This analysis examines CO2 change using a two-way factorial ANOVA to test:
library(readxl) # Read Excel files
library(ggplot2) # Create plots
library(dplyr) # Data wrangling
library(car) # Type II/III ANOVA and Levene's test
library(emmeans) # Estimated marginal means
library(multcomp) # Multiple comparisons
library(tidyr) # Data manipulation#setwd
getwd()## [1] "/Users/ivyvelasco/Downloads"#setwd
setwd("/Users/ivyvelasco/Desktop/Greenhouse 2026")
getwd()## [1] "/Users/ivyvelasco/Desktop/Greenhouse 2026"list.files()## [1] "arthropod_barplot.png"
## [2] "arthropod_boxplot.png"
## [3] "Arthropods_R.xlsx"
## [4] "Book5.xlsx"
## [5] "CarbonFluxLMM.R"
## [6] "CFlux_Anova#1.Rmd"
## [7] "CFlux_R.xlsx"
## [8] "emmeans_Nativity_by_Light_Edited.xlsx"
## [9] "emmeans_Nativity_by_Light.xlsx"
## [10] "emmeans_Nativity_Light.xlsx"
## [11] "emmeans&contrasts_Light_by_Nativity_Edited.xlsx"
## [12] "emmeans&contrasts_PairwiseComparison_Edited.xlsx"
## [13] "height_change_barplot.png"
## [14] "height_change_boxplot.png"
## [15] "height_change_by_species.png"
## [16] "HeightDataCleaning.xlsx"
## [17] "Nativity_"
## [18] "Nativity_WaterContent 18-19"
## [19] "Plant_Height.html"
## [20] "Plant_Height.Rmd"
## [21] "Plant_Height.xlsx"
## [22] "Rplot.pdf"# Read the Excel file
#DOESN'T WORK: data <- read_excel("CFlux_R.xlsx")
# Use the full path instead
data <- read_excel("/Users/ivyvelasco/Desktop/Greenhouse 2026/CFlux_R.xlsx")
# Display the raw data
print(data)## # A tibble: 24 × 4
## Nativity Plot Light CO2_Change
## <chr> <chr> <chr> <dbl>
## 1 NN 1L Light 19
## 2 NN 1D Dark -109
## 3 NN 2L Light 985
## 4 NN 2D Dark -137
## 5 N 3D Dark -76
## 6 N 4D Dark -138
## 7 N 5D Dark -129
## 8 N 6D Dark -174
## 9 N 9D Dark -106
## 10 N 10D Dark -66
## # ℹ 14 more rowscat("Total rows:", nrow(data), "\n")## Total rows: 24# Clean and prepare variables
data$Nativity <- trimws(data$Nativity)
data$Light <- trimws(data$Light)
# Convert to factors with meaningful levels
data$Nativity <- factor(data$Nativity, levels = c("NN", "N"))
data$Light <- factor(data$Light, levels = c("Dark", "Light"))
# Rename for clarity
levels(data$Nativity) <- c("Non-Native", "Native")
# Check the cleaned data
str(data)## tibble [24 × 4] (S3: tbl_df/tbl/data.frame)
## $ Nativity : Factor w/ 2 levels "Non-Native","Native": 1 1 1 1 2 2 2 2 2 2 ...
## $ Plot : chr [1:24] "1L" "1D" "2L" "2D" ...
## $ Light : Factor w/ 2 levels "Dark","Light": 2 1 2 1 1 1 1 1 1 1 ...
## $ CO2_Change: num [1:24] 19 -109 985 -137 -76 -138 -129 -174 -106 -66 ...# Check sample sizes per treatment combination
design_table <- table(data$Nativity, data$Light)
cat("Sample sizes (Nativity × Light):\n")## Sample sizes (Nativity × Light):print(design_table)##
## Dark Light
## Non-Native 6 3
## Native 6 3# Check if design is balanced
if(length(unique(as.vector(design_table))) == 1) {
cat("\n✓ BALANCED DESIGN - all groups have equal sample sizes\n")
cat(" Can use Type I, II, or III ANOVA (results will be identical)\n")
} else {
cat("\n✗ UNBALANCED DESIGN - groups have different sample sizes\n")
cat(" Must use Type II or Type III ANOVA\n")
cat(" Type III recommended for testing main effects with interaction\n")
}##
## ✗ UNBALANCED DESIGN - groups have different sample sizes
## Must use Type II or Type III ANOVA
## Type III recommended for testing main effects with interaction# Total sample size
cat("\nTotal observations:", nrow(data), "\n")##
## Total observations: 24cat("Treatment combinations:", length(design_table), "\n")## Treatment combinations: 4# Summary by both factors
summary_stats <- data %>%
group_by(Nativity, Light) %>%
summarise(
n = n(),
Mean = mean(CO2_Change, na.rm = TRUE),
SD = sd(CO2_Change, na.rm = TRUE),
SE = sd(CO2_Change, na.rm = TRUE) / sqrt(n()),
Min = min(CO2_Change, na.rm = TRUE),
Max = max(CO2_Change, na.rm = TRUE),
.groups = 'drop'
)
cat("CO2 Change by Treatment Combination:\n")## CO2 Change by Treatment Combination:print(summary_stats)## # A tibble: 6 × 8
## Nativity Light n Mean SD SE Min Max
## <fct> <fct> <int> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Non-Native Dark 6 -104. 46.6 19.0 -174 -47
## 2 Non-Native Light 3 343. 556. 321. 19 985
## 3 Native Dark 6 -115. 40.5 16.5 -174 -66
## 4 Native Light 3 114 9.85 5.69 106 125
## 5 Native <NA> 1 NaN NA NA Inf -Inf
## 6 <NA> <NA> 5 NaN NA NA Inf -Inf# Marginal means
cat("\nMARGINAL MEANS:\n")##
## MARGINAL MEANS:marginal_nativity <- data %>%
group_by(Nativity) %>%
summarise(
n = n(),
Mean_CO2 = mean(CO2_Change, na.rm = TRUE),
SD = sd(CO2_Change, na.rm = TRUE),
.groups = 'drop'
)
cat("\nBy Nativity (averaged over Light conditions):\n")##
## By Nativity (averaged over Light conditions):print(marginal_nativity)## # A tibble: 3 × 4
## Nativity n Mean_CO2 SD
## <fct> <int> <dbl> <dbl>
## 1 Non-Native 9 45 359.
## 2 Native 10 -38.6 119.
## 3 <NA> 5 NaN NAmarginal_light <- data %>%
group_by(Light) %>%
summarise(
n = n(),
Mean_CO2 = mean(CO2_Change, na.rm = TRUE),
SD = sd(CO2_Change, na.rm = TRUE),
.groups = 'drop'
)
cat("\nBy Light (averaged over Nativity):\n")##
## By Light (averaged over Nativity):print(marginal_light)## # A tibble: 3 × 4
## Light n Mean_CO2 SD
## <fct> <int> <dbl> <dbl>
## 1 Dark 12 -109. 42.0
## 2 Light 6 228. 374.
## 3 <NA> 6 NaN NAMost important for factorial design! Parallel lines = no interaction; Crossing/diverging lines = interaction present.
p1 <- ggplot(summary_stats, aes(x = Light, y = Mean,
color = Nativity, group = Nativity)) +
geom_point(size = 4) +
geom_line(linewidth = 1.5) +
geom_errorbar(aes(ymin = Mean - SE, ymax = Mean + SE),
width = 0.1, linewidth = 1) +
scale_color_manual(values = c("Non-Native" = "#E74C3C", "Native" = "#27AE60")) +
labs(
title = "Interaction Plot: CO2 Change by Light and Nativity",
subtitle = "Parallel lines = no interaction; Crossing/diverging lines = interaction present",
x = "Light Condition",
y = "Mean CO2 Change",
color = "Plant Type"
) +
theme_minimal(base_size = 14) +
geom_hline(yintercept = 0, linetype = "dashed", color = "gray50")p2 <- ggplot(data, aes(x = Light, y = CO2_Change, fill = Nativity)) +
geom_boxplot(alpha = 0.7, outlier.shape = 16) +
geom_point(position = position_jitterdodge(jitter.width = 0.2),
alpha = 0.5, size = 2) +
scale_fill_manual(values = c("Non-Native" = "#E74C3C", "Native" = "#27AE60")) +
labs(
title = "CO2 Change by Light Condition and Nativity",
x = "Light Condition",
y = "CO2 Change",
fill = "Plant Type"
) +
theme_minimal(base_size = 14) +
geom_hline(yintercept = 0, linetype = "dashed", color = "gray50")p3 <- ggplot(data, aes(x = Light, y = CO2_Change, fill = Light)) +
geom_boxplot(alpha = 0.7) +
geom_jitter(width = 0.2, alpha = 0.5, size = 2) +
facet_wrap(~ Nativity) +
scale_fill_manual(values = c("Dark" = "#34495E", "Light" = "#F39C12")) +
labs(
title = "CO2 Change by Light Condition (Separated by Nativity)",
x = "Light Condition",
y = "CO2 Change",
fill = "Light"
) +
theme_minimal(base_size = 14) +
geom_hline(yintercept = 0, linetype = "dashed", color = "gray50")# First fit the model to get residuals
model_check <- aov(CO2_Change ~ Nativity * Light, data = data)
residuals_check <- residuals(model_check)
# 1. Normality Test
cat("1. NORMALITY TEST (Shapiro-Wilk):\n")## 1. NORMALITY TEST (Shapiro-Wilk):shapiro_test <- shapiro.test(residuals_check)
print(shapiro_test)##
## Shapiro-Wilk normality test
##
## data: residuals_check
## W = 0.68893, p-value = 5.955e-05if(shapiro_test$p.value > 0.05) {
cat("→ Residuals are approximately normal (p > 0.05) ✓\n")
} else {
cat("→ Residuals deviate from normality (p < 0.05)\n")
cat(" Consider transformations (log, sqrt) if severe\n")
}## → Residuals deviate from normality (p < 0.05)
## Consider transformations (log, sqrt) if severe# Q-Q plot doesn't work due to graphics issue
#qqnorm(residuals_check, main = "Q-Q Plot of Residuals")
#qqline(residuals_check, col = "red")
# 2. Homogeneity of Variances
cat("\n2. HOMOGENEITY OF VARIANCE TEST (Levene's Test):\n")##
## 2. HOMOGENEITY OF VARIANCE TEST (Levene's Test):levene_test <- leveneTest(CO2_Change ~ Nativity * Light, data = data)
print(levene_test)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 1.6401 0.2252
## 14if(levene_test$`Pr(>F)`[1] > 0.05) {
cat("→ Variances are homogeneous across groups (p > 0.05) ✓\n")
} else {
cat("→ Variances differ across groups (p < 0.05)\n")
cat(" ANOVA is relatively robust to this with equal sample sizes\n")
}## → Variances are homogeneous across groups (p > 0.05) ✓# Residuals vs Fitted doesn't plot due to graphics issue
#plot(fitted(model_check), residuals_check,
#xlab = "Fitted Values", ylab = "Residuals",
#main = "Residuals vs Fitted Values\n(Should show random scatter)")
#abline(h = 0, col = "red", lty = 2)# Fit the model with interaction
model <- aov(CO2_Change ~ Nativity * Light, data = data)
# Type I ANOVA
cat("ANOVA Table (Type I):\n")## ANOVA Table (Type I):anova_type1 <- summary(model)
print(anova_type1)## Df Sum Sq Mean Sq F value Pr(>F)
## Nativity 1 31417 31417 0.689 0.42036
## Light 1 456075 456075 10.005 0.00691 **
## Nativity:Light 1 47379 47379 1.039 0.32526
## Residuals 14 638160 45583
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 6 observations deleted due to missingness# Type III ANOVA (recommended for unbalanced designs)
cat("\n\nANOVA Table (Type III) - Recommended for unbalanced designs:\n")##
##
## ANOVA Table (Type III) - Recommended for unbalanced designs:cat("(Tests each effect while controlling for all others)\n\n")## (Tests each effect while controlling for all others)model_lm <- lm(CO2_Change ~ Nativity * Light, data = data)
anova_type3 <- Anova(model_lm, type = "III")
print(anova_type3)## Anova Table (Type III tests)
##
## Response: CO2_Change
## Sum Sq Df F value Pr(>F)
## (Intercept) 64688 1 1.4191 0.25335
## Nativity 363 1 0.0080 0.93016
## Light 398724 1 8.7472 0.01039 *
## Nativity:Light 47379 1 1.0394 0.32526
## Residuals 638160 14
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Extract p-values from Type III ANOVA
p_nativity <- anova_type3$`Pr(>F)`[2]
p_light <- anova_type3$`Pr(>F)`[3]
p_interaction <- anova_type3$`Pr(>F)`[4]
cat("P-VALUES:\n")## P-VALUES:cat("Main effect of Nativity:", round(p_nativity, 4), "\n")## Main effect of Nativity: 0.9302cat("Main effect of Light:", round(p_light, 4), "\n")## Main effect of Light: 0.0104cat("Interaction (Nativity × Light):", round(p_interaction, 4), "\n")## Interaction (Nativity × Light): 0.3253cat("\nINTERPRETATION:\n")##
## INTERPRETATION:# Interaction
cat("\n1. INTERACTION (Nativity × Light):\n")##
## 1. INTERACTION (Nativity × Light):if(p_interaction < 0.05) {
cat(" ✓ SIGNIFICANT INTERACTION (p < 0.05)\n")
cat(" → The effect of Light DEPENDS ON Nativity\n")
cat(" → The effect of Nativity DEPENDS ON Light condition\n")
cat(" → Cannot interpret main effects in isolation!\n")
cat(" → Must examine simple effects\n")
} else {
cat(" ✗ NO SIGNIFICANT INTERACTION (p ≥ 0.05)\n")
cat(" → The effect of Light is similar for Native and Non-Native\n")
cat(" → The effect of Nativity is similar in Light and Dark\n")
cat(" → Main effects can be interpreted independently\n")
}## ✗ NO SIGNIFICANT INTERACTION (p ≥ 0.05)
## → The effect of Light is similar for Native and Non-Native
## → The effect of Nativity is similar in Light and Dark
## → Main effects can be interpreted independently# Light main effect
cat("\n2. MAIN EFFECT OF LIGHT:\n")##
## 2. MAIN EFFECT OF LIGHT:if(p_light < 0.05) {
cat(" ✓ SIGNIFICANT MAIN EFFECT (p < 0.05)\n")
cat(" → CO2 change differs significantly between Light and Dark conditions\n")
light_diff <- marginal_light$Mean_CO2[marginal_light$Light == "Light"] -
marginal_light$Mean_CO2[marginal_light$Light == "Dark"]
cat(" → Light condition mean:",
round(marginal_light$Mean_CO2[marginal_light$Light == "Light"], 2), "\n")
cat(" → Dark condition mean:",
round(marginal_light$Mean_CO2[marginal_light$Light == "Dark"], 2), "\n")
cat(" → Difference:", round(light_diff, 2), "\n")
} else {
cat(" ✗ NO SIGNIFICANT MAIN EFFECT (p ≥ 0.05)\n")
}## ✓ SIGNIFICANT MAIN EFFECT (p < 0.05)
## → CO2 change differs significantly between Light and Dark conditions
## → Light condition mean: 228.33 NA
## → Dark condition mean: -109.33 NA
## → Difference: 337.67 NA# Nativity main effect
cat("\n3. MAIN EFFECT OF NATIVITY:\n")##
## 3. MAIN EFFECT OF NATIVITY:if(p_nativity < 0.05) {
cat(" ✓ SIGNIFICANT MAIN EFFECT (p < 0.05)\n")
cat(" → CO2 change differs significantly between Native and Non-Native plants\n")
nativity_diff <- marginal_nativity$Mean_CO2[marginal_nativity$Nativity == "Native"] -
marginal_nativity$Mean_CO2[marginal_nativity$Nativity == "Non-Native"]
cat(" → Native mean:",
round(marginal_nativity$Mean_CO2[marginal_nativity$Nativity == "Native"], 2), "\n")
cat(" → Non-Native mean:",
round(marginal_nativity$Mean_CO2[marginal_nativity$Nativity == "Non-Native"], 2), "\n")
cat(" → Difference:", round(nativity_diff, 2), "\n")
} else {
cat(" ✗ NO SIGNIFICANT MAIN EFFECT (p ≥ 0.05)\n")
}## ✗ NO SIGNIFICANT MAIN EFFECT (p ≥ 0.05)# All treatment combinations
emm <- emmeans(model, ~ Nativity * Light)
cat("Estimated Marginal Means (all combinations):\n")## Estimated Marginal Means (all combinations):print(summary(emm))## Nativity Light emmean SE df lower.CL upper.CL
## Non-Native Dark -104 87.2 14 -290.8 83.1
## Native Dark -115 87.2 14 -301.8 72.1
## Non-Native Light 343 123.0 14 78.3 607.0
## Native Light 114 123.0 14 -150.4 378.4
##
## Confidence level used: 0.95# Marginal means for each factor
emm_nativity <- emmeans(model, ~ Nativity)
emm_light <- emmeans(model, ~ Light)
cat("\nMarginal Means by Nativity:\n")##
## Marginal Means by Nativity:print(summary(emm_nativity))## Nativity emmean SE df lower.CL upper.CL
## Non-Native 119.417 75.5 14 -42.5 281
## Native -0.417 75.5 14 -162.3 161
##
## Results are averaged over the levels of: Light
## Confidence level used: 0.95cat("\nMarginal Means by Light:\n")##
## Marginal Means by Light:print(summary(emm_light))## Light emmean SE df lower.CL upper.CL
## Dark -109 61.6 14 -241.5 22.9
## Light 228 87.2 14 41.4 415.3
##
## Results are averaged over the levels of: Nativity
## Confidence level used: 0.95cat("All Pairwise Comparisons (Tukey HSD):\n")## All Pairwise Comparisons (Tukey HSD):all_pairs <- pairs(emm, adjust = "tukey")
print(summary(all_pairs))## contrast estimate SE df t.ratio p.value
## (Non-Native Dark) - Native Dark 11 123 14 0.089 0.9997
## (Non-Native Dark) - (Non-Native Light) -446 151 14 -2.958 0.0455
## (Non-Native Dark) - Native Light -218 151 14 -1.443 0.4951
## Native Dark - (Non-Native Light) -458 151 14 -3.030 0.0398
## Native Dark - Native Light -229 151 14 -1.516 0.4546
## (Non-Native Light) - Native Light 229 174 14 1.312 0.5709
##
## P value adjustment: tukey method for comparing a family of 4 estimatescat("Effect of Light within each Nativity level:\n")## Effect of Light within each Nativity level:emm_simple_light <- emmeans(model, ~ Light | Nativity)
simple_light_pairs <- pairs(emm_simple_light)
print(summary(simple_light_pairs))## Nativity = Non-Native:
## contrast estimate SE df t.ratio p.value
## Dark - Light -446 151 14 -2.958 0.0104
##
## Nativity = Native:
## contrast estimate SE df t.ratio p.value
## Dark - Light -229 151 14 -1.516 0.1518cat("\nInterpretation:\n")##
## Interpretation:cat("- For Native plants: Does Light significantly differ from Dark?\n")## - For Native plants: Does Light significantly differ from Dark?cat("- For Non-Native plants: Does Light significantly differ from Dark?\n")## - For Non-Native plants: Does Light significantly differ from Dark?cat("Effect of Nativity within each Light condition:\n")## Effect of Nativity within each Light condition:emm_simple_nativity <- emmeans(model, ~ Nativity | Light)
simple_nativity_pairs <- pairs(emm_simple_nativity)
print(summary(simple_nativity_pairs))## Light = Dark:
## contrast estimate SE df t.ratio p.value
## (Non-Native) - Native 11 123 14 0.089 0.9302
##
## Light = Light:
## contrast estimate SE df t.ratio p.value
## (Non-Native) - Native 229 174 14 1.312 0.2107cat("\nInterpretation:\n")##
## Interpretation:cat("- In Dark conditions: Do Native plants differ from Non-Native?\n")## - In Dark conditions: Do Native plants differ from Non-Native?cat("- In Light conditions: Do Native plants differ from Non-Native?\n")## - In Light conditions: Do Native plants differ from Non-Native?# Eta-squared (proportion of variance explained)
ss_total <- sum((data$CO2_Change - mean(data$CO2_Change))^2)
ss_nativity <- anova_type3$`Sum Sq`[2]
ss_light <- anova_type3$`Sum Sq`[3]
ss_interaction <- anova_type3$`Sum Sq`[4]
eta_sq_nativity <- ss_nativity / ss_total
eta_sq_light <- ss_light / ss_total
eta_sq_interaction <- ss_interaction / ss_total
cat("Eta-squared (η²) - Proportion of variance explained:\n")## Eta-squared (η²) - Proportion of variance explained:cat("Nativity:", round(eta_sq_nativity, 3), "\n")## Nativity: NAcat("Light:", round(eta_sq_light, 3), "\n")## Light: NAcat("Interaction:", round(eta_sq_interaction, 3), "\n")## Interaction: NAcat("\nInterpretation of η²:\n")##
## Interpretation of η²:cat(" Small: 0.01\n")## Small: 0.01cat(" Medium: 0.06\n")## Medium: 0.06cat(" Large: 0.14\n")## Large: 0.14# Cohen's f
f_nativity <- sqrt(eta_sq_nativity / (1 - eta_sq_nativity))
f_light <- sqrt(eta_sq_light / (1 - eta_sq_light))
f_interaction <- sqrt(eta_sq_interaction / (1 - eta_sq_interaction))
cat("\nCohen's f:\n")##
## Cohen's f:cat("Nativity:", round(f_nativity, 3), "\n")## Nativity: NAcat("Light:", round(f_light, 3), "\n")## Light: NAcat("Interaction:", round(f_interaction, 3), "\n")## Interaction: NAcat("\nInterpretation of Cohen's f:\n")##
## Interpretation of Cohen's f:cat(" Small: 0.10\n")## Small: 0.10cat(" Medium: 0.25\n")## Medium: 0.25cat(" Large: 0.40\n")## Large: 0.40summary_table <- data.frame(
Source = c("Nativity", "Light", "Nativity × Light", "Residuals"),
df = c(anova_type3$Df[2:5]),
SS = round(anova_type3$`Sum Sq`[2:5], 2),
MS = round(anova_type3$`Sum Sq`[2:5] / anova_type3$Df[2:5], 2),
F_value = round(anova_type3$`F value`[2:5], 2),
p_value = round(anova_type3$`Pr(>F)`[2:5], 4),
Eta_squared = round(c(eta_sq_nativity, eta_sq_light, eta_sq_interaction, NA), 3)
)
print(summary_table)## Source df SS MS F_value p_value Eta_squared
## 1 Nativity 1 363.00 363.00 0.01 0.9302 NA
## 2 Light 1 398724.50 398724.50 8.75 0.0104 NA
## 3 Nativity × Light 1 47378.78 47378.78 1.04 0.3253 NA
## 4 Residuals 14 638160.33 45582.88 NA NA NADoes CO2 differ based on Light condition?
→ Main effect of Light: p = 0.0104
Does CO2 differ between Native and Non-Native
plants?
→ Main effect of Nativity: p = 0.9302
Does the effect of Light depend on Nativity (comparing
slopes)?
→ Interaction: p = 0.3253
if(p_interaction < 0.05) {
cat("### ✓ SIGNIFICANT INTERACTION DETECTED\n\n")
cat("The relationship between Light and CO2 change differs for Native vs Non-Native plants.\n\n")
cat("**This means:**\n\n")
cat("- The effect of Light is different in Native vs Non-Native plants\n")
cat("- You cannot interpret main effects independently\n")
cat("- Must examine simple effects to understand the pattern\n\n")
cat("Look at the interaction plot to see the pattern:\n")
cat("- Crossing lines indicate the factors work differently together\n")
cat("- One group may benefit more from light than the other\n")
} else {
cat("### ✗ NO SIGNIFICANT INTERACTION\n\n")
cat("The effect of Light is similar for both Native and Non-Native plants.\n")
cat("The effect of Nativity is similar in both Light and Dark conditions.\n")
cat("Main effects can be interpreted independently.\n")
}The effect of Light is similar for both Native and Non-Native plants. The effect of Nativity is similar in both Light and Dark conditions. Main effects can be interpreted independently.
if(p_light < 0.05) {
cat("\n### ✓ SIGNIFICANT MAIN EFFECT OF LIGHT\n\n")
cat("Light condition significantly affects CO2 change (p < 0.05).\n\n")
cat("- Light mean:", round(marginal_light$Mean_CO2[marginal_light$Light == "Light"], 2), "\n")
cat("- Dark mean:", round(marginal_light$Mean_CO2[marginal_light$Light == "Dark"], 2), "\n\n")
cat("This makes biological sense: photosynthesis in light, respiration in dark.\n")
}Light condition significantly affects CO2 change (p < 0.05).
This makes biological sense: photosynthesis in light, respiration in dark.
if(p_nativity < 0.05) {
cat("\n### ✓ SIGNIFICANT MAIN EFFECT OF NATIVITY\n\n")
cat("Native and Non-Native plants differ significantly in CO2 change (p < 0.05).\n\n")
cat("- Native mean:", round(marginal_nativity$Mean_CO2[marginal_nativity$Nativity == "Native"], 2), "\n")
cat("- Non-Native mean:", round(marginal_nativity$Mean_CO2[marginal_nativity$Nativity == "Non-Native"], 2), "\n")
}A two-way ANOVA was conducted to examine the effects of plant nativity (Native vs Non-Native) and light condition (Light vs Dark) on CO2 change.
if(p_interaction < 0.05) {
cat("A significant interaction was found between nativity and light condition (F = ",
round(anova_type3$`F value`[4], 2), ", p = ", round(p_interaction, 4),
"), indicating that the effect of light depends on plant nativity.")
} else {
cat("No significant interaction was found (p = ", round(p_interaction, 4), "). ")
if(p_light < 0.05) {
cat("Light condition had a significant effect (F = ",
round(anova_type3$`F value`[3], 2), ", p = ", round(p_light, 4),
"), with higher CO2 change in light conditions. ")
}
if(p_nativity < 0.05) {
cat("Nativity had a significant effect (F = ",
round(anova_type3$`F value`[2], 2), ", p = ", round(p_nativity, 4), ").")
}
}No significant interaction was found (p = 0.3253 ). Light condition had a significant effect (F = 8.75 , p = 0.0104 ), with higher CO2 change in light conditions.