effectsize.md

title	Computing and using estimates of effect size
tags	example statistics

Computing and using estimates of effect size

The following code demonstrates how you can compute and plot the effect size.

% find the interesting segments of data
cfg = [];
cfg.dataset                 = 'Subject01.ds';
cfg.trialdef.eventtype      = 'backpanel trigger';
cfg.trialdef.prestim        = 1;
cfg.trialdef.poststim       = 2;
cfg.trialdef.eventvalue     = [3 5 9];
% 3 = FIC
% 5 = FC
% 9 = IC
cfg = ft_definetrial(cfg);

% preprocess the data
cfg.channel         = {'MEG', '-MLP31', '-MLO12'};
cfg.demean          = 'yes';
cfg.baselinewindow  = [-0.2 0];
% cfg.lpfilter      = 'yes';
% cfg.lpfreq        = 35;
data = ft_preprocessing(cfg);

%%

cfg = [];
cfg.keeptrials = 'yes';
cfg.trials = (data.trialinfo==3);
timelock_FIC = ft_timelockanalysis(cfg, data);
cfg.trials = (data.trialinfo==5);
timelock_FC = ft_timelockanalysis(cfg, data);
cfg.trials = (data.trialinfo==9);
timelock_IC = ft_timelockanalysis(cfg, data);

%%

cfg = [];
cfg.parameter = 'trial';
cfg.method = 'analytic';
cfg.statistic = 'indepsamplesT';
cfg.design = [1*ones(1,size(timelock_FC.trial,1)) 2*ones(1,size(timelock_FIC.trial,1))];
cfg.ivar = 1;
stat_FCvsFIC = ft_timelockstatistics(cfg, timelock_FC, timelock_FIC);

%%

cfg = [];
cfg.layout = 'CTF151_helmet';
cfg.parameter = 'stat';
ft_multiplotER(cfg, stat_FCvsFIC);

%%

% MLF32 shows a large positive p-value that peaks around 600ms
chansel = match_str(timelock_FC.label, 'MLF32');
timesel = nearest(timelock_FC.time, 0.6);

%%

x1 = timelock_FC.trial(:, chansel, timesel)*1e12;
x2 = timelock_FIC.trial(:, chansel, timesel)*1e12;

x1 = mean(mean(x1,3),2);
x2 = mean(mean(x2,3),2);

n1 = length(x1);
n2 = length(x2);

if n1==n2
  % this fails if x1 and x2 are of different length
  figure
  hist([x1 x2], 50); legend({'FC', 'FIC'})
end

pooled_sd = sqrt( ((n1-1)*std(x1)^2 + (n2-1)*std(x2)^2) / (n1+n2-1) );
cohensd = (mean(x1)-mean(x2)) / pooled_sd

% see https://en.wikipedia.org/wiki/Effect_size#Cohen.27s_d

% Very small  0.01
% Small       0.20
% Medium      0.50
% Large       0.80
% Very large  1.20
% Huge        2.00

It is interesting to see how the effect size increases by taking the average over more channels and time points.

%%

chansel = match_str(timelock_FC.label, {'MLF22', 'MLF23', 'MLF32', 'MLF33', 'MLF42', 'MLF43', 'MLF52'});
timesel = nearest(timelock_FC.time, 0.496607) : nearest(timelock_FC.time, 0.765893);

% now repeat the computation of Cohen's d above

Proper preprocessing of the data also increases the effect size.

%%

cfg = [];
cfg.method = 'summary';
data = ft_rejectvisual(cfg, data);

% now repeat the computation of Cohen's d above
% this requires the following code for plotting

edges = linspace(-0.4, 0.4, 30);
h1 = histcounts(x1,edges);
h2 = histcounts(x2,edges);
bar(edges(1:end-1),[h1; h2]'); legend({'FC', 'FIC'})