One-way Repeated Measures ANOVA

This guide covers how to conduct one-way repeated measures ANOVA with the jmv and rstatix packages. Repeated measures ANOVAs are used in cases where an observation from the same subject is taken multiple times. For example, an experimenter may wish to examine the changes in scores from a cognitive assessment gathered from the same participants at multiple ages.

The data set

The chapter_11_table_5 dataset from the AMCP package is from a hypothetical study that tracked the age-normed general cognitive scores from the McCarthy Scales of Children’s Abilities (MSCA) of 12 children at 4 different time points, .

library(AMCP)
library(kableExtra)
# Load data
data("chapter_11_table_5")

# Inspect data
kable(head(chapter_11_table_5))

Months30	Months36	Months42	Months48
108	96	110	122
103	117	127	133
96	107	106	107
84	85	92	99
118	125	125	116
110	107	96	91

Perform ANOVA tests

With the jmv package, coding repeated measures ANOVA is a bit more cumbersome compared to one- and two-way ANOVAS. We will have to set the rm option which takes a “list of lists”. For the one-way repeated measures design, we will need a list of one list that contains a label which will be “Age-in-months”, and a character vector of the levels of the age factor (i.e. 30, 60, 42, 48). Next, we will work on the rmCells by making another list of lists. This list will be made up of 4 lists, one for each level, and each list will have a measure that corresponds to the name of the column of the dataframe containing the data, and a cell that corresponds to each level. Now we can move on to specifying the repeated measure terms in “rmTerms.” For our purposes we will set spherCorr = 'none', but in practice you may want to apply a correction for sphericity depending on your data. We will then set effectSize = 'omega', and set emMeans = TRUE to produce the marginal means by months so that we can plot the data when emmPlots = TRUE.

library(jmv)

# Repeated measures anova with jmv
anovaRM(
  data = chapter_11_table_5,
  rm = list(
    list(
      label = "Age-in-months", 
      levels = c("30", "36", "42", "48"))),
  rmCells = list(
    list(
      measure = "Months30", 
      cell = "30"),
    list(
      measure = "Months36", 
      cell = "36"),
    list(
      measure = "Months42", 
      cell = "42"),
    list(
      measure = "Months48", 
      cell = "48")),
  rmTerms = list(
    "Age-in-months"),
  spherCorr = 'none',
  effectSize = 'partEta',
  emMeans = ~ `Age-in-months`,
  emmPlots = TRUE,
  postHocCorr = "none",
  postHoc = "Age-in-months",
  depLabel = "Mean MSCA Scores")

## 
##  REPEATED MEASURES ANOVA
## 
##  Within Subjects Effects                                                                        
##  ────────────────────────────────────────────────────────────────────────────────────────────── 
##                     Sum of Squares    df    Mean Square    F           p            η²-p        
##  ────────────────────────────────────────────────────────────────────────────────────────────── 
##    Age-in-months          552.0000     3      184.00000    3.026919    0.0432186    0.2157936   
##    Residual              2006.0000    33       60.78788                                         
##  ────────────────────────────────────────────────────────────────────────────────────────────── 
##    Note. Type 3 Sums of Squares
## 
## 
##  Between Subjects Effects                                                           
##  ────────────────────────────────────────────────────────────────────────────────── 
##                Sum of Squares    df    Mean Square    F    p            η²-p        
##  ────────────────────────────────────────────────────────────────────────────────── 
##    Residual          6624.000    11       602.1818                                  
##  ────────────────────────────────────────────────────────────────────────────────── 
##    Note. Type 3 Sums of Squares
## 
## 
##  POST HOC TESTS
## 
##  Post Hoc Comparisons - Age-in-months                                                                          
##  ───────────────────────────────────────────────────────────────────────────────────────────────────────────── 
##    Age-in-months         Age-in-months    Mean Difference    SE          df          t             p           
##  ───────────────────────────────────────────────────────────────────────────────────────────────────────────── 
##    30               -    36                     -4.000000    2.579053    11.00000    -1.5509568    0.1491893   
##                     -    42                     -7.000000    3.045115    11.00000    -2.2987635    0.0421235   
##                     -    48                     -9.000000    3.692745    11.00000    -2.4372115    0.0329854   
##    36               -    42                     -3.000000    2.757909    11.00000    -1.0877807    0.2999517   
##                     -    48                     -5.000000    4.316985    11.00000    -1.1582156    0.2713044   
##    42               -    48                     -2.000000    2.232677    11.00000    -0.8957855    0.3895495   
##  ─────────────────────────────────────────────────────────────────────────────────────────────────────────────

Figure 1: anovaRM plot of means by group.

To perform a repeated measures ANOVA with rstatix, first create a new data frame with the subject id coded by a number. Next, convert the data from wide to long format. Next, convert the subject id and the age information to factor. Then, create the rm_aov object with the anova_test() function. This is the same function that was used in the one- and two-way ANOVA guides, but modified slightly. The modifications are found in the options wid = id to specify the subjects id factor, within = age to specify that our within subjects factor is age, and effect.size = "pes" to correspond with the jmv function. Finally, we will run the get_anova_table() function on our rm_aov object with correction = "none". In practice, you may want to change the correction setting even if your data do not violate the assumption of sphericity.

library(tidyverse)
library(rstatix)
library(ggpubr)

# Create a new data frame with a subject id
rm_data <- cbind(id = c(1:12), chapter_11_table_5)

# Convert from wide to long format then convert id and age to factor
rm_data <- rm_data %>% 
  gather(., age, score, Months30:Months48) %>%
  convert_as_factor(id, age)

# Inspect data
kable(head(rm_data))

id	age	score
1	Months30	108
2	Months30	103
3	Months30	96
4	Months30	84
5	Months30	118
6	Months30	110

Conduct repeated measures ANOVA

rm_aov <- anova_test(data = rm_data, 
                     dv = score, 
                     wid = id, 
                     within = age, 
                     effect.size = "pes", 
                     detailed = TRUE)

# Print anova table
kable(get_anova_table(rm_aov, correction = "none"))

Effect	DFn	DFd	SSn	SSd	F	p	p<.05	pes
(Intercept)	1	11	559872	6624	929.739	0.000	*	0.988
age	3	33	552	2006	3.027	0.043	*	0.216

Pairwise comparisons with pairwise_t_test

pwc <- rm_data %>%
  pairwise_t_test(score ~ age, 
                  paired = TRUE, 
                  p.adjust.method = "none")
kable(pwc)

.y.	group1	group2	n1	n2	statistic	df	p	p.adj	p.adj.signif
score	Months30	Months36	12	12	-1.5509568	11	0.149	0.149	ns
score	Months30	Months42	12	12	-2.2987635	11	0.042	0.042	*
score	Months30	Months48	12	12	-2.4372115	11	0.033	0.033	*
score	Months36	Months42	12	12	-1.0877807	11	0.300	0.300	ns
score	Months36	Months48	12	12	-1.1582156	11	0.271	0.271	ns
score	Months42	Months48	12	12	-0.8957855	11	0.390	0.390	ns

Plot the data

To plot the data, we can use the ggerrorplot() function. We will use the converted long-form rm_data rather than the wide chapter_11_table_5 dataframe. Then we just need to specify what to plot on the x and y axes, set add = "mean", desc_stat = "mean_ci", error.plot = “errorbar”, and width = .1.

ggerrorplot(rm_data,
            x = "age",
            y = "score",
            add = "mean",
            desc_stat = "mean_ci",
            error.plot = "errorbar",
            width = .1)

Figure 2: ggerrorplot plot of means and 95% confidence intervals by group.

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Interpretation

For the omnibus test, we obtain a significant effect of Age [F(33,3) = 3.03, p < 0.05] which suggests that the means of the 4 ages are not equal. The omega squared value is 0.04 which suggest the about 4% of the variance in scores is accounted for by age in the ages studied.

Wrap up

For one-way repeated measures ANOVA, using the jmv package in R will become tedious as each column will need to specified in the rmCells = list(... argument. This will become even more burdensome in two-way repeated measures ANOVA.

References

Kassambara, Alboukadel. 2020a. Ggpubr: ’Ggplot2’ Based Publication Ready Plots. https://CRAN.R-project.org/package=ggpubr.

———. 2020b. Rstatix: Pipe-Friendly Framework for Basic Statistical Tests. https://CRAN.R-project.org/package=rstatix.

Maxwell, Scott, Harold Delaney, and Ken Kelley. 2020. AMCP: A Model Comparison Perspective. https://CRAN.R-project.org/package=AMCP.

Maxwell, Scott E, Harold D Delaney, and Ken Kelley. 2017. Designing Experiments and Analyzing Data: A Model Comparison Perspective. Routledge.

Selker, Ravi, Jonathon Love, and Damian Dropmann. 2020. Jmv: The ’Jamovi’ Analyses. https://CRAN.R-project.org/package=jmv.

Wickham, Hadley. 2019. Tidyverse: Easily Install and Load the ’Tidyverse’. https://CRAN.R-project.org/package=tidyverse.

Last updated on Oct 8, 2023

Months30	Months36	Months42	Months48
108	96	110	122
103	117	127	133
96	107	106	107
84	85	92	99
118	125	125	116
110	107	96	91

Months30	Months36	Months42	Months48
108	96	110	122
103	117	127	133
96	107	106	107
84	85	92	99
118	125	125	116
110	107	96	91

Months30	Months36	Months42	Months48
108	96	110	122
103	117	127	133
96	107	106	107
84	85	92	99
118	125	125	116
110	107	96	91