how to calculate three way repeated anova?

how to perform 3 way repeated anova in Matlab? I have two levels in stress , 2 levels in performers , and 2 levels in feedback as reward / penlaty. Stress and performers are between subject factor and the feedback is within subject factor. I want to apply three way repeated anova ? The data is attached.

[Ayush]

To perform a three-way repeated measures ANOVA in Matlab with stress and performers as between-subject factors and feedback as the within-subject factor, you can use the "fitrm" and "ranova" functions from the Statistics and Machine Learning Toolbox.

You can read more about them from the following links:

Fit repeated measures model - MATLAB fitrm (mathworks.com)

Repeated measures analysis of variance - MATLAB (mathworks.com)

Answer 1

[Scott MacKenzie]

It seems you have a design with three independent variables. Two are between-subjects and one is within-subjects:

• Stress (between-subjects)
• Performance (between-subjects)
• Feedback (within-subjects)

Below is a script for a three-way ANOVA for your data.

Personally, I don't like the table created by MATLAB's ranova function, so I'm also including a function that creates a more conventional ANOVA output table from the ranova output. The dependent variable is just named "DV" in the table since you didn't name the variable in your question.

% load your data into data table
load(websave('data', 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/1305605/data.mat'))
data.Properties.VariableNames = {'Stress', 'Performance', 'Reward', 'Penalty'};

% setup and do the three-way ANOVA
withinDesign = table([1 2]','VariableNames',{'Feedback'});
withinDesign.Feedback = categorical(withinDesign.Feedback);
rm = fitrm(data,'Reward-Penalty ~ Stress*Performance','WithinDesign',withinDesign);
AT = ranova(rm, 'WithinModel', 'Feedback');

% output a conventional ANOVA table from ranova output
disp(anovaTable(AT, 'DV'));

ANOVA table for DV
====================================================================================
Effect                        df          SS             MS         F         p
------------------------------------------------------------------------------------
Stress                         1        5.79207        5.79207      0.657     0.4199
Performance                    1        5.53506        5.53506      0.628     0.4304
Stress:Performance             1        5.91156        5.91156      0.671     0.4152
Participant                   82      722.72762        8.81375                      
Feedback                       1        0.17949        0.17949      0.175     0.6770
Stress:Feedback                1        0.12170        0.12170      0.119     0.7315
Performance:Feedback           1        0.00098        0.00098      0.001     0.9754
Stress:Performance:Feedback    1        0.07972        0.07972      0.078     0.7812
Participant(Feedback)         82       84.21282        1.02699                      
====================================================================================

% -------------------------------------------------------------------------
% function to create a conventional ANOVA table from the overly-complicated
% 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) = {''};
    end
    if c{i,5} == .5
        c(i,5) = {''};
    end
end

% 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};
end

% 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)];

end