How to Perform
Repeated Measures
ANOVA in R

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What is a Repeated Measures ANOVA?

Repeated-measures ANOVA is used when we have one group on which we measured something more than once. In other words, repeated measures designs, also known as within-subjects designs, can seem like oddball experiments. When you think of a typical experiment, you probably picture an experimental design that uses mutually exclusive, independent groups. These experiments have a control group and treatment groups that have clear divisions between them. Each subject is in only one of these groups.

When Should a Repeated Measures ANOVA Used?

GLM Repeated Measures is an ANOVA with repeated measures. We use ANOVA with repeated measures when we want to determine whether there is a difference between continuous variables measured multiple times in the same group of participants. For example, we want to determine whether exercise has an effect on weight loss in a group of 20 participants. Therefore, we will measure the weight of those participants before exercise, after 3 months of exercise, and after 6 months of exercise and we will compare the mean values of each group using an ANOVA with repeated measures.

An Example Of Repeated ANOVA

For example, a researcher wants to examine whether psychotherapy is beneficial. Therefore, it measures the level of anxiety before the start of psychotherapy, 3 months after psychotherapy, and 6 months after psychotherapy. Therefore, we have one variable – the level of anxiety, which we measure in three time periods.

Therefore, we test the following hypotheses:

Null hypothesis: There is no significant effect of psychotherapy on the level of anxiety.

Alternative hypothesis: There is a significant effect of psychotherapy on the level of anxiety.

R function to Compute Repeated Measures ANOVA

The code to run a repeated measures ANOVA using R is as follows:

aov (DV~ factor (time) + Error (factor (IV)), data = dataframe)

DV: dependent variable

IV: Independent variable

Running Repeated Measures ANOVA in Rstudio

In this section, we will show you how to run the repeated measures ANOVA using the r studio program and how to interpret the test results after we obtain the result of the test. In the first part, we present the r program code and function for the repeated measures ANOVA. Next, you will see the outputs as a result of running the r codes. In the last section, you can find the interpretation of the repeated ANOVA in APA format.

# LOAD DATA
library(readxl)
Data <- read_excel(“Data.xlsx“)
# VIEW DATA
View(Data)
# NAME VARIABLES
data <- Data
time <- data$time
score <- data$score
student <- data$student

# PERFORM REPEATED MEASURES ANOVA
model <- aov(score~factor(time)+Error(factor(student)), data = data)
summary(model)

> model <- aov(score~factor(time)+Error(factor(student)), data = data)
> summary(model)

## 
## Error: factor(student)
##           Df Sum Sq Mean Sq F value Pr(>F)
## Residuals 32  11365   355.2               
## 
## Error: Within
##              Df Sum Sq Mean Sq F value Pr(>F)
## factor(time)  2    198    98.9   0.203  0.817
## Residuals    64  31229   488.0

Reporting Repeated Measures ANOVA in R

Repeated measures ANOVA was conducted to determine the effect of psychotherapy (before the start of psychotherapy, 3 months after psychotherapy, and 6 months after psychotherapy) on anxiety levels.The results indicate a non-significant effect of psychotherapy, F(2, 64) = 0.20, p = 0.817. We, therefore, fail to reject the null hypothesis and conclude that there is no effect of psychotherapy (before the start of psychotherapy, 3 months after psychotherapy and 6 months after psychotherapy) on anxiety levels.

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How to Perform Repeated Measures ANOVA in R