Install and load libraries

# Install necessary packages (if you haven't already)
#install.packages("tidyverse")  # Include ggplot2 (for plotting) and dplyr (for data manipulation)
#install.packages("rstatix") # For Shapiro-Wilk test (more robust version)
#install.packages("gridExtra") # For creating multiple plots on a grid
#install.packages("car") # For using Levene's Test (to test for equal variances) 
#install.packages("dunn.test") # For using Dunn's Test (non-parameteric post-hoc test) 

# Load necessary libraries
library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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## ✔ lubridate 1.9.4     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
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## ✖ dplyr::filter() masks stats::filter()
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## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(rstatix)

## 
## Attaching package: 'rstatix'
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## 
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library(gridExtra)

## 
## Attaching package: 'gridExtra'
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library(car)

## Loading required package: carData
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## Attaching package: 'car'
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library(dunn.test)

Trial 1 - Tick survival parameters

Steps for comparing differences between groups

Check for Normality:
- For each tick survival parameter and each vaccine group, assess whether the data is approximately normally distributed. Use the Shapiro-Wilk test.
- Note: With only 4 values per group, interpret the Shapiro-Wilk test results cautiously, as the test has low power. Supplement with visual inspection (histograms, Q-Q plots) if feasible, but understand that visual inspection can also be unreliable with such small samples
Check for Equality of Variances:
- For each tick survival parameter, assess whether the variances are approximately equal across the vaccine groups. Use Levene’s test.
- Note: Similar to normality, the test for equal variances also has limited power with small sample sizes.
Choose the appropriate test:
- Case 1: Approximately Normal Data & Equal Variances: Use ANOVA followed by a post-hoc test (Tukey’s HSD if comparing all pairs, Dunnett’s test if comparing to a control group).
- Case 2: Data Not Approximately Normal: Use the Kruskal-Wallis test followed by a post-hoc test (Dunn’s test or Mann-Whitney U with Bonferroni correction).
- Case 3: Approximately Normal Data & Unequal Variances: Use Welch’s ANOVA followed by Games-Howell.
Perform the test.
Interpret the results:
- Examine the p-values associated with the main test (ANOVA, Kruskal-Wallis, Welch’s ANOVA). A p-value below your chosen significance level (e.g., 0.05) indicates a statistically significant difference between at least some of the groups.
- If the main test is significant, examine the p-values from the post-hoc test to determine which specific groups differ significantly from each other.
Report the findings:
- Clearly state which statistical tests were used (including the normality and equal variance tests).
- Report the test statistics (e.g., F-statistic for ANOVA, chi-squared statistic for Kruskal-Wallis), degrees of freedom, and p-values for both the main test and the post-hoc tests.
- Clearly state your conclusions, being careful not to overstate the significance of your findings given the small sample size.
- Acknowledge the limitations of your analysis due to the small number of replicates per group.

Important Considerations for Your Data

Small Sample Size: You only have 4 animals per group. This limits the statistical power of your tests (makes it harder to find significant differences).

High Variability: The high variability within groups further reduces statistical power.

Note: Non-parametric tests are generally more robust to violations of assumptions when sample sizes are small (e.g. Kruskal Wallis rather than ANOVA).

Read in the data

Note that I have transposed and cleaned up the data so that it is easy to use in R.

setwd("/Users/nanette/Documents/Stats_help/Christian_2025/")
data <- read_tsv("Trial1_all_data_per_Bovine.txt")

## Rows: 16 Columns: 12
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: "\t"
## chr (3): Tag, Group, Rep
## dbl (9): Number_females, Weight_females, Egg_weight, Efficacy, Bm86_IgG, OD_...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Shapiro-Wilk Test for normality

Interpretation: If the p-value is less than 0.05 (or your chosen alpha level), you reject the null hypothesis of normality, suggesting the data is likely not normally distributed.

column_name <- "Number_females"
data %>%
  group_by(Group) %>%
  shapiro_test(column_name)

## # A tibble: 4 × 4
##   Group     variable       statistic     p
##   <chr>     <chr>              <dbl> <dbl>
## 1 Bm86      Number_females     0.873 0.311
## 2 Combi     Number_females     0.868 0.290
## 3 Combi.CpG Number_females     0.925 0.563
## 4 control   Number_females     0.887 0.368

Conclusion: “Total # engorged female ticks collected” likely normally distributed.

column_name <- "Weight_females"
data %>%
  group_by(Group) %>%
  shapiro_test(column_name)

## # A tibble: 4 × 4
##   Group     variable       statistic     p
##   <chr>     <chr>              <dbl> <dbl>
## 1 Bm86      Weight_females     0.995 0.982
## 2 Combi     Weight_females     0.928 0.581
## 3 Combi.CpG Weight_females     0.880 0.340
## 4 control   Weight_females     0.998 0.994

Conclusion: “Mean weight engorged females” likely normally distributed.

column_name <- "Egg_weight"
data %>%
  group_by(Group) %>%
  shapiro_test(column_name)

## # A tibble: 4 × 4
##   Group     variable   statistic     p
##   <chr>     <chr>          <dbl> <dbl>
## 1 Bm86      Egg_weight     0.998 0.995
## 2 Combi     Egg_weight     0.910 0.484
## 3 Combi.CpG Egg_weight     0.939 0.651
## 4 control   Egg_weight     0.875 0.319

Conclusion: “Mean egg weight” likely normally distributed.

column_name <- "Efficacy"
data %>%
  filter(Group != "control") %>% # Exclude rows where Group is "control"
  group_by(Group) %>%
  shapiro_test(column_name)

## # A tibble: 3 × 4
##   Group     variable statistic     p
##   <chr>     <chr>        <dbl> <dbl>
## 1 Bm86      Efficacy     0.812 0.124
## 2 Combi     Efficacy     0.900 0.432
## 3 Combi.CpG Efficacy     0.945 0.687

Conclusion: “Calculated efficacy %” likely normally distributed.

Visual inspection: QQPlots for normality

qqplot_ggplot <- function(data, group_name, column_name) {
  # Calculate theoretical quantiles (normal distribution)
  theoretical_quantiles <- qnorm(ppoints(nrow(data)))
  
  # Order the sample data
  sample_quantiles <- sort(data[[column_name]])
  
  # Create a data frame for plotting
  qq_data <- data.frame(theoretical = theoretical_quantiles,
                        sample = sample_quantiles)
  
  # Create the ggplot QQ plot
  ggplot(qq_data, aes(x = theoretical, y = sample)) +
    geom_point() +
    geom_abline(intercept = mean(sample_quantiles), slope = sd(sample_quantiles), color = "red") +  # Add a line to show the distribution
    labs(title = paste("QQ Plot for Group", group_name),
         x = "Theoretical Quantiles (Normal)",
         y = "Sample Quantiles") +
    theme_bw()
}

column_name <- "Number_females"

# Get unique group names
group_names <- unique(data$Group)

# Create a list to store the QQ plots
qq_plots <- list()

# Loop through groups and create QQ plots
for (i in seq_along(group_names)) {
  group_name <- group_names[i]
  
  # Subset the data for the current group
  group_data <- data %>% filter(Group == group_name)
  
  # Create the QQ plot using the custom function
  qq_plot <- qqplot_ggplot(group_data, group_name, column_name)
  
  # Store the plot in the list
  qq_plots[[i]] <- qq_plot
}

# Arrange the plots in a grid
grid.arrange(grobs = qq_plots, nrow = 2, ncol = 2)  # Adjust nrow and ncol as needed

Conclusion: “Total # engorged female ticks collected” likely normally distributed.

column_name <- "Weight_females"

# Get unique group names
group_names <- unique(data$Group)

# Create a list to store the QQ plots
qq_plots <- list()

# Loop through groups and create QQ plots
for (i in seq_along(group_names)) {
  group_name <- group_names[i]
  
  # Subset the data for the current group
  group_data <- data %>% filter(Group == group_name)
  
  # Create the QQ plot using the custom function
  qq_plot <- qqplot_ggplot(group_data, group_name, column_name)
  
  # Store the plot in the list
  qq_plots[[i]] <- qq_plot
}

# Arrange the plots in a grid
grid.arrange(grobs = qq_plots, nrow = 2, ncol = 2)  # Adjust nrow and ncol as needed

Conclusion: “Mean weight engorged females” likely normally distributed.

column_name <- "Egg_weight"

# Get unique group names
group_names <- unique(data$Group)

# Create a list to store the QQ plots
qq_plots <- list()

# Loop through groups and create QQ plots
for (i in seq_along(group_names)) {
  group_name <- group_names[i]
  
  # Subset the data for the current group
  group_data <- data %>% filter(Group == group_name)
  
  # Create the QQ plot using the custom function
  qq_plot <- qqplot_ggplot(group_data, group_name, column_name)
  
  # Store the plot in the list
  qq_plots[[i]] <- qq_plot
}

# Arrange the plots in a grid
grid.arrange(grobs = qq_plots, nrow = 2, ncol = 2)  # Adjust nrow and ncol as needed

Conclusion: “Mean egg weight” likely normally distributed.

column_name <- "Efficacy"

# Get unique group names
group_names <- unique(data$Group)[-1]

# Create a list to store the QQ plots
qq_plots <- list()

# Loop through groups and create QQ plots
for (i in seq_along(group_names)) {
  group_name <- group_names[i]
  
  # Subset the data for the current group
  group_data <- data %>% filter(Group == group_name)
  
  # Create the QQ plot using the custom function
  qq_plot <- qqplot_ggplot(group_data, group_name, column_name)
  
  # Store the plot in the list
  qq_plots[[i]] <- qq_plot
}

# Arrange the plots in a grid
grid.arrange(grobs = qq_plots, nrow = 2, ncol = 2)  # Adjust nrow and ncol as needed

Conclusion: “Calculated efficacy %” likely normally distributed.

Levene’s Test for equality of variances

Note: This test is not very sensitive to the assumption of normality (this is good).

Interpretation: If the p-value is less than 0.05 (or your chosen alpha level), you reject the null hypothesis of equal variances, suggesting the variances between groups are likely not significantly different.

column_name <- "Number_females"
#Assuming you already have the column and variable selected.
data %>%
   leveneTest(get(column_name) ~ Group, data = .)

## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3   1.327 0.3114
##       12

Conclusion: “Total # engorged female ticks collected” likely equal variances.

column_name <- "Weight_females"
#Assuming you already have the column and variable selected.
data %>%
   leveneTest(get(column_name) ~ Group, data = .)

## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3  0.8778 0.4798
##       12

Conclusion: “Mean weight engorged females” likely normally distributed.

column_name <- "Egg_weight"
#Assuming you already have the column and variable selected.
data %>%
   leveneTest(get(column_name) ~ Group, data = .)

## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  3  1.8154  0.198
##       12

Conclusion: “Mean egg weight” likely normally distributed.

column_name <- "Efficacy"
#Assuming you already have the column and variable selected.

data %>%
  filter(Group != "control") %>% # Exclude rows where Group is "control"
  leveneTest(get(column_name) ~ Group, data = .)

## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.

## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  2  0.2593 0.7772
##        9

Conclusion: “Calculated efficacy %” likely normally distributed.

One-way ANOVA

# Specify the tick survival parameter
column_name <- "Number_females"

# Perform ANOVA
anova_results <- aov(get(column_name) ~ Group, data = data)
summary(anova_results)

##             Df Sum Sq Mean Sq F value Pr(>F)
## Group        3 332163  110721   1.941  0.177
## Residuals   12 684669   57056

# Perform Post-Hoc Test (if ANOVA is significant)
TukeyHSD(anova_results)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = get(column_name) ~ Group, data = data)
## 
## $Group
##                     diff       lwr      upr     p adj
## Combi-Bm86        -342.0 -843.4532 159.4532 0.2325104
## Combi.CpG-Bm86    -337.0 -838.4532 164.4532 0.2428334
## control-Bm86      -135.5 -636.9532 365.9532 0.8521070
## Combi.CpG-Combi      5.0 -496.4532 506.4532 0.9999901
## control-Combi      206.5 -294.9532 707.9532 0.6251502
## control-Combi.CpG  201.5 -299.9532 702.9532 0.6424212

# Graphing (Optional but Recommended)
# Boxplot of sample
boxplot(get(column_name) ~ Group, data = data,
        main = "Number of Females by Group",
        xlab = "Group",
        ylab = column_name)

Conclusion: There is no significant differences between means of groups for “Total # engorged female ticks collected”.

# Specify the tick survival parameter
column_name <- "Weight_females"

# Perform ANOVA
anova_results <- aov(get(column_name) ~ Group, data = data)
summary(anova_results)

##             Df Sum Sq Mean Sq F value Pr(>F)
## Group        3   1064   354.5   0.699  0.571
## Residuals   12   6088   507.3

# Perform Post-Hoc Test (if ANOVA is significant)
TukeyHSD(anova_results)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = get(column_name) ~ Group, data = data)
## 
## $Group
##                      diff       lwr      upr     p adj
## Combi-Bm86        -19.725 -67.01081 27.56081 0.6158937
## Combi.CpG-Bm86     -0.200 -47.48581 47.08581 0.9999992
## control-Bm86      -10.125 -57.41081 37.16081 0.9184606
## Combi.CpG-Combi    19.525 -27.76081 66.81081 0.6232239
## control-Combi       9.600 -37.68581 56.88581 0.9292425
## control-Combi.CpG  -9.925 -57.21081 37.36081 0.9226645

# Graphing (Optional but Recommended)
# Boxplot of sample
boxplot(get(column_name) ~ Group, data = data,
        main = "Number of Females by Group",
        xlab = "Group",
        ylab = column_name)

Conclusion: There is no significant differences between means of groups for “Mean weight engorged females”.

# Specify the tick survival parameter
column_name <- "Egg_weight"

# Perform ANOVA
anova_results <- aov(get(column_name) ~ Group, data = data)
summary(anova_results)

##             Df Sum Sq Mean Sq F value Pr(>F)
## Group        3    298   99.37   0.361  0.782
## Residuals   12   3301  275.05

# Perform Post-Hoc Test (if ANOVA is significant)
TukeyHSD(anova_results)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = get(column_name) ~ Group, data = data)
## 
## $Group
##                     diff       lwr      upr     p adj
## Combi-Bm86        -6.825 -41.64159 27.99159 0.9356108
## Combi.CpG-Bm86    -5.400 -40.21659 29.41659 0.9662505
## control-Bm86       3.975 -30.84159 38.79159 0.9859293
## Combi.CpG-Combi    1.425 -33.39159 36.24159 0.9993210
## control-Combi     10.800 -24.01659 45.61659 0.7943865
## control-Combi.CpG  9.375 -25.44159 44.19159 0.8533786

# Graphing (Optional but Recommended)
# Boxplot of sample
boxplot(get(column_name) ~ Group, data = data,
        main = "Number of Females by Group",
        xlab = "Group",
        ylab = column_name)

Conclusion: There is no significant differences between means of groups for “Mean egg weight”.

# Specify the tick survival parameter
column_name <- "Efficacy"

data_no_control <- data %>%
  filter(Group != "control") # Exclude rows where Group is "control"

# Perform ANOVA
anova_results <- aov(get(column_name) ~ Group, data = data_no_control)
summary(anova_results)

##             Df Sum Sq Mean Sq F value Pr(>F)
## Group        2   4144  2071.8   2.557  0.132
## Residuals    9   7293   810.3

# Perform Post-Hoc Test (if ANOVA is significant)
TukeyHSD(anova_results)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = get(column_name) ~ Group, data = data_no_control)
## 
## $Group
##                    diff       lwr      upr     p adj
## Combi-Bm86      41.7075 -14.49112 97.90612 0.1508811
## Combi.CpG-Bm86  36.6400 -19.55862 92.83862 0.2174754
## Combi.CpG-Combi -5.0675 -61.26612 51.13112 0.9657947

# Graphing (Optional but Recommended)
# Boxplot of sample
boxplot(get(column_name) ~ Group, data = data,
        main = "Number of Females by Group",
        xlab = "Group",
        ylab = column_name)

Conclusion: There is no significant differences between means of groups for “Calculated efficacy %”.

Kruskal-Wallis test

# Specify the column to analyze
column_name <- "Number_females"

# Perform Kruskal-Wallis test
kruskal_results <- kruskal.test(get(column_name) ~ Group, data = data)
print(kruskal_results)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  get(column_name) by Group
## Kruskal-Wallis chi-squared = 4.6324, df = 3, p-value = 0.2008

# Perform Dunn's post-hoc test (if Kruskal-Wallis is significant or of interest)
dunn_results <- dunn.test(data[[column_name]], g = data$Group,
                       method = "bonferroni")  #or other correction methods

##   Kruskal-Wallis rank sum test
## 
## data: x and group
## Kruskal-Wallis chi-squared = 4.6324, df = 3, p-value = 0.2
## 
## 
##                            Comparison of x by group                            
##                                  (Bonferroni)                                  
## Col Mean-|
## Row Mean |       Bm86      Combi   Combi.Cp
## ---------+---------------------------------
##    Combi |   1.633743
##          |     0.3069
##          |
## Combi.Cp |   1.782265   0.148522
##          |     0.2241     1.0000
##          |
##  control |   0.445566  -1.188177  -1.336699
##          |     1.0000     0.7043     0.5440
## 
## alpha = 0.05
## Reject Ho if p <= alpha/2

print(dunn_results)

## $chi2
## [1] 4.632353
## 
## $Z
## [1]  1.6337434  1.7822656  0.1485221  0.4455664 -1.1881771 -1.3366992
## 
## $P
## [1] 0.05115637 0.03735297 0.44096536 0.32795525 0.11738183 0.09066042
## 
## $P.adjusted
## [1] 0.3069382 0.2241178 1.0000000 1.0000000 0.7042910 0.5439625
## 
## $comparisons
## [1] "Bm86 - Combi"        "Bm86 - Combi.CpG"    "Combi - Combi.CpG"  
## [4] "Bm86 - control"      "Combi - control"     "Combi.CpG - control"

Conclusion: There is no significant differences between medians of groups for “Total # engorged female ticks collected”.

# Specify the column to analyze
column_name <- "Weight_females"

# Perform Kruskal-Wallis test
kruskal_results <- kruskal.test(get(column_name) ~ Group, data = data)
print(kruskal_results)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  get(column_name) by Group
## Kruskal-Wallis chi-squared = 2.2721, df = 3, p-value = 0.5179

# Perform Dunn's post-hoc test (if Kruskal-Wallis is significant or of interest)
dunn_results <- dunn.test(data[[column_name]], g = data$Group,
                       method = "bonferroni")  #or other correction methods

##   Kruskal-Wallis rank sum test
## 
## data: x and group
## Kruskal-Wallis chi-squared = 2.2721, df = 3, p-value = 0.52
## 
## 
##                            Comparison of x by group                            
##                                  (Bonferroni)                                  
## Col Mean-|
## Row Mean |       Bm86      Combi   Combi.Cp
## ---------+---------------------------------
##    Combi |   1.039654
##          |     0.8955
##          |
## Combi.Cp |  -0.371305  -1.410960
##          |     1.0000     0.4748
##          |
##  control |   0.519827  -0.519827   0.891132
##          |     1.0000     1.0000     1.0000
## 
## alpha = 0.05
## Reject Ho if p <= alpha/2

print(dunn_results)

## $chi2
## [1] 2.272059
## 
## $Z
## [1]  1.0396549 -0.3713053 -1.4109602  0.5198275 -0.5198275  0.8911328
## 
## $P
## [1] 0.14925013 0.35520506 0.07912817 0.30159192 0.30159192 0.18642897
## 
## $P.adjusted
## [1] 0.8955008 1.0000000 0.4747690 1.0000000 1.0000000 1.0000000
## 
## $comparisons
## [1] "Bm86 - Combi"        "Bm86 - Combi.CpG"    "Combi - Combi.CpG"  
## [4] "Bm86 - control"      "Combi - control"     "Combi.CpG - control"

Conclusion: There is no significant differences between medians of groups for “Mean weight engorged females”.

# Specify the column to analyze
column_name <- "Egg_weight"

# Perform Kruskal-Wallis test
kruskal_results <- kruskal.test(get(column_name) ~ Group, data = data)
print(kruskal_results)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  get(column_name) by Group
## Kruskal-Wallis chi-squared = 1.1912, df = 3, p-value = 0.7551

# Perform Dunn's post-hoc test (if Kruskal-Wallis is significant or of interest)
dunn_results <- dunn.test(data[[column_name]], g = data$Group,
                       method = "bonferroni")  #or other correction methods

##   Kruskal-Wallis rank sum test
## 
## data: x and group
## Kruskal-Wallis chi-squared = 1.1912, df = 3, p-value = 0.76
## 
## 
##                            Comparison of x by group                            
##                                  (Bonferroni)                                  
## Col Mean-|
## Row Mean |       Bm86      Combi   Combi.Cp
## ---------+---------------------------------
##    Combi |   0.594088
##          |     1.0000
##          |
## Combi.Cp |   0.594088   0.000000
##          |     1.0000     1.0000
##          |
##  control |  -0.297044  -0.891132  -0.891132
##          |     1.0000     1.0000     1.0000
## 
## alpha = 0.05
## Reject Ho if p <= alpha/2

print(dunn_results)

## $chi2
## [1] 1.191176
## 
## $Z
## [1]  0.5940885  0.5940885  0.0000000 -0.2970443 -0.8911328 -0.8911328
## 
## $P
## [1] 0.2762265 0.2762265 0.5000000 0.3832164 0.1864290 0.1864290
## 
## $P.adjusted
## [1] 1 1 1 1 1 1
## 
## $comparisons
## [1] "Bm86 - Combi"        "Bm86 - Combi.CpG"    "Combi - Combi.CpG"  
## [4] "Bm86 - control"      "Combi - control"     "Combi.CpG - control"

Conclusion: There is no significant differences between medians of groups for “Mean egg weight”.

# Specify the column to analyze
column_name <- "Efficacy"

# Perform Kruskal-Wallis test
kruskal_results <- kruskal.test(get(column_name) ~ Group, data = data_no_control)
print(kruskal_results)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  get(column_name) by Group
## Kruskal-Wallis chi-squared = 4.1538, df = 2, p-value = 0.1253

# Perform Dunn's post-hoc test (if Kruskal-Wallis is significant or of interest)
dunn_results <- dunn.test(data[[column_name]], g = data$Group,
                       method = "bonferroni")  #or other correction methods

##   Kruskal-Wallis rank sum test
## 
## data: x and group
## Kruskal-Wallis chi-squared = 4.1538, df = 2, p-value = 0.13
## 
## 
##                            Comparison of x by group                            
##                                  (Bonferroni)                                  
## Col Mean-|
## Row Mean |       Bm86      Combi
## ---------+----------------------
##    Combi |  -1.765045
##          |     0.1163
##          |
## Combi.Cp |  -1.765045   0.000000
##          |     0.1163     1.0000
## 
## alpha = 0.05
## Reject Ho if p <= alpha/2

print(dunn_results)

## $chi2
## [1] 4.153846
## 
## $Z
## [1] -1.765045 -1.765045  0.000000
## 
## $P
## [1] 0.03877808 0.03877808 0.50000000
## 
## $P.adjusted
## [1] 0.1163343 0.1163343 1.0000000
## 
## $comparisons
## [1] "Bm86 - Combi"      "Bm86 - Combi.CpG"  "Combi - Combi.CpG"

Conclusion: There is no significant differences between medians of groups for “Calculated efficacy %”.

Tick project

Dr N Christie

2025-04-09

Install and load libraries

Trial 1 - Tick survival parameters

Steps for comparing differences between groups

Important Considerations for Your Data

Read in the data

Shapiro-Wilk Test for normality

Visual inspection: QQPlots for normality

Levene’s Test for equality of variances

One-way ANOVA

Kruskal-Wallis test