Here is an example of how to perform ANOVA in R:
First, let's say we have a dataset with three variables: "group" (the group to which each observation belongs), "x" (the independent variable), and "y" (the dependent variable). We want to use ANOVA to determine whether there is a significant difference in the mean value of "y" between the groups.
First, we need to load the necessary libraries:
library(tidyverse)
library(broom)
Next, let's read in the data and take a look at it:
data <- read_csv("data.csv")
head(data)
# group x y
# 1 A 1 2.5164708
# 2 A 2 3.4593287
# 3 A 3 4.7047409
# 4 A 4 5.4292901
# 5 A 5 6.8230604
# 6 A 6 7.8731561
Now, let's fit the ANOVA model:
model <- aov(y ~ group, data=data)
We can then use the summary function to get a summary of the model fit:
summary(model)
# Call:
# aov(formula = y ~ group, data = data)
#
# Terms:
# group Residuals
# Sum of Squares 0.481 4.959
# Deg. of Freedom 2 27
#
# Residual standard error: 0.7068
# Estimated effects may be unbalanced
From the summary, we can see that there is a significant difference in the mean values of "y" between the groups (as indicated by the "Sum of Squares" value for the "group" term).
We can also use the Anova function from the car library to get a more detailed ANOVA table:
library(car)
Anova(model)
# Anova Table (Type II tests)
#
# Response: y
# Sum Sq Df F value Pr(>F)
# group 0.481 2 4.4154 0.0234737 *
# Residual 4.959 27
# ---
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
From the ANOVA table, we can see that the p-value for the "group" term
is significant (p < 0.05), indicating that there is a significant
difference in the mean values of "y" between the groups.