I tooled around a bit with the anova1 function and reacquainted myself with the math. The below function appears to return the same values as looping through anova1, but a fair bit faster (I didn't time it), as I originally wanted. It could probably be improved substantially by vectorizing, etc., but it gets the job done. As Star Strider pointed out, it should never be used for significance testing unless coupled with a correction for multiple comparisons.
GDIM is the dimension along which groups are defined (columns in anova1) and MDIM is the dimension along which within groups measures are defined (rows in anova1). All F-statistics are calculated independently.
function [F,DFR,DFE]=NDfstat(X,GDIM,MDIM)
if exist('GDIM','var') && exist('MDIM','var')
D=size(X);
X=permute(X,[GDIM MDIM setdiff(1:numel(D),[GDIM MDIM])]);
end
D=size(X);
DFE = D(1)-1;
DFR = D(1)*(D(2)-1);
xm = squeeze(mean(X,2));
gm = squeeze(mean(xm));
SSE = squeeze(D(2)*sum((xm-repmat(shiftdim(gm,-1),[D(1) ones(1,numel(D)-1)])).^2));
SST = squeeze(sum(sum((X-repmat(shiftdim(gm,-2),[D(1:2) ones(1,numel(D)-1)])).^2)));
SSR = SST-SSE;
F = (SSE/DFE)./(SSR/DFR);
end
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