How to perform 1way-ANOVA with matrices

Hello,

I would like to perform a 1-way ANOVA test to compare 3 groups such as I get group1 VS group2, group1 VS group3, group2 VS group3.

My "groups" are 100x3 matrices in which each column conrespond to a coordinates (x,y,z).

My question is, should I perform the ANOVA for each coordinate such as I get a comparison between the x axis of each group, then the y and so on?

Or do you have any other suggestion?

Thanks!

Answer 1

[Jeff Miller]

manova might be a better approach, since it allows you to combine information from all three variables (x,y,z) into a single test of group equality.

[Elisa Iovene]

So, let's say that I have 2 group to compare: TR1 and TR2. Both of them are 100x3 matrices where the first column contains x data, the second column contains y data and the third contains z data.

To perform a manova as you suggested, I should first fit a repeated mesures model:

% 1way ANOVA test set-up1 VS set-up2 on TR
t = table(TR1(:,1),TR1(:,2),TR1(:,3),TR2(:,1),TR2(:,2),TR2(:,3),...
    'VariableNames',{'TR1_X','TR1_Y','TR1_Z','TR2_X','TR2_Y','TR2_Z'});
TR = table([1 2 3 4 5 6]','VariableNames',{'Measurements'});

and then:

rm = fitrm(t,'TR1_X-TR2_Z~1','WithinDesign',TR);
manovatbl = manova(rm);

But doing so I think all the variables are analysed together instead of x data of TR1 with x data of TR2. Am I right?

[Jeff Miller]

No, that doesn't really look right to me. At least as I understand your design, you want something like this:

X = [tr1; tr2];
Group = [ones(size(tr1,1),1); 2*ones(size(tr2,1),1)];
[d,p,stats] = manova1(X,Group)