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Is there a way to Run a One-Way Repeated Measures ANOVA to Compare Two Test Scores (Midterm Exam vs Final Exam) in RStudio?

I have two columns of data (one column for midterm exam grades for each student and one column for final exam grades for each student).

I want to compare each student's midterm and final exam grades (dependent groups with same subjects) using a repeated measures ANOVA just to see.

How would you go about that in RStudio? What's the easiest way to do this?

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1 Answer 1

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It's actually better if you provide your dataset, or in R, you can do dput() and paste the output.

Based on your description, i simulate data that might look like yours:

library(tidyr)
set.seed(111)
df = data.frame(student=factor(1:100),midterm=rnorm(100,50,5),final=rnorm(100,50,5))

head(df)
  student  midterm    final
1       1 51.17610 52.99810
2       2 48.34632 44.19835
3       3 48.44188 52.19547
4       4 38.48827 51.02427
5       5 49.14562 46.50409
6       6 50.70139 45.36687

Above, if your id is numeric, you need to ensure it's a factor for the remaining analysis to be correct. Now you need to pivot the data columns long:

df_long = pivot_longer(df,cols=c("midterm","final"),names_to="exam_type")

     student exam_type value
  <fct>   <chr>     <dbl>
1 1       midterm    51.2
2 1       final      53.0
3 2       midterm    48.3
4 2       final      44.2
5 3       midterm    48.4
6 3       final      52.2

I store the long format as a new data.frame and apply the anova, since it is a one-way repeated measure, you want to partition the variance or sum of squares (SS) into $SS_{total} = SS_{exam type} + SS_{within_student} + SS_{error}$.

Depending on the package used in R, there are many ways of specifying this structure above, you can check out this link. Below I show one way of doing repeated measure anova using aov(), where the error term specified as (student/):

anova_test = aov(value ~ exam_type + Error(student/exam_type),data=df_long)
summary(anova_test)

Error: student
          Df Sum Sq Mean Sq F value Pr(>F)
Residuals 99   2552   25.77               

Error: student:exam_type
          Df Sum Sq Mean Sq F value Pr(>F)
exam_type  1      0    0.02   0.001  0.979
Residuals 99   2857   28.86       
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  • $\begingroup$ Thanks man. Sorry I didn't provide the data. May I ask why the error is necessary in repeated measures ANOVA? I never encountered this with some RStudio codes. $\endgroup$
    – Dew Man
    Commented Jun 22, 2020 at 18:49
  • $\begingroup$ Hi @DewMan, sorry just realized I made a mistake. The answer is now correct, I got a bit confused with something else I normally use. I have also added an explanation of why you need to have the Error().. $\endgroup$
    – StupidWolf
    Commented Jun 22, 2020 at 19:31
  • $\begingroup$ Or are you supposed to do actually something else that is not repeated measure? $\endgroup$
    – StupidWolf
    Commented Jun 22, 2020 at 19:31
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    $\begingroup$ No this is what I wanted. Thanks. I know how to use a paired t-test for this situation but not a repeated measures ANOVA (very similar to paired t-test but an extension of it). I just wanted to compare the results for both on two groups (midterm vs final). $\endgroup$
    – Dew Man
    Commented Jun 22, 2020 at 19:56
  • $\begingroup$ I ran the Repeated Measures ANOVA test and t-test separately but I got very different answers for some reasons. $\endgroup$
    – Dew Man
    Commented Jun 24, 2020 at 17:48

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