How to use ranova?

I have a set of data. The data is from 5 subjects, the same measure is taken from each subject 3 times. Each measure has a different condition applied. I want to look for differences between conditions.

Because I have repeated measures from each subject, I assume I should use ranova. However, it seems like I need a variable that is not "within subject" to get ranova to work. For example, if I had the same experiemental design but male and female subjects then ranova would work. I don't want to use anova1 because to my understanding that treats every measure as a different subject. Any help would be greatly appreciated.

I have tried using ranova with all subjects as 1 groups, and each subject as a different group. Neither has worked for me.

clear,clc
close all

Measurement=[101.053914979877,39.9882799952772,1.10267662721688;216.136311110424,70.1362721192365,1.25119134782814;26.5334559925966,81.1211148269482,1.54372037819131;231.177535625968,135.886529812943,0.890020347986787;140.395359593013,37.2109788038507,0.00626713939985805];

sub=table([1 2 3]','VariableNames',{'Condition'});

subject1=['1'; '2'; '3'; '4'; '5'];
t1=table(subject1,Measurement(:,1),Measurement(:,2),Measurement(:,3),'VariableNames',{'subject','A','B','C'});
rm1=fitrm(t1,'A-C ~ subject','WithinDesign',sub);
ranovatbl1=ranova(rm1,'WithinModel','Condition');
c3=multcompare(rm1,'Condition');

subject2=['1'; '1'; '1'; '1'; '1'];
t2=table(subject2,Measurement(:,1),Measurement(:,2),Measurement(:,3),'VariableNames',{'subject','A','B','C'});
rm2=fitrm(t2,'A-C ~ subject','WithinDesign',sub);
ranovatbl2=ranova(rm2,'WithinModel','Condition');
c4=multcompare(rm2,'Condition');

Answer 1

[Scott MacKenzie]

You note: it seems like I need a variable that is not "within subject" to get ranova to work.

Actually, that's not the case. You can use ranova for a design that has just one within-subjects factor, as is the case with your data.

Here's what I put together for the data in your question. I used the labels "Condition" for the independent variable and "Measure" for the dependent variable. As seen in the anova table below, there is a significant effect of Condition on Measure: F(2,8) = 10.439, p < .01.

The code below includes a function I wrote that creates a more conventional anova table from the overly-complicated table produced by ranova.

% data from question (1 within-subjects factor with 3 levels, 5 participants)
M = [1 101.05  39.99 1.10;
    2  216.14  70.14 1.25;
    3   26.53  81.12 1.54;
    4  231.18 135.89 0.89;
    5  140.40  37.21 0.01];

% organize the data in a table
T = array2table(M(:,2:end));
T.Properties.VariableNames = {'A' 'B' 'C'};

% create the within-subjects design
withinDesign = table([1 2 3]','VariableNames',{'Condition'});
withinDesign.Condition = categorical(withinDesign.Condition);

% create the repeated measures model and do the anova
rm = fitrm(T,'A-C ~ 1','WithinDesign',withinDesign);
AT = ranova(rm,'WithinModel','Condition'); % remove comma to see ranova's table

% output a conventional anova table
disp(anovaTable(AT, 'Measure (units)'));

ANOVA table for Measure (units)
===============================================================================
Effect                   df          SS             MS         F         p
-------------------------------------------------------------------------------
Participant               4      15513.713       3878.428                      
Condition                 2      50484.917      25242.459     10.439     0.0059
Participant(Condition)    8      19344.377       2418.047                      
===============================================================================

% ---------------------------------------------------------------------
% Scott's 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) = {''};
        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 %11s %14s %9s %9s\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