Why should I use the cfg.correcttail option when using statistics_montecarlo?
When running statistics using ft_freqstatistics, ft_timelockstatistics, or ft_sourcestatistics with cfg.method = 'montecarlo' you are presented with the option cfg.correcttail, which is relevant when you are doing a two-sided test:
% cfg.correcttail = correct p-values or alpha-values when doing a two-sided test, 'alpha','prob' or 'no' (default = 'no')
In case of a two-tailed test, the type-I error rate (alpha) refers to both tails of the distribution, whereas the stat.prob value computed with the montecarlo method corresponds to one tail, i.e. the probability, under the assumption of no effect or no difference (the null hypothesis), of obtaining a result equal to or more extreme than what was actually observed. The decision rule whether the null-hypothesis should be rejected given the observed probability therefore should consider alpha divided by two, to correspond with the probability in one of the tails (the most extreme tail).
In case of a two-sided test, with alpha = 0.05, the configuration would contain:
cfg.alpha = 0.05; cfg.tail = 0; % two-sided test cfg.correcttail = 'alpha';
This is conceptually equivalent to performing a Bonferroni correction for the two tails, i.e., divide alpha by two. Each tail will be tested with alpha = 0.025.
An alternative solution to distribute the alpha level over both tails is achieved by multiplying the probability with a factor of two, prior to thresholding it with cfg.alpha. The advantage of this solution is that it results in a p-value that corresponds with a parametric probability. Use the following configuration:
cfg.alpha = 0.05; cfg.tail = 0; % two-sided test cfg.correcttail = 'prob';
Effectively, this means multiplying the p-values (in stat.prob, stat.posclusters.prob and stat.negclusters.prob) with a factor of two.
Please note that, when doing a two-sided test with alpha = 0.05 and not correcting, you are effectively testing with alpha = 0.1.