MO273 -0.70324847 0.481900915 0.7940413
## 376 MO263 - MO273 -1.59402988 0.110929344 0.5245029
## 377 MO267 - MO273 -0.06251098 0.950155922 0.9817526
## 378 MO269 - MO273 0.03906936 0.968835090 0.9869866
## 379 MO201 - MO279 1.05487271 0.291483544 0.7245448
## 380 MO202 - MO279 -0.72669009 0.467415825 0.7790264
## 381 MO203 - MO279 0.67980686 0.496626763 0.7913284
## 382 MO204 - MO279 0.36725198 0.713431069 0.9154646
## 383 MO221 - MO279 -0.75794558 0.448483563 0.7711081
## 384 MO222 - MO279 -1.09394207 0.273980385 0.7094135
## 385 MO223 - MO279 0.00000000 1.000000000 1.0000000
## 386 MO224 - MO279 -0.91422302 0.360599672 0.7651749
## 387 MO230 - MO279 -1.69561021 0.089959723 0.4891560
## 388 MO232 - MO279 0.16409131 0.869659262 0.9750046
## 389 MO234 - MO279 -0.05469710 0.956379777 0.9835111
## 390 MO236 - MO279 -0.30474101 0.760563416 0.9372382
## 391 MO237 - MO279 -0.17971905 0.857373134 0.9712430
## 392 MO238 - MO279 -0.53915716 0.589778415 0.8356795
## 393 MO239 - MO279 -0.11720808 0.906695165 0.9738578
## 394 MO240 - MO279 -0.14846357 0.881976937 0.9712911
## 395 MO241 - MO279 0.86733979 0.385755864 0.7592932
## 396 MO242 - MO279 0.14846357 0.881976937 0.9737563
## 397 MO243 - MO279 0.26567165 0.790492102 0.9525320
## 398 MO253 - MO279 -1.55496052 0.119955473 0.5066081
## 399 MO255 - MO279 -1.41431082 0.157270661 0.5517156
## 400 MO257 - MO279 -1.57058826 0.116278319 0.5109199
## 401 MO259 - MO279 -2.22695350 0.025950382 0.2970636
## 402 MO261 - MO279 0.09376646 0.925294673 0.9745840
## 403 MO263 - MO279 -0.79701494 0.425442356 0.7743407
## 404 MO267 - MO279 0.73450396 0.462641646 0.7770236
## 405 MO269 - MO279 0.83608430 0.403107482 0.7657282
## 406 MO273 - MO279 0.79701494 0.425442356 0.7775942
## 407 MO201 - MO288 0.00000000 1.000000000 1.0000000
## 408 MO202 - MO288 -1.78156280 0.074820555 0.4716948
## 409 MO203 - MO288 -0.37506585 0.707611492 0.9161042
## 410 MO204 - MO288 -0.68762073 0.491691650 0.7980816
## 411 MO221 - MO288 -1.81281829 0.069859852 0.4604399
## 412 MO222 - MO288 -2.14881478 0.031649085 0.3201710
## 413 MO223 - MO288 -1.05487271 0.291483544 0.7287089
## 414 MO224 - MO288 -1.96909573 0.048942099 0.4257963
## 415 MO230 - MO288 -2.75048292 0.005950749 0.3235720
## 416 MO232 - MO288 -0.89078140 0.373046455 0.7618554
## 417 MO234 - MO288 -1.10956982 0.267184444 0.7086904
## 418 MO236 - MO288 -1.35961372 0.173952195 0.5689414
## 419 MO237 - MO288 -1.23459177 0.216982475 0.6420910
## 420 MO238 - MO288 -1.59402988 0.110929344 0.5302666
## 421 MO239 - MO288 -1.17208079 0.241164621 0.6768168
## 422 MO240 - MO288 -1.20333628 0.228846216 0.6592590
## 423 MO241 - MO288 -0.18753293 0.851242810 0.9796048
## 424 MO242 - MO288 -0.90640914 0.364719334 0.7627544
## 425 MO243 - MO288 -0.78920107 0.429994499 0.7665886
## 426 MO253 - MO288 -2.60983323 0.009058637 0.3283756
## 427 MO255 - MO288 -2.46918353 0.013542174 0.3100445
## 428 MO257 - MO288 -2.62546097 0.008653173 0.3764130
## 429 MO259 - MO288 -3.28182621 0.001031371 0.4486466
## 430 MO261 - MO288 -0.96110625 0.336498748 0.7584298
## 431 MO263 - MO288 -1.85188765 0.064041958 0.4643042
## 432 MO267 - MO288 -0.32036875 0.748688812 0.9358610
## 433 MO269 - MO288 -0.21878841 0.826814872 0.9720661
## 434 MO273 - MO288 -0.25785777 0.796516675 0.9518812
## 435 MO279 - MO288 -1.05487271 0.291483544 0.7329211
##
## **Dunn's Test (Post-hoc with Bonferroni correction):**## Dunn (1964) Kruskal-Wallis multiple comparison## p-values adjusted with the Bonferroni method.
## Comparison Z P.unadj P.adj
## 1 MO201 - MO202 1.78156280 0.074820555 1.0000000
## 2 MO201 - MO203 0.37506585 0.707611492 1.0000000
## 3 MO202 - MO203 -1.40649695 0.159576610 1.0000000
## 4 MO201 - MO204 0.68762073 0.491691650 1.0000000
## 5 MO202 - MO204 -1.09394207 0.273980385 1.0000000
## 6 MO203 - MO204 0.31255488 0.754618864 1.0000000
## 7 MO201 - MO221 1.81281829 0.069859852 1.0000000
## 8 MO202 - MO221 0.03125549 0.975065789 1.0000000
## 9 MO203 - MO221 1.43775244 0.150504309 1.0000000
## 10 MO204 - MO221 1.12519756 0.260505327 1.0000000
## 11 MO201 - MO222 2.14881478 0.031649085 1.0000000
## 12 MO202 - MO222 0.36725198 0.713431069 1.0000000
## 13 MO203 - MO222 1.77374893 0.076104689 1.0000000
## 14 MO204 - MO222 1.46119405 0.143962195 1.0000000
## 15 MO221 - MO222 0.33599649 0.736873511 1.0000000
## 16 MO201 - MO223 1.05487271 0.291483544 1.0000000
## 17 MO202 - MO223 -0.72669009 0.467415825 1.0000000
## 18 MO203 - MO223 0.67980686 0.496626763 1.0000000
## 19 MO204 - MO223 0.36725198 0.713431069 1.0000000
## 20 MO221 - MO223 -0.75794558 0.448483563 1.0000000
## 21 MO222 - MO223 -1.09394207 0.273980385 1.0000000
## 22 MO201 - MO224 1.96909573 0.048942099 1.0000000
## 23 MO202 - MO224 0.18753293 0.851242810 1.0000000
## 24 MO203 - MO224 1.59402988 0.110929344 1.0000000
## 25 MO204 - MO224 1.28147500 0.200026876 1.0000000
## 26 MO221 - MO224 0.15627744 0.875814339 1.0000000
## 27 MO222 - MO224 -0.17971905 0.857373134 1.0000000
## 28 MO223 - MO224 0.91422302 0.360599672 1.0000000
## 29 MO201 - MO230 2.75048292 0.005950749 1.0000000
## 30 MO202 - MO230 0.96892012 0.332585046 1.0000000
## 31 MO203 - MO230 2.37541707 0.017529131 1.0000000
## 32 MO204 - MO230 2.06286219 0.039125723 1.0000000
## 33 MO221 - MO230 0.93766463 0.348416785 1.0000000
## 34 MO222 - MO230 0.60166814 0.547395062 1.0000000
## 35 MO223 - MO230 1.69561021 0.089959723 1.0000000
## 36 MO224 - MO230 0.78138719 0.434574801 1.0000000
## 37 MO201 - MO232 0.89078140 0.373046455 1.0000000
## 38 MO202 - MO232 -0.89078140 0.373046455 1.0000000
## 39 MO203 - MO232 0.51571555 0.606053094 1.0000000
## 40 MO204 - MO232 0.20316067 0.839009452 1.0000000
## 41 MO221 - MO232 -0.92203689 0.356509334 1.0000000
## 42 MO222 - MO232 -1.25803338 0.208379684 1.0000000
## 43 MO223 - MO232 -0.16409131 0.869659262 1.0000000
## 44 MO224 - MO232 -1.07831433 0.280893505 1.0000000
## 45 MO230 - MO232 -1.85970152 0.062927767 1.0000000
## 46 MO201 - MO234 1.10956982 0.267184444 1.0000000
## 47 MO202 - MO234 -0.67199299 0.501588161 1.0000000
## 48 MO203 - MO234 0.73450396 0.462641646 1.0000000
## 49 MO204 - MO234 0.42194908 0.673062182 1.0000000
## 50 MO221 - MO234 -0.70324847 0.481900915 1.0000000
## 51 MO222 - MO234 -1.03924497 0.298690822 1.0000000
## 52 MO223 - MO234 0.05469710 0.956379777 1.0000000
## 53 MO224 - MO234 -0.85952591 0.390050430 1.0000000
## 54 MO230 - MO234 -1.64091311 0.100815454 1.0000000
## 55 MO232 - MO234 0.21878841 0.826814872 1.0000000
## 56 MO201 - MO236 1.35961372 0.173952195 1.0000000
## 57 MO202 - MO236 -0.42194908 0.673062182 1.0000000
## 58 MO203 - MO236 0.98454786 0.324846210 1.0000000
## 59 MO204 - MO236 0.67199299 0.501588161 1.0000000
## 60 MO221 - MO236 -0.45320457 0.650401440 1.0000000
## 61 MO222 - MO236 -0.78920107 0.429994499 1.0000000
## 62 MO223 - MO236 0.30474101 0.760563416 1.0000000
## 63 MO224 - MO236 -0.60948201 0.542204993 1.0000000
## 64 MO230 - MO236 -1.39086920 0.164265093 1.0000000
## 65 MO232 - MO236 0.46883232 0.639189499 1.0000000
## 66 MO234 - MO236 0.25004390 0.802553398 1.0000000
## 67 MO201 - MO237 1.23459177 0.216982475 1.0000000
## 68 MO202 - MO237 -0.54697104 0.584398631 1.0000000
## 69 MO203 - MO237 0.85952591 0.390050430 1.0000000
## 70 MO204 - MO237 0.54697104 0.584398631 1.0000000
## 71 MO221 - MO237 -0.57822652 0.563111194 1.0000000
## 72 MO222 - MO237 -0.91422302 0.360599672 1.0000000
## 73 MO223 - MO237 0.17971905 0.857373134 1.0000000
## 74 MO224 - MO237 -0.73450396 0.462641646 1.0000000
## 75 MO230 - MO237 -1.51589116 0.129546877 1.0000000
## 76 MO232 - MO237 0.34381037 0.730988905 1.0000000
## 77 MO234 - MO237 0.12502195 0.900506172 1.0000000
## 78 MO236 - MO237 -0.12502195 0.900506172 1.0000000
## 79 MO201 - MO238 1.59402988 0.110929344 1.0000000
## 80 MO202 - MO238 -0.18753293 0.851242810 1.0000000
## 81 MO203 - MO238 1.21896402 0.222857848 1.0000000
## 82 MO204 - MO238 0.90640914 0.364719334 1.0000000
## 83 MO221 - MO238 -0.21878841 0.826814872 1.0000000
## 84 MO222 - MO238 -0.55478491 0.579041791 1.0000000
## 85 MO223 - MO238 0.53915716 0.589778415 1.0000000
## 86 MO224 - MO238 -0.37506585 0.707611492 1.0000000
## 87 MO230 - MO238 -1.15645305 0.247495894 1.0000000
## 88 MO232 - MO238 0.70324847 0.481900915 1.0000000
## 89 MO234 - MO238 0.48446006 0.628059403 1.0000000
## 90 MO236 - MO238 0.23441616 0.814661916 1.0000000
## 91 MO237 - MO238 0.35943811 0.719267370 1.0000000
## 92 MO201 - MO239 1.17208079 0.241164621 1.0000000
## 93 MO202 - MO239 -0.60948201 0.542204993 1.0000000
## 94 MO203 - MO239 0.79701494 0.425442356 1.0000000
## 95 MO204 - MO239 0.48446006 0.628059403 1.0000000
## 96 MO221 - MO239 -0.64073750 0.521693246 1.0000000
## 97 MO222 - MO239 -0.97673399 0.328700862 1.0000000
## 98 MO223 - MO239 0.11720808 0.906695165 1.0000000
## 99 MO224 - MO239 -0.79701494 0.425442356 1.0000000
## 100 MO230 - MO239 -1.57840213 0.114473256 1.0000000
## 101 MO232 - MO239 0.28129939 0.778480778 1.0000000
## 102 MO234 - MO239 0.06251098 0.950155922 1.0000000
## 103 MO236 - MO239 -0.18753293 0.851242810 1.0000000
## 104 MO237 - MO239 -0.06251098 0.950155922 1.0000000
## 105 MO238 - MO239 -0.42194908 0.673062182 1.0000000
## 106 MO201 - MO240 1.20333628 0.228846216 1.0000000
## 107 MO202 - MO240 -0.57822652 0.563111194 1.0000000
## 108 MO203 - MO240 0.82827043 0.407517368 1.0000000
## 109 MO204 - MO240 0.51571555 0.606053094 1.0000000
## 110 MO221 - MO240 -0.60948201 0.542204993 1.0000000
## 111 MO222 - MO240 -0.94547850 0.344414640 1.0000000
## 112 MO223 - MO240 0.14846357 0.881976937 1.0000000
## 113 MO224 - MO240 -0.76575945 0.443819446 1.0000000
## 114 MO230 - MO240 -1.54714664 0.121827889 1.0000000
## 115 MO232 - MO240 0.31255488 0.754618864 1.0000000
## 116 MO234 - MO240 0.09376646 0.925294673 1.0000000
## 117 MO236 - MO240 -0.15627744 0.875814339 1.0000000
## 118 MO237 - MO240 -0.03125549 0.975065789 1.0000000
## 119 MO238 - MO240 -0.39069360 0.696023732 1.0000000
## 120 MO239 - MO240 0.03125549 0.975065789 1.0000000
## 121 MO201 - MO241 0.18753293 0.851242810 1.0000000
## 122 MO202 - MO241 -1.59402988 0.110929344 1.0000000
## 123 MO203 - MO241 -0.18753293 0.851242810 1.0000000
## 124 MO204 - MO241 -0.50008780 0.617013253 1.0000000
## 125 MO221 - MO241 -1.62528536 0.104101769 1.0000000
## 126 MO222 - MO241 -1.96128186 0.049846153 1.0000000
## 127 MO223 - MO241 -0.86733979 0.385755864 1.0000000
## 128 MO224 - MO241 -1.78156280 0.074820555 1.0000000
## 129 MO230 - MO241 -2.56295000 0.010378700 1.0000000
## 130 MO232 - MO241 -0.70324847 0.481900915 1.0000000
## 131 MO234 - MO241 -0.92203689 0.356509334 1.0000000
## 132 MO236 - MO241 -1.17208079 0.241164621 1.0000000
## 133 MO237 - MO241 -1.04705884 0.295072441 1.0000000
## 134 MO238 - MO241 -1.40649695 0.159576610 1.0000000
## 135 MO239 - MO241 -0.98454786 0.324846210 1.0000000
## 136 MO240 - MO241 -1.01580335 0.309723040 1.0000000
## 137 MO201 - MO242 0.90640914 0.364719334 1.0000000
## 138 MO202 - MO242 -0.87515366 0.381490305 1.0000000
## 139 MO203 - MO242 0.53134329 0.595180911 1.0000000
## 140 MO204 - MO242 0.21878841 0.826814872 1.0000000
## 141 MO221 - MO242 -0.90640914 0.364719334 1.0000000
## 142 MO222 - MO242 -1.24240564 0.214086936 1.0000000
## 143 MO223 - MO242 -0.14846357 0.881976937 1.0000000
## 144 MO224 - MO242 -1.06268658 0.287924107 1.0000000
## 145 MO230 - MO242 -1.84407378 0.065172389 1.0000000
## 146 MO232 - MO242 0.01562774 0.987531372 1.0000000
## 147 MO234 - MO242 -0.20316067 0.839009452 1.0000000
## 148 MO236 - MO242 -0.45320457 0.650401440 1.0000000
## 149 MO237 - MO242 -0.32818262 0.742773587 1.0000000
## 150 MO238 - MO242 -0.68762073 0.491691650 1.0000000
## 151 MO239 - MO242 -0.26567165 0.790492102 1.0000000
## 152 MO240 - MO242 -0.29692713 0.766522140 1.0000000
## 153 MO241 - MO242 0.71887622 0.472217191 1.0000000
## 154 MO201 - MO243 0.78920107 0.429994499 1.0000000
## 155 MO202 - MO243 -0.99236174 0.321021098 1.0000000
## 156 MO203 - MO243 0.41413521 0.678775086 1.0000000
## 157 MO204 - MO243 0.10158034 0.919089789 1.0000000
## 158 MO221 - MO243 -1.02361722 0.306016107 1.0000000
## 159 MO222 - MO243 -1.35961372 0.173952195 1.0000000
## 160 MO223 - MO243 -0.26567165 0.790492102 1.0000000
## 161 MO224 - MO243 -1.17989466 0.238042113 1.0000000
## 162 MO230 - MO243 -1.96128186 0.049846153 1.0000000
## 163 MO232 - MO243 -0.10158034 0.919089789 1.0000000
## 164 MO234 - MO243 -0.32036875 0.748688812 1.0000000
## 165 MO236 - MO243 -0.57041265 0.568397851 1.0000000
## 166 MO237 - MO243 -0.44539070 0.656037432 1.0000000
## 167 MO238 - MO243 -0.80482881 0.420918474 1.0000000
## 168 MO239 - MO243 -0.38287972 0.701808945 1.0000000
## 169 MO240 - MO243 -0.41413521 0.678775086 1.0000000
## 170 MO241 - MO243 0.60166814 0.547395062 1.0000000
## 171 MO242 - MO243 -0.11720808 0.906695165 1.0000000
## 172 MO201 - MO253 2.60983323 0.009058637 1.0000000
## 173 MO202 - MO253 0.82827043 0.407517368 1.0000000
## 174 MO203 - MO253 2.23476737 0.025432625 1.0000000
## 175 MO204 - MO253 1.92221250 0.054579025 1.0000000
## 176 MO221 - MO253 0.79701494 0.425442356 1.0000000
## 177 MO222 - MO253 0.46101844 0.644785372 1.0000000
## 178 MO223 - MO253 1.55496052 0.119955473 1.0000000
## 179 MO224 - MO253 0.64073750 0.521693246 1.0000000
## 180 MO230 - MO253 -0.14064969 0.888146688 1.0000000
## 181 MO232 - MO253 1.71905183 0.085604935 1.0000000
## 182 MO234 - MO253 1.50026341 0.133546183 1.0000000
## 183 MO236 - MO253 1.25021951 0.211219372 1.0000000
## 184 MO237 - MO253 1.37524146 0.169056598 1.0000000
## 185 MO238 - MO253 1.01580335 0.309723040 1.0000000
## 186 MO239 - MO253 1.43775244 0.150504309 1.0000000
## 187 MO240 - MO253 1.40649695 0.159576610 1.0000000
## 188 MO241 - MO253 2.42230030 0.015422600 1.0000000
## 189 MO242 - MO253 1.70342408 0.088488734 1.0000000
## 190 MO243 - MO253 1.82063216 0.068662791 1.0000000
## 191 MO201 - MO255 2.46918353 0.013542174 1.0000000
## 192 MO202 - MO255 0.68762073 0.491691650 1.0000000
## 193 MO203 - MO255 2.09411768 0.036249499 1.0000000
## 194 MO204 - MO255 1.78156280 0.074820555 1.0000000
## 195 MO221 - MO255 0.65636524 0.511589148 1.0000000
## 196 MO222 - MO255 0.32036875 0.748688812 1.0000000
## 197 MO223 - MO255 1.41431082 0.157270661 1.0000000
## 198 MO224 - MO255 0.50008780 0.617013253 1.0000000
## 199 MO230 - MO255 -0.28129939 0.778480778 1.0000000
## 200 MO232 - MO255 1.57840213 0.114473256 1.0000000
## 201 MO234 - MO255 1.35961372 0.173952195 1.0000000
## 202 MO236 - MO255 1.10956982 0.267184444 1.0000000
## 203 MO237 - MO255 1.23459177 0.216982475 1.0000000
## 204 MO238 - MO255 0.87515366 0.381490305 1.0000000
## 205 MO239 - MO255 1.29710274 0.194595838 1.0000000
## 206 MO240 - MO255 1.26584725 0.205567774 1.0000000
## 207 MO241 - MO255 2.28165061 0.022509976 1.0000000
## 208 MO242 - MO255 1.56277439 0.118105671 1.0000000
## 209 MO243 - MO255 1.67998247 0.092960727 1.0000000
## 210 MO253 - MO255 -0.14064969 0.888146688 1.0000000
## 211 MO201 - MO257 2.62546097 0.008653173 1.0000000
## 212 MO202 - MO257 0.84389817 0.398726311 1.0000000
## 213 MO203 - MO257 2.25039512 0.024423875 1.0000000
## 214 MO204 - MO257 1.93784024 0.052642717 1.0000000
## 215 MO221 - MO257 0.81264268 0.416422953 1.0000000
## 216 MO222 - MO257 0.47664619 0.633614088 1.0000000
## 217 MO223 - MO257 1.57058826 0.116278319 1.0000000
## 218 MO224 - MO257 0.65636524 0.511589148 1.0000000
## 219 MO230 - MO257 -0.12502195 0.900506172 1.0000000
## 220 MO232 - MO257 1.73467957 0.082797577 1.0000000
## 221 MO234 - MO257 1.51589116 0.129546877 1.0000000
## 222 MO236 - MO257 1.26584725 0.205567774 1.0000000
## 223 MO237 - MO257 1.39086920 0.164265093 1.0000000
## 224 MO238 - MO257 1.03143110 0.302338705 1.0000000
## 225 MO239 - MO257 1.45338018 0.146118226 1.0000000
## 226 MO240 - MO257 1.42212469 0.154990056 1.0000000
## 227 MO241 - MO257 2.43792804 0.014771714 1.0000000
## 228 MO242 - MO257 1.71905183 0.085604935 1.0000000
## 229 MO243 - MO257 1.83625991 0.066319227 1.0000000
## 230 MO253 - MO257 0.01562774 0.987531372 1.0000000
## 231 MO255 - MO257 0.15627744 0.875814339 1.0000000
## 232 MO201 - MO259 3.28182621 0.001031371 0.4486466
## 233 MO202 - MO259 1.50026341 0.133546183 1.0000000
## 234 MO203 - MO259 2.90676036 0.003651928 1.0000000
## 235 MO204 - MO259 2.59420548 0.009480980 1.0000000
## 236 MO221 - MO259 1.46900792 0.141830640 1.0000000
## 237 MO222 - MO259 1.13301143 0.257209453 1.0000000
## 238 MO223 - MO259 2.22695350 0.025950382 1.0000000
## 239 MO224 - MO259 1.31273049 0.189273781 1.0000000
## 240 MO230 - MO259 0.53134329 0.595180911 1.0000000
## 241 MO232 - MO259 2.39104481 0.016800502 1.0000000
## 242 MO234 - MO259 2.17225640 0.029836329 1.0000000
## 243 MO236 - MO259 1.92221250 0.054579025 1.0000000
## 244 MO237 - MO259 2.04723445 0.040635071 1.0000000
## 245 MO238 - MO259 1.68779634 0.091450331 1.0000000
## 246 MO239 - MO259 2.10974542 0.034880290 1.0000000
## 247 MO240 - MO259 2.07848994 0.037664257 1.0000000
## 248 MO241 - MO259 3.09429329 0.001972824 0.8581783
## 249 MO242 - MO259 2.37541707 0.017529131 1.0000000
## 250 MO243 - MO259 2.49262515 0.012680264 1.0000000
## 251 MO253 - MO259 0.67199299 0.501588161 1.0000000
## 252 MO255 - MO259 0.81264268 0.416422953 1.0000000
## 253 MO257 - MO259 0.65636524 0.511589148 1.0000000
## 254 MO201 - MO261 0.96110625 0.336498748 1.0000000
## 255 MO202 - MO261 -0.82045655 0.411955887 1.0000000
## 256 MO203 - MO261 0.58604040 0.557848369 1.0000000
## 257 MO204 - MO261 0.27348552 0.784480023 1.0000000
## 258 MO221 - MO261 -0.85171204 0.394373936 1.0000000
## 259 MO222 - MO261 -1.18770853 0.234948260 1.0000000
## 260 MO223 - MO261 -0.09376646 0.925294673 1.0000000
## 261 MO224 - MO261 -1.00798948 0.313459513 1.0000000
## 262 MO230 - MO261 -1.78937667 0.073554173 1.0000000
## 263 MO232 - MO261 0.07032485 0.943935106 1.0000000
## 264 MO234 - MO261 -0.14846357 0.881976937 1.0000000
## 265 MO236 - MO261 -0.39850747 0.690256154 1.0000000
## 266 MO237 - MO261 -0.27348552 0.784480023 1.0000000
## 267 MO238 - MO261 -0.63292363 0.526783518 1.0000000
## 268 MO239 - MO261 -0.21097454 0.832907137 1.0000000
## 269 MO240 - MO261 -0.24223003 0.808601927 1.0000000
## 270 MO241 - MO261 0.77357332 0.439183154 1.0000000
## 271 MO242 - MO261 0.05469710 0.956379777 1.0000000
## 272 MO243 - MO261 0.17190518 0.863512072 1.0000000
## 273 MO253 - MO261 -1.64872698 0.099203580 1.0000000
## 274 MO255 - MO261 -1.50807728 0.131534748 1.0000000
## 275 MO257 - MO261 -1.66435472 0.096041563 1.0000000
## 276 MO259 - MO261 -2.32071997 0.020301962 1.0000000
## 277 MO201 - MO263 1.85188765 0.064041958 1.0000000
## 278 MO202 - MO263 0.07032485 0.943935106 1.0000000
## 279 MO203 - MO263 1.47682180 0.139723412 1.0000000
## 280 MO204 - MO263 1.16426692 0.244315858 1.0000000
## 281 MO221 - MO263 0.03906936 0.968835090 1.0000000
## 282 MO222 - MO263 -0.29692713 0.766522140 1.0000000
## 283 MO223 - MO263 0.79701494 0.425442356 1.0000000
## 284 MO224 - MO263 -0.11720808 0.906695165 1.0000000
## 285 MO230 - MO263 -0.89859527 0.368868278 1.0000000
## 286 MO232 - MO263 0.96110625 0.336498748 1.0000000
## 287 MO234 - MO263 0.74231783 0.457894789 1.0000000
## 288 MO236 - MO263 0.49227393 0.622525706 1.0000000
## 289 MO237 - MO263 0.61729588 0.537039582 1.0000000
## 290 MO238 - MO263 0.25785777 0.796516675 1.0000000
## 291 MO239 - MO263 0.67980686 0.496626763 1.0000000
## 292 MO240 - MO263 0.64855137 0.516628396 1.0000000
## 293 MO241 - MO263 1.66435472 0.096041563 1.0000000
## 294 MO242 - MO263 0.94547850 0.344414640 1.0000000
## 295 MO243 - MO263 1.06268658 0.287924107 1.0000000
## 296 MO253 - MO263 -0.75794558 0.448483563 1.0000000
## 297 MO255 - MO263 -0.61729588 0.537039582 1.0000000
## 298 MO257 - MO263 -0.77357332 0.439183154 1.0000000
## 299 MO259 - MO263 -1.42993856 0.152734652 1.0000000
## 300 MO261 - MO263 0.89078140 0.373046455 1.0000000
## 301 MO201 - MO267 0.32036875 0.748688812 1.0000000
## 302 MO202 - MO267 -1.46119405 0.143962195 1.0000000
## 303 MO203 - MO267 -0.05469710 0.956379777 1.0000000
## 304 MO204 - MO267 -0.36725198 0.713431069 1.0000000
## 305 MO221 - MO267 -1.49244954 0.135581336 1.0000000
## 306 MO222 - MO267 -1.82844603 0.067482638 1.0000000
## 307 MO223 - MO267 -0.73450396 0.462641646 1.0000000
## 308 MO224 - MO267 -1.64872698 0.099203580 1.0000000
## 309 MO230 - MO267 -2.43011417 0.015094067 1.0000000
## 310 MO232 - MO267 -0.57041265 0.568397851 1.0000000
## 311 MO234 - MO267 -0.78920107 0.429994499 1.0000000
## 312 MO236 - MO267 -1.03924497 0.298690822 1.0000000
## 313 MO237 - MO267 -0.91422302 0.360599672 1.0000000
## 314 MO238 - MO267 -1.27366113 0.202783539 1.0000000
## 315 MO239 - MO267 -0.85171204 0.394373936 1.0000000
## 316 MO240 - MO267 -0.88296753 0.377253816 1.0000000
## 317 MO241 - MO267 0.13283582 0.894323223 1.0000000
## 318 MO242 - MO267 -0.58604040 0.557848369 1.0000000
## 319 MO243 - MO267 -0.46883232 0.639189499 1.0000000
## 320 MO253 - MO267 -2.28946448 0.022052380 1.0000000
## 321 MO255 - MO267 -2.14881478 0.031649085 1.0000000
## 322 MO257 - MO267 -2.30509222 0.021161409 1.0000000
## 323 MO259 - MO267 -2.96145746 0.003061868 1.0000000
## 324 MO261 - MO267 -0.64073750 0.521693246 1.0000000
## 325 MO263 - MO267 -1.53151890 0.125641199 1.0000000
## 326 MO201 - MO269 0.21878841 0.826814872 1.0000000
## 327 MO202 - MO269 -1.56277439 0.118105671 1.0000000
## 328 MO203 - MO269 -0.15627744 0.875814339 1.0000000
## 329 MO204 - MO269 -0.46883232 0.639189499 1.0000000
## 330 MO221 - MO269 -1.59402988 0.110929344 1.0000000
## 331 MO222 - MO269 -1.93002637 0.053603571 1.0000000
## 332 MO223 - MO269 -0.83608430 0.403107482 1.0000000
## 333 MO224 - MO269 -1.75030731 0.080065300 1.0000000
## 334 MO230 - MO269 -2.53169451 0.011351284 1.0000000
## 335 MO232 - MO269 -0.67199299 0.501588161 1.0000000
## 336 MO234 - MO269 -0.89078140 0.373046455 1.0000000
## 337 MO236 - MO269 -1.14082530 0.253942629 1.0000000
## 338 MO237 - MO269 -1.01580335 0.309723040 1.0000000
## 339 MO238 - MO269 -1.37524146 0.169056598 1.0000000
## 340 MO239 - MO269 -0.95329238 0.340441953 1.0000000
## 341 MO240 - MO269 -0.98454786 0.324846210 1.0000000
## 342 MO241 - MO269 0.03125549 0.975065789 1.0000000
## 343 MO242 - MO269 -0.68762073 0.491691650 1.0000000
## 344 MO243 - MO269 -0.57041265 0.568397851 1.0000000
## 345 MO253 - MO269 -2.39104481 0.016800502 1.0000000
## 346 MO255 - MO269 -2.25039512 0.024423875 1.0000000
## 347 MO257 - MO269 -2.40667256 0.016098597 1.0000000
## 348 MO259 - MO269 -3.06303780 0.002191024 0.9530954
## 349 MO261 - MO269 -0.74231783 0.457894789 1.0000000
## 350 MO263 - MO269 -1.63309924 0.102448127 1.0000000
## 351 MO267 - MO269 -0.10158034 0.919089789 1.0000000
## 352 MO201 - MO273 0.25785777 0.796516675 1.0000000
## 353 MO202 - MO273 -1.52370503 0.127582413 1.0000000
## 354 MO203 - MO273 -0.11720808 0.906695165 1.0000000
## 355 MO204 - MO273 -0.42976296 0.667368082 1.0000000
## 356 MO221 - MO273 -1.55496052 0.119955473 1.0000000
## 357 MO222 - MO273 -1.89095701 0.058630083 1.0000000
## 358 MO223 - MO273 -0.79701494 0.425442356 1.0000000
## 359 MO224 - MO273 -1.71123795 0.087037195 1.0000000
## 360 MO230 - MO273 -2.49262515 0.012680264 1.0000000
## 361 MO232 - MO273 -0.63292363 0.526783518 1.0000000
## 362 MO234 - MO273 -0.85171204 0.394373936 1.0000000
## 363 MO236 - MO273 -1.10175594 0.270567789 1.0000000
## 364 MO237 - MO273 -0.97673399 0.328700862 1.0000000
## 365 MO238 - MO273 -1.33617210 0.181493028 1.0000000
## 366 MO239 - MO273 -0.91422302 0.360599672 1.0000000
## 367 MO240 - MO273 -0.94547850 0.344414640 1.0000000
## 368 MO241 - MO273 0.07032485 0.943935106 1.0000000
## 369 MO242 - MO273 -0.64855137 0.516628396 1.0000000
## 370 MO243 - MO273 -0.53134329 0.595180911 1.0000000
## 371 MO253 - MO273 -2.35197545 0.018674007 1.0000000
## 372 MO255 - MO273 -2.21132576 0.027013287 1.0000000
## 373 MO257 - MO273 -2.36760320 0.017903726 1.0000000
## 374 MO259 - MO273 -3.02396844 0.002494825 1.0000000
## 375 MO261 - MO273 -0.70324847 0.481900915 1.0000000
## 376 MO263 - MO273 -1.59402988 0.110929344 1.0000000
## 377 MO267 - MO273 -0.06251098 0.950155922 1.0000000
## 378 MO269 - MO273 0.03906936 0.968835090 1.0000000
## 379 MO201 - MO279 1.05487271 0.291483544 1.0000000
## 380 MO202 - MO279 -0.72669009 0.467415825 1.0000000
## 381 MO203 - MO279 0.67980686 0.496626763 1.0000000
## 382 MO204 - MO279 0.36725198 0.713431069 1.0000000
## 383 MO221 - MO279 -0.75794558 0.448483563 1.0000000
## 384 MO222 - MO279 -1.09394207 0.273980385 1.0000000
## 385 MO223 - MO279 0.00000000 1.000000000 1.0000000
## 386 MO224 - MO279 -0.91422302 0.360599672 1.0000000
## 387 MO230 - MO279 -1.69561021 0.089959723 1.0000000
## 388 MO232 - MO279 0.16409131 0.869659262 1.0000000
## 389 MO234 - MO279 -0.05469710 0.956379777 1.0000000
## 390 MO236 - MO279 -0.30474101 0.760563416 1.0000000
## 391 MO237 - MO279 -0.17971905 0.857373134 1.0000000
## 392 MO238 - MO279 -0.53915716 0.589778415 1.0000000
## 393 MO239 - MO279 -0.11720808 0.906695165 1.0000000
## 394 MO240 - MO279 -0.14846357 0.881976937 1.0000000
## 395 MO241 - MO279 0.86733979 0.385755864 1.0000000
## 396 MO242 - MO279 0.14846357 0.881976937 1.0000000
## 397 MO243 - MO279 0.26567165 0.790492102 1.0000000
## 398 MO253 - MO279 -1.55496052 0.119955473 1.0000000
## 399 MO255 - MO279 -1.41431082 0.157270661 1.0000000
## 400 MO257 - MO279 -1.57058826 0.116278319 1.0000000
## 401 MO259 - MO279 -2.22695350 0.025950382 1.0000000
## 402 MO261 - MO279 0.09376646 0.925294673 1.0000000
## 403 MO263 - MO279 -0.79701494 0.425442356 1.0000000
## 404 MO267 - MO279 0.73450396 0.462641646 1.0000000
## 405 MO269 - MO279 0.83608430 0.403107482 1.0000000
## 406 MO273 - MO279 0.79701494 0.425442356 1.0000000
## 407 MO201 - MO288 0.00000000 1.000000000 1.0000000
## 408 MO202 - MO288 -1.78156280 0.074820555 1.0000000
## 409 MO203 - MO288 -0.37506585 0.707611492 1.0000000
## 410 MO204 - MO288 -0.68762073 0.491691650 1.0000000
## 411 MO221 - MO288 -1.81281829 0.069859852 1.0000000
## 412 MO222 - MO288 -2.14881478 0.031649085 1.0000000
## 413 MO223 - MO288 -1.05487271 0.291483544 1.0000000
## 414 MO224 - MO288 -1.96909573 0.048942099 1.0000000
## 415 MO230 - MO288 -2.75048292 0.005950749 1.0000000
## 416 MO232 - MO288 -0.89078140 0.373046455 1.0000000
## 417 MO234 - MO288 -1.10956982 0.267184444 1.0000000
## 418 MO236 - MO288 -1.35961372 0.173952195 1.0000000
## 419 MO237 - MO288 -1.23459177 0.216982475 1.0000000
## 420 MO238 - MO288 -1.59402988 0.110929344 1.0000000
## 421 MO239 - MO288 -1.17208079 0.241164621 1.0000000
## 422 MO240 - MO288 -1.20333628 0.228846216 1.0000000
## 423 MO241 - MO288 -0.18753293 0.851242810 1.0000000
## 424 MO242 - MO288 -0.90640914 0.364719334 1.0000000
## 425 MO243 - MO288 -0.78920107 0.429994499 1.0000000
## 426 MO253 - MO288 -2.60983323 0.009058637 1.0000000
## 427 MO255 - MO288 -2.46918353 0.013542174 1.0000000
## 428 MO257 - MO288 -2.62546097 0.008653173 1.0000000
## 429 MO259 - MO288 -3.28182621 0.001031371 0.4486466
## 430 MO261 - MO288 -0.96110625 0.336498748 1.0000000
## 431 MO263 - MO288 -1.85188765 0.064041958 1.0000000
## 432 MO267 - MO288 -0.32036875 0.748688812 1.0000000
## 433 MO269 - MO288 -0.21878841 0.826814872 1.0000000
## 434 MO273 - MO288 -0.25785777 0.796516675 1.0000000
## 435 MO279 - MO288 -1.05487271 0.291483544 1.0000000
##
##
## --- Analyzing Live_Pupa_Percentage ---
##
## **Performing ANOVA on original data:**
## Analysis of Variance Table
##
## Response: Live_Pupa_Percentage
## Df Sum Sq Mean Sq F value Pr(>F)
## Strain 29 19382 668.35 1.6709 0.04715 *
## Residuals 60 24000 400.00
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Eta-squared: 0.446778
## $statistics
## MSerror Df Mean CV MSD
## 400 60 78.44444 25.49575 64.27442
##
## $parameters
## test name.t ntr StudentizedRange alpha
## Tukey Strain 30 5.566328 0.05
##
## $means
## Live_Pupa_Percentage std r se Min Max Q25 Q50 Q75
## MO201 93.33333 11.54701 3 11.54701 80 100 90 100 100
## MO202 86.66667 23.09401 3 11.54701 60 100 80 100 100
## MO203 80.00000 20.00000 3 11.54701 60 100 70 80 90
## MO204 73.33333 11.54701 3 11.54701 60 80 70 80 80
## MO221 86.66667 11.54701 3 11.54701 80 100 80 80 90
## MO222 73.33333 30.55050 3 11.54701 40 100 60 80 90
## MO223 80.00000 34.64102 3 11.54701 40 100 70 100 100
## MO224 100.00000 0.00000 3 11.54701 100 100 100 100 100
## MO230 60.00000 0.00000 3 11.54701 60 60 60 60 60
## MO232 86.66667 11.54701 3 11.54701 80 100 80 80 90
## MO234 86.66667 11.54701 3 11.54701 80 100 80 80 90
## MO236 93.33333 11.54701 3 11.54701 80 100 90 100 100
## MO237 80.00000 0.00000 3 11.54701 80 80 80 80 80
## MO238 73.33333 11.54701 3 11.54701 60 80 70 80 80
## MO239 73.33333 30.55050 3 11.54701 40 100 60 80 90
## MO240 80.00000 20.00000 3 11.54701 60 100 70 80 90
## MO241 86.66667 11.54701 3 11.54701 80 100 80 80 90
## MO242 93.33333 11.54701 3 11.54701 80 100 90 100 100
## MO243 60.00000 34.64102 3 11.54701 40 100 40 40 70
## MO253 93.33333 11.54701 3 11.54701 80 100 90 100 100
## MO255 53.33333 30.55050 3 11.54701 20 80 40 60 70
## MO257 80.00000 20.00000 3 11.54701 60 100 70 80 90
## MO259 60.00000 20.00000 3 11.54701 40 80 50 60 70
## MO261 26.66667 30.55050 3 11.54701 0 60 10 20 40
## MO263 86.66667 11.54701 3 11.54701 80 100 80 80 90
## MO267 80.00000 34.64102 3 11.54701 40 100 70 100 100
## MO269 80.00000 0.00000 3 11.54701 80 80 80 80 80
## MO273 93.33333 11.54701 3 11.54701 80 100 90 100 100
## MO279 80.00000 20.00000 3 11.54701 60 100 70 80 90
## MO288 73.33333 23.09401 3 11.54701 60 100 60 60 80
##
## $comparison
## NULL
##
## $groups
## Live_Pupa_Percentage groups
## MO224 100.00000 a
## MO201 93.33333 a
## MO236 93.33333 a
## MO242 93.33333 a
## MO253 93.33333 a
## MO273 93.33333 a
## MO202 86.66667 ab
## MO221 86.66667 ab
## MO232 86.66667 ab
## MO234 86.66667 ab
## MO241 86.66667 ab
## MO263 86.66667 ab
## MO203 80.00000 ab
## MO223 80.00000 ab
## MO237 80.00000 ab
## MO240 80.00000 ab
## MO257 80.00000 ab
## MO267 80.00000 ab
## MO269 80.00000 ab
## MO279 80.00000 ab
## MO204 73.33333 ab
## MO222 73.33333 ab
## MO238 73.33333 ab
## MO239 73.33333 ab
## MO288 73.33333 ab
## MO230 60.00000 ab
## MO243 60.00000 ab
## MO259 60.00000 ab
## MO255 53.33333 ab
## MO261 26.66667 b
##
## attr(,"class")
## [1] "group"Technical Discussion Points and Considerations:
ANOVA Results: 1. F-statistic and P-value: If ANOVA is performed, examine the F-statistic and its associated p-value. A significant p-value (p < 0.05) indicates that there are statistically significant differences in the means of the trait across at least some of the strains. 2. Eta-squared: Interpret the eta-squared value as the proportion of variance in the trait that is explained by the Strain factor. A higher eta-squared indicates a stronger effect of strain on the trait.
Tukey’s HSD Test: 1. Pairwise Comparisons: If ANOVA is significant, examine the Tukey’s HSD results to identify which specific strain pairs have significantly different means for the trait. 2. Confidence Intervals: Look at the confidence intervals for the mean differences. If the interval doesn’t include zero, it indicates a significant difference. 3. Compact Letter Displays (CLDs): Use the CLDs to visually summarize the results of Tukey’s HSD, grouping strains that are not significantly different from each other.
Kruskal-Wallis Test: 1. Chi-squared Statistic and P-value: If the Kruskal-Wallis test is performed, examine the chi-squared statistic and its associated p-value. A significant p-value (p < 0.05) indicates that there are statistically significant differences in the medians of the trait across at least some of the strains. 2. Epsilon-squared: Interpret epsilon-squared as the proportion of variance in the ranked data that is explained by the Strain factor.
Dunn’s Test: 1. Pairwise Comparisons: If the Kruskal-Wallis test is significant, examine the Dunn’s test results to identify which specific strain pairs have significantly different medians for the trait. 2. Adjusted P-values: Focus on the adjusted p-values (either Benjamini-Hochberg or Bonferroni) to account for multiple comparisons and control the risk of Type I errors.
Multivariate Analysis
We’ll now explore the relationships among the traits and strains using multivariate techniques.
1. Principal Component Analysis (PCA): PCA helps us understand the main sources of variation in the data and visualize the relationships between individuals (silkworms) and variables (traits).
# Perform PCA
pca_result <- PCA(analysis_data, scale.unit = TRUE, graph = FALSE)
# Scree plot to visualize variance explained by each PC (with revised labels)
fviz_eig(pca_result, addlabels = TRUE, ylim = c(0, 50)) +
labs(x = "Principal Component", y = "Percentage of Explained Variance") 
# Define a color palette with at least 30 distinct colors
my_colors <- colorRampPalette(brewer.pal(8, "Dark2"))(30) # Generate 30 colors
# Separate plots for individuals and variables
fviz_pca_ind(pca_result, repel = TRUE,
col.ind = data$Strain, # Color individuals by strain
palette = my_colors, # Use the custom color palette
addEllipses = TRUE, ellipse.type = "confidence",
legend.title = "Strain",
title = "PCA - Individuals Plot")
fviz_pca_var(pca_result, repel = TRUE,
col.var = "contrib", gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
title = "PCA - Variables Plot")
Technical Discussion Points and Considerations:
Scree Plot: 1. Examine the proportion of variance explained by each principal component (PC). 2. Look for the “elbow” point where the explained variance starts to level off, indicating the number of PCs to retain for further analysis.
Individuals Plot: 1. Observe how the individual silkworms are distributed in the PCA space based on their trait values. 2. Look for clusters or patterns that might indicate similarities or differences between strains. 3. Consider the implications of the positioning of individuals relative to the PC axes and the ellipses representing strain confidence intervals.
Variables Plot: 1. Interpret the contribution of each trait to the principal components. 2. Arrows pointing in the same direction suggest positive correlations between traits, while arrows pointing in opposite directions suggest negative correlations. 3. The length of the arrow represents the strength of the contribution.
2. Hierarchical Clustering on Principal Components: We’ll perform hierarchical clustering on the first few principal components to group similar individuals together.
# Extract the principal components
pca_coords <- pca_result$ind$coord
# Perform hierarchical clustering
hc_result <- hclust(dist(pca_coords[, 1:3]), method = "ward.D2")
# Visualize the dendrogram (with vertical labels)
plot(hc_result, hang = -1, main = "Hierarchical Clustering on PCs",
xlab = "", sub = "",
labels = FALSE) # Remove default labels
# Add vertical labels (adjusted y position and margin)
par(mar = c(5, 4, 4, 8) + 0.1) # Increase right margin for labels
text(x = 1:nrow(pca_coords),
y = rep(-0.2, nrow(pca_coords)), # Set all labels at the same y position
labels = rownames(pca_coords),
srt = 90, adj = 1, xpd = TRUE)
Technical Discussion Points and Considerations:
- Examine the branching pattern of the dendrogram to understand how individuals are grouped based on their similarity in the PCA space.
- The height of the branches represents the dissimilarity between clusters.
- Look for clusters that correspond to specific strains or groups of strains, providing insights into phenotypic relationships.
3. K-means Clustering: K-means clustering will partition the individuals into a predefined number of clusters based on their principal component scores.
# Determine optimal number of clusters (Elbow method)
set.seed(123)
wss <- fviz_nbclust(pca_coords, kmeans, method = "wss")
# Perform k-means clustering
k <- 3 # Adjust based on the elbow plot
kmeans_result <- kmeans(pca_coords, centers = k, nstart = 25)
# Visualize clusters
fviz_cluster(kmeans_result, data = pca_coords, geom = "point", ellipse.type = "convex",
ggtheme = theme_minimal(),
main = "K-means Clustering on PCs")
# Calculate silhouette score
library(cluster) # Load the cluster library for silhouette analysis
sil <- silhouette(kmeans_result$cluster, dist(pca_coords))
fviz_silhouette(sil)## cluster size ave.sil.width
## 1 1 39 0.13
## 2 2 48 0.36
## 3 3 3 0.03
Technical Discussion Points and Considerations:
Elbow Plot: 1. Use the elbow plot to help determine the optimal number of clusters (k) for k-means clustering. 2. Look for the point where the within-cluster sum of squares (WSS) starts to level off, indicating diminishing returns from adding more clusters.
Cluster Plot: 1. Observe how the individuals are partitioned into clusters in the PCA space. 2. Interpret the meaning of each cluster in terms of the phenotypic traits and strains. 3. Consider the separation between clusters and the tightness within clusters.
Correlation Analysis
We will explore the relationships between the phenotypic traits using both Pearson and Spearman correlation coefficients.
1. Correlation Matrices and Correlograms:
# Calculate Pearson and Spearman correlation matrices
cor_pearson <- cor(analysis_data, method = "pearson")
cor_spearman <- cor(analysis_data, method = "spearman")
# Visualize correlograms
corrplot(cor_pearson, method = "color", type = "upper", order = "hclust",
tl.col = "black", tl.srt = 45, sig.level = 0.05, title = "Pearson Correlation",
mar = c(0, 0, 2, 0)) # Add top margin for title)
# Create heatmap of Pearson correlations (with adjusted label size)
heatmap(cor_pearson, Rowv = NA, Colv = NA, col = colorRampPalette(c("blue", "white", "red"))(20),
scale = "none", margins = c(5, 10), cexRow = 0.6, cexCol = 0.6) # Reduce font size of trait names further
corrplot(cor_spearman, method = "color", type = "upper", order = "hclust",
tl.col = "black", tl.srt = 45, sig.level = 0.05, title = "Spearman Correlation",
mar = c(0, 0, 2, 0)) # Add top margin for title)
# Create heatmap of Spearman correlations (with adjusted label size)
heatmap(cor_spearman, Rowv = NA, Colv = NA, col = colorRampPalette(c("blue", "white", "red"))(20),
scale = "none", margins = c(5, 10), cexRow = 0.6, cexCol = 0.6)
# Partial Correlation Analysis
for (i in 1:(length(traits) - 2)) {
for (j in (i + 1):(length(traits) - 1)) {
for (k in (j + 1):length(traits)) {
trait1 <- traits[i]
trait2 <- traits[j]
trait3 <- traits[k] # Controlling variable
# Calculate partial correlation
partial_cor <- pcor.test(data[[trait1]], data[[trait2]], data[[trait3]])
cat("\n\nPartial Correlation between", trait1, "and", trait2,
"controlling for", trait3, ":\n")
cat(" Correlation Coefficient:", partial_cor$estimate, "\n")
cat(" P-value:", partial_cor$p.value, "\n")
}
}
}##
##
## Partial Correlation between Hatching_Percentage and Larval_Weight controlling for Single_Cocoon_Weight :
## Correlation Coefficient: -0.03823062
## P-value: 0.7220664
##
##
## Partial Correlation between Hatching_Percentage and Larval_Weight controlling for Cocoon_Shell_Weight :
## Correlation Coefficient: 0.08398262
## P-value: 0.4339361
##
##
## Partial Correlation between Hatching_Percentage and Larval_Weight controlling for Cocoon_Shell_Percentage :
## Correlation Coefficient: 0.1263566
## P-value: 0.2380277
##
##
## Partial Correlation between Hatching_Percentage and Larval_Weight controlling for Live_Pupa_Percentage :
## Correlation Coefficient: 0.0361241
## P-value: 0.7368059
##
##
## Partial Correlation between Hatching_Percentage and Single_Cocoon_Weight controlling for Cocoon_Shell_Weight :
## Correlation Coefficient: 0.1929467
## P-value: 0.07005009
##
##
## Partial Correlation between Hatching_Percentage and Single_Cocoon_Weight controlling for Cocoon_Shell_Percentage :
## Correlation Coefficient: 0.1445977
## P-value: 0.1763864
##
##
## Partial Correlation between Hatching_Percentage and Single_Cocoon_Weight controlling for Live_Pupa_Percentage :
## Correlation Coefficient: 0.109231
## P-value: 0.3082178
##
##
## Partial Correlation between Hatching_Percentage and Cocoon_Shell_Weight controlling for Cocoon_Shell_Percentage :
## Correlation Coefficient: 0.2014343
## P-value: 0.05836915
##
##
## Partial Correlation between Hatching_Percentage and Cocoon_Shell_Weight controlling for Live_Pupa_Percentage :
## Correlation Coefficient: -0.01367728
## P-value: 0.8987718
##
##
## Partial Correlation between Hatching_Percentage and Cocoon_Shell_Percentage controlling for Live_Pupa_Percentage :
## Correlation Coefficient: -0.1693143
## P-value: 0.1126933
##
##
## Partial Correlation between Larval_Weight and Single_Cocoon_Weight controlling for Cocoon_Shell_Weight :
## Correlation Coefficient: 0.528226
## P-value: 1.037243e-07
##
##
## Partial Correlation between Larval_Weight and Single_Cocoon_Weight controlling for Cocoon_Shell_Percentage :
## Correlation Coefficient: 0.7839878
## P-value: 1.044649e-19
##
##
## Partial Correlation between Larval_Weight and Single_Cocoon_Weight controlling for Live_Pupa_Percentage :
## Correlation Coefficient: 0.6738436
## P-value: 4.595282e-13
##
##
## Partial Correlation between Larval_Weight and Cocoon_Shell_Weight controlling for Cocoon_Shell_Percentage :
## Correlation Coefficient: 0.734609
## P-value: 2.541697e-16
##
##
## Partial Correlation between Larval_Weight and Cocoon_Shell_Weight controlling for Live_Pupa_Percentage :
## Correlation Coefficient: 0.6156631
## P-value: 1.355692e-10
##
##
## Partial Correlation between Larval_Weight and Cocoon_Shell_Percentage controlling for Live_Pupa_Percentage :
## Correlation Coefficient: 0.0512551
## P-value: 0.6333495
##
##
## Partial Correlation between Single_Cocoon_Weight and Cocoon_Shell_Weight controlling for Cocoon_Shell_Percentage :
## Correlation Coefficient: 0.9553125
## P-value: 7.967362e-48
##
##
## Partial Correlation between Single_Cocoon_Weight and Cocoon_Shell_Weight controlling for Live_Pupa_Percentage :
## Correlation Coefficient: 0.5311511
## P-value: 8.556171e-08
##
##
## Partial Correlation between Single_Cocoon_Weight and Cocoon_Shell_Percentage controlling for Live_Pupa_Percentage :
## Correlation Coefficient: -0.3898179
## P-value: 0.000159319
##
##
## Partial Correlation between Cocoon_Shell_Weight and Cocoon_Shell_Percentage controlling for Live_Pupa_Percentage :
## Correlation Coefficient: 0.534102
## P-value: 7.032948e-08Technical Discussion Points and Considerations:
Correlation Matrices (Pearson and Spearman): 1. Correlation Coefficients: Examine the strength and direction of the correlations between traits. 2. P-values: Assess the statistical significance of the correlations. 3. Comparison: Compare the Pearson and Spearman correlations to see if there are any notable differences, which might indicate non-linear relationships between traits.
Correlograms: 1. Visual Patterns: Observe the overall patterns in the correlograms. 2. Clusters: Identify clusters of traits that are highly correlated with each other. 3. Potential Multicollinearity: Be mindful of strong correlations between multiple traits, as this might indicate multicollinearity, which can affect the interpretation of regression or other multivariate analyses.
2. Individual Correlation Tests and Scatterplots: We will visualize and test the correlations between specific pairs of traits.
# Function to perform correlation test and plot
plot_correlation <- function(trait1, trait2, method = "pearson") {
cor_test <- cor.test(data[[trait1]], data[[trait2]], method = method)
p_value <- cor_test$p.value
cor_coef <- cor_test$estimate
ggplot(data, aes_string(x = trait1, y = trait2)) +
geom_point() +
geom_smooth(method = "lm", se = FALSE, color = "red") +
labs(title = paste("Correlation between", trait1, "and", trait2),
subtitle = paste(method, "correlation:", round(cor_coef, 3), ", p-value:", round(p_value, 5)))
}
# Example usage (adjust trait names as needed)
plot_correlation("Hatching_Percentage", "Larval_Weight")## `geom_smooth()` using formula = 'y ~ x'
plot_correlation("Hatching_Percentage", "Larval_Weight", method = "spearman")## `geom_smooth()` using formula = 'y ~ x'
Technical Discussion Points and Considerations:
- Scatterplots: Visually inspect the scatterplots to assess the linearity or monotonicity of the relationships between trait pairs.
- Correlation Coefficients and P-values: Interpret the correlation coefficients and p-values to quantify the strength and significance of the relationships.
3. Scatterplot Matrix: Visualize all pairwise relationships between traits using a scatterplot matrix.
# Scatterplot matrix with Pearson correlations (with adjusted label size and margin)
ggpairs(analysis_data, upper = list(continuous = wrap("cor", method = "pearson", size = 3))) + # Reduce cor font size
theme(axis.text = element_text(size = 8)) +
theme(plot.margin = margin(5, 10, 5, 5)) # Adjust margins as needed
# Scatterplot matrix with Spearman correlations (with adjusted label size and margin)
ggpairs(analysis_data, upper = list(continuous = wrap("cor", method = "spearman", size = 3))) +
theme(axis.text = element_text(size = 8)) +
theme(plot.margin = margin(5, 10, 5, 5)) 
Technical Discussion Points and Considerations:
- Overall Patterns: Gain a comprehensive overview of the pairwise relationships between all traits.
- Outliers: Identify any potential outliers that might be influencing the correlations.
- Non-linear Relationships: Look for any patterns in the scatterplots that suggest non-linear relationships between traits.
4. Heatmap of Trait Values by Strain:
# Create a copy of the original data for the heatmap
heatmap_data <- data
# Apply transformations to the relevant traits within heatmap_data
for (trait in non_parametric_traits) {
if (exists("transformed_data") && trait %in% names(transformed_data)) {
heatmap_data[[trait]] <- transformed_data[[trait]]
}
}
# Reshape data for heatmap (keep rows with missing values)
heatmap_data <- heatmap_data %>%
pivot_longer(cols = traits, names_to = "Trait", values_to = "Value", values_drop_na = FALSE)
# Convert 'Strain' and 'Trait' to factors to ensure all levels are included
heatmap_data$Strain <- factor(heatmap_data$Strain, levels = levels(data$Strain))
heatmap_data$Trait <- factor(heatmap_data$Trait, levels = traits)
# Create heatmap (handle missing values with na.value)
ggplot(heatmap_data, aes(x = Strain, y = Trait, fill = Value)) +
geom_tile() +
scale_fill_gradient(low = "lightblue", high = "steelblue", na.value = "grey90") + # Set color for missing values
labs(title = "Heatmap of Trait Values by Strain") +
theme_minimal() +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
CONCLUSION
This comprehensive analysis has provided insights into the distribution, relationships, and differences in silkworm phenotypic traits across various strains. We’ve addressed issues of non-normality and heteroscedasticity using transformations and non-parametric tests where appropriate. Multivariate techniques like PCA and clustering helped uncover underlying patterns in the data, while correlation analysis revealed the interdependencies between traits. These findings can guide further research and breeding efforts in silkworms.
Remember:
Interpret the results in the context of your specific research questions and biological knowledge. Consider exploring additional analyses or visualizations to gain further insights into your data. Clearly document your findings and conclusions, highlighting the key takeaways and their implications.
Note that the echo = FALSE parameter was added to the
code chunk to prevent printing of the R code that generated the
plot.
R TO PYTHON CONVERSION
**Installation of necessary Python libraries:**
pip install pandas numpy matplotlib seaborn scipy statsmodels pingouin scikit-learn yellowbrick factor_analyzer
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import
shapiro, levene, pearsonr, spearmanr
from statsmodels.formula.api import ols
from statsmodels.stats.anova import anova_lm
from statsmodels.stats.multicomp import pairwise_tukeyhsd
from pingouin import dunn
from sklearn.decomposition import PCA
from sklearn.preprocessing import StandardScaler
from sklearn.cluster import AgglomerativeClustering,
KMeans
from scipy.cluster.hierarchy import dendrogram, linkage
from yellowbrick.cluster import KElbowVisualizer
from statsmodels.stats.outliers_influence import variance_inflation_factor
from factor_analyzer import FactorAnalyzer
**Load the data:**
data = pd.read_excel("Hatching_percentage.xls")
**Pre-process the 'Strain' column:**
data['Strain'] = data['Strain'].astype(str).str.split(" - ", expand=True)[1]
data['Strain'] = data['Strain'].astype('category')
**List of traits to analyze:**
traits = ["Hatching_Percentage", "Larval_Weight", "Single_Cocoon_Weight",
"Cocoon_Shell_Weight", "Cocoon_Shell_Percentage", "Live_Pupa_Percentage"]
**Traits for transformation and potential non-parametric tests:**
non_parametric_traits = ["Hatching_Percentage", "Cocoon_Shell_Percentage", "Live_Pupa_Percentage"]
**Function to visualize model diagnostics:**
def check_model(model):
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10, 8))
# Residuals vs Fitted
sns.residplot(x=model.fittedvalues, y=model.resid, ax=axes[0, 0])
axes[0, 0].set_xlabel("Fitted values")
axes[0, 0].set_ylabel("Residuals")
axes[0, 0].set_title("Residuals vs Fitted")
# Normal Q-Q
import statsmodels.api as sm
sm.qqplot(model.resid, line='s', ax=axes[0, 1])
axes[0, 1].set_title("Normal Q-Q")
# Scale-Location
sns.scatterplot(x=model.fittedvalues, y=np.sqrt(np.abs(model.resid)), ax=axes[1, 0])
axes[1, 0].set_xlabel("Fitted values")
axes[1, 0].set_ylabel("√|Standardized residuals|")
axes[1, 0].set_title("Scale-Location")
# Residuals vs Leverage
sm.graphics.influence_plot(model, ax=axes[1, 1], criterion="cooks")
axes[1, 1].set_title("Residuals vs Leverage")
plt.tight_layout()
plt.show()
**Loop through each trait:**
for trait in traits:
print("\n--- Analyzing", trait, "---\n")
# Fit a temporary linear model to check assumptions
formula = f"{trait} ~ Strain"
model = ols(formula, data=data).fit()
# Boxplot with outliers
print("\nBoxplot for", trait, ":\n")
sns.boxplot(x="Strain", y=trait, data=data, showmeans=True)
plt.xticks(rotation=45)
plt.title(f"Boxplot of {trait} by Strain")
plt.show()
# Outlier Detection and Treatment (using Tukey's fences)
Q1 = data[trait].quantile(0.25)
Q3 = data[trait].quantile(0.75)
IQR = Q3 - Q1
lower_bound = Q1 - 1.5 * IQR
upper_bound = Q3 + 1.5 * IQR
outliers = data[(data[trait] < lower_bound) | (data[trait] > upper_bound)][["Strain", trait]]
if not outliers.empty:
print("\nOutliers for", trait, ":\n")
print(outliers)
else:
print("\nNo outliers found for", trait, "\n")
# Normality test (Shapiro-Wilk)
normality_test = shapiro(model.resid)
print("\nNormality Test (Shapiro-Wilk):\n")
print(f"Statistic: {normality_test.statistic}, p-value: {normality_test.pvalue}\n")
# Homogeneity of variance test (Levene's)
variance_test = levene(data[trait], data['Strain'])
print("\nHomogeneity of Variance Test (Levene's):\n")
print(f"Statistic: {variance_test.statistic}, p-value: {variance_test.pvalue}\n")
# Distribution plots with strain labels on individual plots
print("\nDistribution Plots for", trait, ":\n")
# Combined distribution plot
sns.displot(data[trait], kind="kde", fill=True)
plt.title(f"Distribution of {trait} (All Strains)")
plt.show()
# Distribution plots by strain (one plot per strain)
g = sns.FacetGrid(data, col="Strain", col_wrap=6, height=3)
g.map(sns.kdeplot, trait, fill=True)
g.set_titles(col_template="{col_name}")
plt.show()
## ANOVA, Transformation, and Non-Parametric Testing
**Subset the data for multivariate and correlation analyses (excluding "Replicate"):**
analysis_data = data.select_dtypes(include=np.number).drop(columns=["Replicate"])
**Loop through each trait:**
for trait in traits:
print(f"\n\n--- Analyzing {trait} ---\n")
# Fit the linear model
formula = f"{trait} ~ Strain"
model = ols(formula, data=data).fit()
check_model(model) # Check model assumptions
# Check for non-normality or heteroscedasticity
normality_p_value = shapiro(model.resid).pvalue
homogeneity_p_value = levene(data[trait], data['Strain']).pvalue
if normality_p_value >= 0.05 and homogeneity_p_value >= 0.05:
# Perform ANOVA directly on original data if both assumptions are met
print("\n**Performing ANOVA on original data:**\n")
anova_result = anova_lm(model, typ=2) # Type 2 ANOVA
print(anova_result)
# Calculate and print eta-squared
eta_squared = anova_result['sum_sq'][0] / anova_result['sum_sq'].sum()
print("Eta-squared:", eta_squared, "\n")
# Tukey's HSD if ANOVA is significant
if anova_result['PR(>F)'][0] < 0.05:
tukey_result = pairwise_tukeyhsd(data[trait], data['Strain'])
print(tukey_result)
else:
print("\nANOVA not significant. No post-hoc test needed.\n")
else:
# Attempt log transformation if at least one assumption is not met
print("\n**Attempting log transformation...**\n")
transformed_data = data.copy()
transformed_data[trait] = np.log1p(transformed_data[trait])
transformed_model = ols(formula, data=transformed_data).fit()
check_model(transformed_model)
# Re-check assumptions after transformation
normality_p_value = shapiro(transformed_model.resid).pvalue
homogeneity_p_value = levene(transformed_data[trait], transformed_data['Strain']).pvalue
# Print the results of assumption checks after transformation
print("\nAssumption Checks after Transformation:\n")
print(f" Normality (Shapiro-Wilk) p-value: {normality_p_value}\n")
print(f" Homogeneity of Variance (Levene's) p-value: {homogeneity_p_value}\n")
if normality_p_value >= 0.05 and homogeneity_p_value >= 0.05:
# Use ANOVA on transformed data if both assumptions are now met
print("\n**Performing ANOVA on transformed data:**\n")
anova_result = anova_lm(transformed_model, typ=2)
print(anova_result)
# Tukey's HSD if ANOVA is significant
if anova_result['PR(>F)'][0] < 0.05:
tukey_result = pairwise_tukeyhsd(transformed_data[trait], transformed_data['Strain'])
print(tukey_result)
else:
print("\nANOVA not significant. No post-hoc test needed.\n")
else:
# Use Kruskal-Wallis if at least one assumption is still violated after transformation
print("\n**Performing Kruskal-Wallis test:**\n")
from scipy.stats import kruskal
kruskal_result = kruskal(*[group[trait].values for name, group in data.groupby("Strain")])
print(f"Statistic: {kruskal_result.statistic}, p-value: {kruskal_result.pvalue}\n")
# Calculate and print epsilon-squared (effect size for Kruskal-Wallis)
k = data['Strain'].nunique() # Number of groups
n = len(data) # Total number of observations
epsilon_squared = (kruskal_result.statistic - (k - 1)) / (n - k)
print("Epsilon-squared:", epsilon_squared, "\n")
# Dunn's Test if Kruskal-Wallis is significant
if kruskal_result.pvalue < 0.05:
print("\n**Dunn's Test (Post-hoc with Benjamini-Hochberg correction):**\n")
dunn_result = dunn(*[group[trait].values for name, group in data.groupby("Strain")], method='bh')
print(dunn_result)
print("\n**Dunn's Test (Post-hoc with Bonferroni correction):**\n")
dunn_result_bonferroni = dunn(*[group[trait].values for name, group in data.groupby("Strain")], method='bonferroni')
print(dunn_result_bonferroni)
## Multivariate Analysis
**1. Principal Component Analysis (PCA):**
*Perform PCA*
scaler = StandardScaler()
scaled_data = scaler.fit_transform(analysis_data)
pca = PCA()
pca_result = pca.fit_transform(scaled_data)
*Scree plot to visualize variance explained by each PC*
plt.figure(figsize=(8, 6))
plt.plot(np.arange(1, len(pca.explained_variance_ratio_) + 1), pca.explained_variance_ratio_ * 100, marker='o')
plt.xlabel("Principal Component")
plt.ylabel("Percentage of Explained Variance")
plt.title("Scree Plot")
plt.ylim(0, 50) # Adjust y-axis limits if needed
plt.xticks(np.arange(1, len(pca.explained_variance_ratio_) + 1))
for i, var in enumerate(pca.explained_variance_ratio_ * 100):
plt.annotate(f"{var:.1f}%", (i + 1, var + 1))
plt.show()
*Biplot (Individuals and Variables)*
plt.figure(figsize=(10, 8))
for i, strain in enumerate(data['Strain'].unique()):
plt.scatter(pca_result[data['Strain'] == strain, 0], pca_result[data['Strain'] == strain, 1], label=strain)
*Add ellipses for each strain*
from matplotlib.patches import Ellipse
for i, strain in enumerate(data['Strain'].unique()):
strain_data = pca_result[data['Strain'] == strain, :2]
cov = np.cov(strain_data, rowvar=False)
lambda_, v = np.linalg.eig(cov)
ellipse = Ellipse(xy=strain_data.mean(axis=0), width=lambda_[0]*2, height=lambda_[1]*2,
angle=np.rad2deg(np.arccos(v[0, 0])), alpha=0.5)
plt.gca().add_artist(ellipse)
*Add variable loadings as arrows*
for i, col in enumerate(analysis_data.columns):
plt.arrow(0, 0, pca.components_[0, i]*3, pca.components_[1, i]*3,
color='r', alpha=0.5, head_width=0.1)
plt.text(pca.components_[0, i]*3.2, pca.components_[1, i]*3.2, col, color='r', ha='center', va='center')
plt.xlabel("PC1")
plt.ylabel("PC2")
plt.title("PCA Biplot")
plt.legend()
plt.grid(True)
plt.show()
**2. Hierarchical Clustering on Principal Components:**
*Perform hierarchical clustering (using first 3 PCs)*
hc = AgglomerativeClustering(n_clusters=None, distance_threshold=0, linkage='ward')
hc_result = hc.fit(pca_result[:, :3])
*Visualize the dendrogram*
plt.figure(figsize=(10, 7))
dendrogram(linkage(pca_result[:, :3], method='ward'),
orientation='top',
labels=data.index,
distance_sort='descending',
show_leaf_counts=True)
plt.title("Hierarchical Clustering on PCs")
plt.xlabel("Samples")
plt.ylabel("Distance")
plt.show()
**3. K-means Clustering:**
*Determine optimal number of clusters (Elbow method)**
visualizer = KElbowVisualizer(KMeans(), k=(1,10))
visualizer.fit(pca_result)
visualizer.show()
*Perform k-means clustering*
k = 3 # Adjust based on the elbow plot
kmeans = KMeans(n_clusters=k, random_state=123)
kmeans_result = kmeans.fit_predict(pca_result)
*Visualize clusters*
plt.figure(figsize=(8, 6))
plt.scatter(pca_result[:, 0], pca_result[:, 1], c=kmeans_result, cmap='viridis')
plt.xlabel("PC1")
plt.ylabel("PC2")
plt.title("K-means Clustering on PCs")
plt.show()
*Calculate silhouette score*
from sklearn.metrics import silhouette_score
silhouette_avg = silhouette_score(pca_result, kmeans_result)
print(f"Silhouette Score: {silhouette_avg}")
## Correlation Analysis
**1. Correlation Matrices and Correlograms:**
*Calculate Pearson and Spearman correlation matrices*
cor_pearson = analysis_data.corr(method='pearson')
cor_spearman = analysis_data.corr(method='spearman')
*Visualize correlograms*
plt.figure(figsize=(10, 8))
sns.heatmap(cor_pearson, annot=True, cmap='coolwarm', fmt=".2f", linewidths=.5)
plt.title("Pearson Correlation")
plt.show()
plt.figure(figsize=(10, 8))
sns.heatmap(cor_spearman, annot=True, cmap='coolwarm', fmt=".2f", linewidths=.5)
plt.title("Spearman Correlation")
plt.show()
*Partial Correlation Analysis (using pingouin)*
from pingouin import partial_corr
for i in range(len(traits) - 2):
for j in range(i + 1, len(traits) - 1):
for k in range(j + 1, len(traits)):
trait1 = traits[i]
trait2 = traits[j]
trait3 = traits[k] # Controlling variable
# Calculate partial correlation
partial_cor = partial_corr(data=data, x=trait1, y=trait2, covar=trait3, method='pearson')
print(f"\n\nPartial Correlation between {trait1} and {trait2}, controlling for {trait3}:\n")
print(f" Correlation Coefficient: {partial_cor['r'].values[0]}")
print(f" P-value: {partial_cor['p-val'].values[0]}\n")
**2. Individual Correlation Tests and Scatterplots:**
*Function to perform correlation test and plot*
def plot_correlation(trait1, trait2, method="pearson"):
if method == "pearson":
corr_coef, p_value = pearsonr(data[trait1], data[trait2])
elif method == "spearman":
corr_coef, p_value = spearmanr(data[trait1], data[trait2])
else:
raise ValueError("Invalid method. Choose 'pearson' or 'spearman'.")
sns.scatterplot(x=trait1, y=trait2, data=data)
sns.regplot(x=trait1, y=trait2, data=data, scatter=False, color='red')
plt.title(f"Correlation between {trait1} and {trait2}\n{method} correlation: {corr_coef:.3f}, p-value: {p_value:.5f}")
plt.show()
*Example usage*
plot_correlation("Hatching_Percentage", "Larval_Weight")
plot_correlation("Hatching_Percentage", "Larval_Weight", method="spearman")
**3. Scatterplot Matrix:**
*Scatterplot matrix with Pearson correlations*
sns.pairplot(analysis_data)
plt.suptitle("Scatterplot Matrix with Pearson Correlations", y=1.02)
plt.show()
*Scatterplot matrix with Spearman correlations*
#You'll need to adapt this if you want to display Spearman correlations directly on the plots
sns.pairplot(analysis_data)
plt.suptitle("Scatterplot Matrix (Spearman correlations can be calculated separately)", y=1.02)
plt.show()
**4. Heatmap of Trait Values by Strain:**
*Create a copy of the original data for the heatmap*
heatmap_data = data.copy()
*Apply transformations to the relevant traits within heatmap_data*
for trait in non_parametric_traits:
if 'transformed_data' in locals() and trait in transformed_data.columns:
heatmap_data[trait] = transformed_data[trait]
*Reshape data for heatmap (keep rows with missing values)*
heatmap_data = heatmap_data.melt(id_vars=["Strain"], value_vars=traits, var_name="Trait", value_name="Value")
*Create heatmap (handle missing values with na.value)*
plt.figure(figsize=(12, 8))
sns.heatmap(heatmap_data.pivot("Trait", "Strain", "Value"), cmap="Blues", annot=True, fmt=".2f")
plt.title("Heatmap of Trait Values by Strain")
plt.show()