Repeated measures ANOVA with two variables

Hello,

I'm trying to carry out a repeated-measures ANOVA for the following data:

Normally, I would get the significance value for the two main factors (i.e. Crowding and Beta) as well as the significance value for the interaction (Crowding*Beta). Also, I would like to run the post-hoc analyses. I can't find the proper code to run this simple analysis, would very much appreciate any help.

-Mikel

[Scott MacKenzie]

It would help if you post the actual data, rather than an image of the data.

[Mikel Jimenez]

Hi Scott,

Here.

-Mikel

Answer 1

[Scott MacKenzie]

Here's what I put together. None of the effects are statistically significant. See below. Were the data in the Value column just randomly generated? Fair enough, since you're mostly just trying get off and running with ranova.

BTW, I'm including a function at the end to re-work the table generated by ranova into a more conventional format. If you want to compare my table to the one generated by ranova, just remove the semicolon at the end of the ranova line.

% read data (sorted, 2x2 within-subjects design with 17 participants)
f = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/696039/Q2.xls';
T = readtable(f);

% ingore extra data at end
T = T(1:2*2*17,:);

% organize the data in a 17x4 matrix (1 row per participant)
dv = array2table(reshape(T.Value, 17, [])); % dependent variable is 'Value'

% codes for column names: gr=grouped, ug=ungrouped, b1=beta1, b2=beta2
dv.Properties.VariableNames = {'grb1', 'grb2', 'ugb1', 'ugb2' };

% create the within-subjects design
withinDesign = table([1 1 2 2]',[1 2 1 2]','VariableNames',{'Crowding','Beta'});
withinDesign.Crowding = categorical(withinDesign.Crowding);
withinDesign.Beta = categorical(withinDesign.Beta);

% create repeated measures model
rm = fitrm(dv, 'grb1-ugb2 ~ 1', 'WithinDesign', withinDesign);

% perform anova (remove semicolon to view table generated by ranova)
AT = ranova(rm, 'WithinModel', 'Crowding*Beta');

% output an improved version of the anova table
disp(anovaTable(AT, 'Value'));

ANOVA table for Value
===================================================================================
Effect                       df         SS             MS          F          p
-----------------------------------------------------------------------------------
Participant                  16          0.992          0.062                      
Crowding                      1          0.064          0.064      0.607     0.4472
Participant(Crowding)        16          1.679          0.105                      
Beta                          1          0.281          0.281      3.295     0.0883
Participant(Beta)            16          1.364          0.085                      
Crowding:Beta                 1          0.000          0.000      0.005     0.9473
Participant(Crowding:Beta)   16          1.306          0.082                      
===================================================================================

% -----------------------------------------------------------------------------------
% Scott's function to create a standard-looking ANOVA table from the
% terrible 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; % field needed for df, SS, MS, F, and p columns

barDouble = sprintf('%s\n', repmat('=', 1, fieldWidth1 + fieldWidth2));
barSingle = sprintf('%s\n', 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 barDouble];
s = [s sprintf('%-*s %4s %10s %14s %10s %10s\n', fieldWidth1, 'Effect', 'df', 'SS', 'MS', 'F', 'p')];
s = [s barSingle];
s = [s, sprintf('%-*s %4d %14.3f %14.3f %10.3f %10.4f\n', c{:})];
s = [s, barDouble];

end

[Mikel Jimenez]

Hi Scott,

Thank you very very much for your time. Indeed I generated the values randomly so it is not surprising that there is no significant effect.

The code is great, I got the results and the cusom table looks fantastic. Now, if I would have to run post-hoc analyses on a significant interaction, I would need to use the "multcompare" function, is it correct?

Best,

Mikel

[Scott MacKenzie]

@Mikel Jimenez, you're welcome. Glad to help.

Yes, multcompare is your tool for post hoc pairwise testing. Since your factors only have two levels each, such a test isn't necessary. If you want to do the comparisons between your 2x2 = 4 conditions, then you need to define a new/fake variable for the 4 conditions. The following code can be added to my answer for this purpose. Spioler alert: None of the pairs differ significantly.

% post hoc comparisons between the 4 columns (2 factors merged)
withinDesign2 = table([1 2 3 4]', 'VariableNames', {'IV2'});
withinDesign2.IV2 = categorical(withinDesign2.IV2);
rm2 = fitrm(dv, 'grb1-ugb2 ~ 1', 'WithinDesign', withinDesign2);
multcompare(rm2, 'IV2')

[Mikel Jimenez]

Hi Scott,

If the interaction would have been significant, I think I would've need to look to the pairwise tests. Anyway, thank you very very much again, the code with the multcompare seems to work fine too!

Best,

Mikel