I was teaching on a field course and when the students started analysing their data in R, one of them noticed that if they switched around the independent variables in an `lm()`

they got different results with different methods of computing analysis of variance tables. I wanted to investigate it more, and this is the resulting R Markdown report that I wrote:

The report can be found here and is also pasted below

# Clear console

cat("\014")

# Add factors for the anova analyses

mtcars$group <- mtcars$cyl %>% gsub(4, "A", .) %>% gsub(6, "B", .) %>% gsub(8, "C", .) %>% as.factor(.)

mtcars$group2 <- as.factor(rep(c("D", "E", "F", "G"), times = 8))

mtcars$group3 <- as.factor(rep(c("H", "I"), times = 16))

mtcars$group4 <- as.factor(rep(c("J", "J", "K", "K", "L", "L", "M", "M", "J", "K", "L", "M", "M", "L", "K", "J"), times = 2))

head(mtcars)

summary(mod1)

mod <- lm(y ~ continuous + grouping)

Anova(mod, method = "II")