LoftusMasson.m

function CI = LoftusMasson(dat)
% function CI = LoftusMasson(dat)
% this function produces Loftus-Masson corrected errorbars for your data.
% It assumes that your subjects are the rows of the data and the columns
% are different treatments (i.e., within-subject design).

% Implementation based on Kahana96 pascal file, which is based on
% Loftus, G. R. & Masson, MEJ (1994) PB&R 1(4):476-490. This is
% valid for a within-subject design.


% normalize the data
grandMean = nanmean(dat(:));
subjMean = nanmean(dat,2);
subjMean = repmat(subjMean,1,size(dat,2));
dat = dat-(subjMean-grandMean);
% compute sums
Tc = nansum(dat,1);
Nsubj = sum(~isnan(dat),1);
Ts = nansum(dat,2);
Ncond = sum(~isnan(dat),2);
T = nansum(dat(:));
SS_T = nansum(dat(:).^2);
Nvalid = sum(~isnan(dat(:)));

SS_C = sum(Tc.^2./Nsubj);
SS_S = sum(Ts.^2./Ncond);
% compute average number of valid subjects
NsubValid = sum(Nsubj)/size(dat,2);
NcondValid = sum(Ncond)/size(dat,1);

% compute final sums of squares
SS_T = SS_T - (T^2)/Nvalid;
SS_S = SS_S - (T^2)/Nvalid;
SS_C = SS_C - (T^2)/Nvalid;
SS_SxC = SS_T - SS_S - SS_C;
% mean square of the interaction
MS_SxC = SS_SxC/(Nvalid-NsubValid-NcondValid-1);
% mean square w, i.e., variance between individuals (p.484)
MS_w = (nansum(dat.^2,1)-((Tc.^2)./Nsubj))./(Nsubj-1);
% p.484
estimator = (NcondValid/(NcondValid-1))*(MS_w- (MS_SxC./NcondValid));
CI = sqrt(estimator./Nsubj)*tinv(.975,size(dat,1)-1);


%old implementation
% This script assumes that the variances for the different treatment groups
% are equal, in other words, the sphericity assumption. If this is not the
% case, then only errorbars can be computed for each contrast between treatments.

% numRows = size(dat,1);
% numCols = size(dat,2);
% D1data = reshape(dat,1,numRows*numCols);
% grandMean = mean(D1data);
% grandTotal = sum(D1data);
% % total sum squares
% SS_T = sum((D1data-grandMean).^2);

% % sum squares for rows (subjects)
% Srow = sum(dat,2);
% SSrow = sum(Srow.^2/numCols) - (grandTotal^2)/(numRows*numCols);
% % sum squares for columns (treatments)
% Scol = sum(dat,1);
% SScol = sum(Scol.^2/numRows) - (grandTotal^2)/(numRows*numCols);

% % compute the mean sum squares for the interaction between rows and columns
% SSint = SS_T - SSrow - SScol;
% df_int = (numRows*numCols-1) - (numRows-1) - (numCols-1);
% MSint = SSint/df_int;
% criterion = tinv(.975,df_int);

% % implementation of Loftus-Masson (1994), equation (2)
% CI = sqrt(MSint/numRows)*criterion*ones(1,numCols);