相关软件（R代码）

# 单因素方差分析
fertilizer_data <- data.frame(
  height = c(18.3, 19.3, 24.7, 20.2, 20.4, 25.1, 21.4, 16.2, 17.9, 18.7,
             13.0, 20.4, 24.4, 7.3, 21.1, 21.5, 16.1, 16.3, 16.2, 14.5,
             20.9, 19.1, 26.0, 23.3, 23.3, 28.1, 23.1, 25.0, 27.1, 24.2,
             15.3, 16.5, 17.2, 20.9, 13.0, 19.0, 14.3, 21.8, 15.5, 19.7),
  group = factor(rep(c("A", "B", "C", "D"), each = 10))
)
# ANOVA
anova_result <- aov(height ~ group, data = fertilizer_data)
summary(anova_result)
# 方差齐性检验（Levene检验）
# install.packages("car")
library(car)
leveneTest(height ~ group, data = fertilizer_data)
# 事后检验：Tukey HSD
TukeyHSD(anova_result)
# 可视化
boxplot(height ~ group, data = fertilizer_data, 
        main = "不同肥料对植物高度的影响", ylab = "高度(cm)", col = "lightblue")
# 双因素方差分析示例
# 假设研究肥料类型和光照条件对植物高度的影响
two_way_data <- data.frame(
  height = c(rnorm(10, 20, 2), rnorm(10, 25, 2), rnorm(10, 18, 2), rnorm(10, 22, 2)),
  fertilizer = factor(rep(c("A", "A", "B", "B"), each = 10)),
  light = factor(rep(c("Low", "High"), each = 20))
)
aov_two <- aov(height ~ fertilizer * light, data = two_way_data)
summary(aov_two)

2.2.6 多重检验校正