How to do ANOVA repeated measures?

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I have 12 Female and 11 Male rats which participate in a sucrose tracking experiment for 4 different levels of sucrose concentration. I have approach rate data (between 0 and 1) for each animal for 4 different concentration. I have attached the figure. I want to do ANOVA repeated measures for the experiment to check the effect of concentration as well as gender. I wrote this following code. But I'm not sure if this is correct or how to interpret the result.
dataForFemale = loadFile.featureForEachSubjectId{1};
dataForMale = loadFile.featureForEachSubjectId{2};
for i = 1:4
dataMatrix(:,i) = [dataForFemale{i} dataForMale{i}]';
Gender = [repmat({'F'},1,length(dataForFemale{1})),repmat({'M'},1,length(dataForMale{1}))]';
t = [Gender, array2table(dataMatrix)];
t.Properties.VariableNames = {'Gender','c1','c2','c3','c4'};
rm = fitrm(t, 'c1-c4 ~ Gender', 'WithinDesign', table([1, 2, 3, 4]','VariableNames', {'Concentration'}));
result = ranova(rm);
multcompare(rm, 'Concentration', 'By', 'Gender');
Scott MacKenzie
Scott MacKenzie on 1 May 2023
Edited: Scott MacKenzie on 1 May 2023
You're welcome. I just had another look and notice that you omitted the within-subjects IV (sucrose concentration) in the ranova function. I've added it, rearranged the code slightly, and posted an answer. Hope this helps.

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Accepted Answer

Scott MacKenzie
Scott MacKenzie on 1 May 2023
Edited: Scott MacKenzie on 1 May 2023
Here's a script for the ANOVA that includes both the within-subjects IV (sucrose concentration and the between-subjects IV (gender).
As you can see, the effect of gender on approach_avoid was not statistically significant (F1,21 = 3.83, p > .05), but the effect of sucrose_concentration on approach_avoid was (F3,63 = 118.5, p < .001). If you examine m (the output from multcompare), you'll see which pairwise differences by gender were statistically significant. There were lots!
Note: I don't like the ANOVA table generated by ranova. The script below below includes a function to create a more conventional ANOVA table from the ranova output. Of course, for your research, "Participants" is "Rats".
load(websave('tmp', ''));
dataForFemale = featureForEachSubjectId{1};
dataForMale = featureForEachSubjectId{2};
for i = 1:4
dataMatrix(:,i) = [dataForFemale{i} dataForMale{i}]';
Gender = [repmat({'F'},1,length(dataForFemale{1})),repmat({'M'},1,length(dataForMale{1}))]';
t = [Gender, array2table(dataMatrix)];
t.Properties.VariableNames = {'Gender','c1','c2','c3','c4'};
% setup and do the ANOVA
withinDesign = table([1 2 3 4]', 'VariableNames', {'Sucrose_Concentration'});
withinDesign.Sucrose_Concentration = categorical(withinDesign.Sucrose_Concentration);
rm = fitrm(t,'c1-c4 ~ Gender', 'WithinDesign', withinDesign);
result = ranova(rm, 'WithinModel', 'Sucrose_Concentration');
% do post hoc multiple comparisons (check m for significant pairwise differences)
m = multcompare(rm, 'Sucrose_Concentration', 'By', 'Gender');
% output a conventional ANOVA table
disp(anovaTable(result, 'Approach_Avoid'));
ANOVA table for Approach_Avoid =========================================================================================== Effect df SS MS F p ------------------------------------------------------------------------------------------- Gender 1 0.07668 0.07668 3.827 0.0639 Participant 21 0.42081 0.02004 Sucrose_Concentration 3 7.05085 2.35028 118.527 0.0000 Gender:Sucrose_Concentration 3 0.13201 0.04400 2.219 0.0946 Participant(Sucrose_Concentration) 63 1.24924 0.01983 ===========================================================================================
% -------------------------------------------------------------------------
% function to create a conventional ANOVA table from the overly-complicated
% and confusing anova table created by the ranova function.
function [s] = anovaTable(AT, dvName)
c = table2cell(AT);
% remove erroneous entries in F and p columns
for i=1:size(c,1)
if c{i,4} == 1
c(i,4) = {''};
if c{i,5} == .5
c(i,5) = {''};
% use conventional labels in Effect column
effect = AT.Properties.RowNames;
for i=1:length(effect)
tmp = effect{i};
tmp = erase(tmp, '(Intercept):');
tmp = strrep(tmp, 'Error', 'Participant');
effect(i) = {tmp};
% determine the required width of the table
fieldWidth1 = max(cellfun('length', effect)); % width of Effect column
fieldWidth2 = 57; % width for df, SS, MS, F, and p columns
barDouble = repmat('=', 1, fieldWidth1 + fieldWidth2);
barSingle = repmat('-', 1, fieldWidth1 + fieldWidth2);
% re-organize the data
c = c(2:end,[2 1 3 4 5]);
c = [num2cell(repmat(fieldWidth1, size(c,1), 1)), effect(2:end), c]';
% create the ANOVA table
s = sprintf('ANOVA table for %s\n', dvName);
s = [s sprintf('%s\n', barDouble)];
s = [s sprintf('%-*s %4s %11s %14s %9s %9s\n', fieldWidth1, 'Effect', 'df', 'SS', 'MS', 'F', 'p')];
s = [s sprintf('%s\n', barSingle)];
s = [s sprintf('%-*s %4d %14.5f %14.5f %10.3f %10.4f\n', c{:})];
s = [s sprintf('%s\n', barDouble)];
Scott MacKenzie
Scott MacKenzie on 3 May 2023
You're welcome. Good luck with your research.

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