Two-way repeated measures ANOVA

Two-way repeated measures ANOVA, for designs with two within-subjects variables.

Description

%
% function stats = rm_anova2(Y,S,F1,F2,FACTNAMES)
%
% Two-factor, within-subject repeated measures ANOVA.
% For designs with two within-subject factors.
%
% Parameters:
% Y dependent variable (numeric) in a column vector
% S grouping variable for SUBJECT
% F1 grouping variable for factor #1
% F2 grouping variable for factor #2
% FACTNAMES a cell array w/ two char arrays: {'factor1', 'factor2'}
%
% Y should be a 1-d column vector with all of your data (numeric).
% The grouping variables should also be 1-d numeric, each with same
% length as Y. Each entry in each of the grouping vectors indicates the
% level # (or subject #) of the corresponding entry in Y.
%
% Returns:
% stats is a cell array with the usual ANOVA table:
% Source / ss / df / ms / F / p
%
% Notes:
% Program does not do any input validation, so it is up to you to make
% sure that you have passed in the parameters in the correct form:
%
% Y, S, F1, and F2 must be numeric vectors all of the same length.
%
% There must be at least one value in Y for each possible combination
% of S, F1, and F2 (i.e. there must be at least one measurement per
% subject per condition).
%
% If there is more than one measurement per subject X condition, then
% the program will take the mean of those measurements.
%
% Aaron Schurger (2005.02.04)
% Derived from Keppel & Wickens (2004) "Design and Analysis" ch. 18
%

• Required Products: Statistics Toolbox
• MATLAB release: MATLAB 6.5.1 (R13SP1)

[Aaron Schurger]

A very well-written program (of course, I wrote it myself). One or two additional features are of interest, so I would not yet call it excellent.

[Ted Zanto]

Excellent program...does exactly what it's designed for. Easy to implement and coded in a very straightforward manner. Results were confirmed in SPSS...right on the mark.

One tiny error on line 133: FACTNAMES{1} should be FACTNAMES{2}...but this merely a labeling issue.

Nonetheless, it's a great program, thanks Aaron!

[dojoon yi]

It is great. Thank you!!!

[Teck Por Lim]

The author had corrected the code after Ted Zanto's comment in 2005.

[adam mcnamara]

Examples with data are always very helpful.. this is what this lacks

[malia mason]

This worked well for me.

[Ashwin Sundar]

 

[Perspicacity Slim]

It would make my day if you could add Greenhouse-Geiser correction for violating the sphericity assumption of repeated measures ANVOA.

[keidit chankhachon]

 

[terence hill]

 

[piyush singhal]

 

[Zachary Danziger]

The stats output is a cell array of NaNs. Is this software capable of dealing with unequally distributed data? I.e., 7 subjects are evaluated on factor 1, but only 6 are evaluated on factor 2.

[Aaron Schurger]

Hi, Zachary,
Good question. No, it was not designed to deal with a different number of subjects on each factor. Sorry about that. It might not be too complicated to code, but I imagine that there are some statistical issues to be mindful of, and I would want to look into that before changing the code. In the meantime, you might be able to insert a dummy value, which is just the mean of the other values, just to make the program work. One thing that I can do is to make the program generate an error instead of just giving back nan's. It would help to see the data, just as you passed them to the program. -Aaron

[Negar]

Hi,

Can someone give me a one line example of how to enter FACTNAMES? I'd appreciate it.

[Robert]

I would also appreciate a one line example of how to enter FACTNAMES. I'm getting an error. Thanks!

[Alberich Qi]

I think it should be written as :

FACTNAMES = {F1name, F2name};
F1name = {'abc' , ..., 'xyz'};
F2name = {'xx', ..., 'yy'};

It can work well in my script.

[Marieke Rohde]

There's a mistake in this script: if several measurements are provided for one cell, it gives wrong values for the interaction. help says it would take the average in that case, which it does for the most part, but at some point it gets confused with the number of measurements taken and F and p are then really wrong (only concerns interaction with several values per cell).

By the way, RMAOV2 --> same functionality, even though a bit bulky, takes the variance across repeated measurements for the same cell into consideration.

[Jamie]

I agree this is a very well written script. However, I am somewhat confused about the Y input variable. In the comments above it says that 'Y' should be a column vector (I assume this means (:, 1)). My confusion comes from the following lines:

for i=1:a % F1
    for j=1:b % F2
        for k=1:n % Subjs
            INDS{i,j,k} = ...
            CELLS{i,j,k} = Y(INDS{i,j,k});
            MEANS(i,j,k) = mean(CELLS{i,j,k});
        end
    end
end

The '...' was placed instead of the code to create the indices. The line CELLS{i,j,k} = Y(INDS{i,j,k}); generates a 3D cell from Y, which makes sense to have the data in three dimensions, however Y is a 1D column and creates a large number of NaNs.

Also, Matlab produces the following error:

??? Error using ==> horzcat
CAT arguments dimensions are not consistent.

Error in ==> rm_anova2 at 138
stats = {'Source','SS','df','MS','F','p';...

Long story short, what am I not getting about this?

[titou]

Thanks a lot.

I precise I just needed to change :

F1==F1_lvls(i)

in

strcmp(F1,F1_lvls(i))==1

and it works great ! (same results as Statistica)

[Marieke Rohde]

for the data that made me spot the bug the script displays the following first three lines of the ANOVA tables.

If you take the average from multiple cells by hand:

'Source'SS df MS F p
'cond' 1.0413 1 1.0413 1.8483 0.1971
'hand' 0.2325 1 0.2325 1.7135 0.2132
'cxh' 0.1184 1 0.1184 2.7210 0.1230

if you enter several values for multiple cells, according to documentation, it should do the same thing automatically, but doesn't:

Source SS df MS F p
'cond' 1.0413 1 1.0413 1.8483 0.1971
'hand' 0.2325 1 0.2325 1.7135 0.2132
cdxhd 0.1184 1 0.1184 1.4417e-05 0.9970

which is jsut plainly wrong (note that first 3 columns are identical). i would be surprised if Statistica did the same. i did the calculations by hand at the time to figure out what exactly went wrong but cannot remember - if you're interested in the data please be in touch.

[Erin]

Good submission. I found this script gives the same results as anovan. To do repeated measures with anovan, its necessary to make another factor for subjects, and specify that factor as 'random'.

[Marieke]

the script works now - I appear to have had an old version of the script.

[Jordan]

This seems very promising, but I can't figure out what kind of input is needed. For instance, what is d in the function definitions, and are Y and grouping vectors meant to comprise one column or multiple columns? It would be very helpful if the author could include with his download a small .mat file with sample inputs for Y, F1, F2 etc.