# bug in statistics_montecarlo?

Maren Grigutsch grigu at CBS.MPG.DE
Thu Jul 5 13:57:51 CEST 2007

```Dear Robert, Eric and other fellows of the Fieldtrip team,

useful and well designed statistics functions. Many thanks for this
great and generous gift to the neuroscience community!

I would like to point you to an inconsistency I seem to have found  in
the implementation of the statistics_montecarlo function. When I
compared the probabilities computed with statistics_analytic and
statistics_montecarlo for the depsamplesT test, the probabilities
determined via the randomization test turned out to be too low by a
factor of about 1/2, see code and Matlab output below.

-------------------------

N = 50;
M = 0.25;
alpha = 0.05;
tail = 0;     % 'both'

% construct a normally distributed difference vector
% with unit variance and mean M
d = randn(1,N);
d = d ./ sqrt(var(d,1,2));
d = d -mean(d) + M;

% compute a  paired t-test
[H,P,CI,stat] = ttest(d,0,alpha,tail)

H =

0

P =

0.0864

CI =

-0.0371    0.5371

stat =

tstat: 1.7500
df: 49
sd: 1.0102

% generate two sample vectors with their difference given by d
x =randn(1,N);
y = x + d;

% generate the design matrix for testing with fieldtrip
design = [
1:N              1:N                                % subject number
repmat(1,[1 N])  repmat(2,[1 N])     % condition number
];

cfg = [];
cfg.statistic        = 'depsamplesT';
cfg.method           = 'analytic';
cfg.correctm         = 'no';
cfg.alpha            = 0.05;
cfg.tail             = 0;
cfg.uvar             = 1;
cfg.ivar             = 2;

[stat_analytic, cfg] = statistics_analytic(cfg,[x y],design)

stat_analytic =

stat: -1.7500
df: 49
critval: [-2.0096 2.0096]
prob: 0.0864

cfg.numrandomization = 5000;
[stat_montecarlo, cfg] = statistics_montecarlo(cfg,[x y],design)

using "statfun_depsamplesT" for the single-sample statistics
constructing randomized design
total number of measurements     = 100
total number of variables        = 2
number of independent variables  = 1
number of unit variables         = 1
number of control variables      = 0
number of within-block variables = 0
repeated measurement in variable 1 over 50 levels
number of repeated measurements in each level is 2 2 2 2 2 2 2 2 2 2 2 2
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
estimated time per randomization is 0 seconds
not performing a correction for multiple comparisons

stat_montecarlo =

prob: 0.0394
stat: -1.7500

--------------------

Maybe I'm missing something. But I think you should replace

stat.prob = min(prb_neg, prb_pos);
by
stat.prob = 2 *min(prb_neg, prb_pos);

in line 344 of statistics_montecarlo(),  for the two-tailed test.

Maybe it would be even better to compare the absolute values of the
observed and the randomized statistics, i.e. doing something like this

for i=1:Nrand,
....
if tail == 0,
prb_pos = prb_pos + (abs(statobs)<abs(statrand));
end
...
end
if tail == 0,
stat.prob = prb_pos./Nrand;
end

What do you think?

Best regards,
--Maren

--
Max Planck Institute for Human Cognitive and Brain Sciences
Dipl.-Phys. Maren Grigutsch     mailto:grigu at cbs.mpg.de
Stephanstr.1a                   http://www.cbs.mpg.de
04103 Leipzig, Germany          phone/fax: +49 341 9940-136/-260

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```