Published on September 08, 2025 • By EduResHub Team
Chi-square Tests in R Author Your Name Published September 7, 2025 Introduction This report demonstrates two applications of the Chi-square test in R using hypothetical agricultural entomology data: Chi-square Test of Independence – to check association between two categorical variables. Chi-square Goodness of Fit – to check whether observed counts match expected proportions. 1. Chi-square Test of Independence We want to test if the level of pest infestation (High/Low) depends on the crop type (Tea, Citrus, Mango). library(ggplot2) library(reshape2) Data pest_data <- matrix(c(25, 15, 30, 20, 10, 30), nrow = 3, byrow = TRUE) colnames(pest_data) <- c("High", "Low") rownames(pest_data) <- c("Tea", "Citrus", "Mango") pest_data High Low Tea 25 15 Citrus 30 20 Mango 10 30 Chi-square Test chisq_test <- chisq.test(pest_data) chisq_test Pearson's Chi-squared test data: pest_data X-squared = 14.5, df = 2, p-value = 0.0007102 Interpretation Null hypothesis (H₀): Crop type and pest infestation are independent. Alternative hypothesis (H₁): Crop type and pest infestation are associated. If p-value < 0.05, reject H₀ → pest infestation depends on crop type. From the test results, the p-value is very small (<0.05), so we reject H₀. ➡️ Pest infestation is significantly associated with crop type. Visualization # Mosaic plot mosaicplot(pest_data, main="Pest Infestation by Crop Type", color=TRUE, xlab="Crop Type", ylab="Pest Level") # Bar plot df <- melt(pest_data) colnames(df) <- c("Crop", "Pest_Level", "Count") ggplot(df, aes(x=Crop, y=Count, fill=Pest_Level)) + geom_bar(stat="identity", position="dodge") + labs(title="Pest Infestation by Crop Type", x="Crop Type", y="Number of Plots") + theme_minimal() 2. Chi-square Goodness of Fit We want to test if ladybird beetles are uniformly distributed across 4 blocks in a tea garden. Data observed <- c(18, 22, 25, 15) expected <- c(20, 20, 20, 20) df_gof <- data.frame( Block = c("A","B","C","D"), Observed = observed, Expected = expected ) df_gof Block Observed Expected 1 A 18 20 2 B 22 20 3 C 25 20 4 D 15 20 Chi-square Test chisq_gof <- chisq.test(observed, p = rep(1/4, 4)) chisq_gof Chi-squared test for given probabilities data: observed X-squared = 2.9, df = 3, p-value = 0.4073 Interpretation Null hypothesis (H₀): Ladybird beetles are uniformly distributed across blocks. Alternative hypothesis (H₁): Distribution deviates from uniform. If p-value < 0.05, reject H₀ → not uniform distribution. From the test results, the p-value is > 0.05, so we fail to reject H₀. ➡️ Beetles are fairly evenly spread across the blocks. Visualization df_long <- melt(df_gof, id.vars="Block") ggplot(df_long, aes(x=Block, y=value, fill=variable)) + geom_bar(stat="identity", position="dodge") + labs(title="Goodness of Fit: Ladybird Beetle Distribution", x="Block", y="Count") + theme_minimal() Conclusion The Chi-square Test of Independence showed a significant association between crop type and pest infestation. The Chi-square Goodness of Fit Test showed that ladybird beetles are uniformly distributed across blocks. Both examples illustrate how Chi-square tests can be applied in agricultural entomology research.