Combining p-values by Fisher's method
The basic idea is that if $$p_i (i=1 \ldots n)$$ are the one-sided $$p$$-values for $$n$$ independent statistics then $$-2 \sum\log(p_i)$$ has is a $$\chi^2(2n)$$ statistic which reflects whether the combined $$p$$-values are smaller than would be expected if they were Uniform(0,1) variates.
The following MATLAB code evaluates this statistic and its p-value.
function p = pfast(p) % Fisher's method for combination of independent p-values
- product=prod(p); n=length(p);
if n<=0
- error('pfast was passed an empty array of p-values')
- p = product; return
- p = 0; return
- x = -log(product); t=product; p=product; for i = 1:n-1
- t = t * x / i; p = p + t;
>> pvals=[0.1 0.01 0.01 0.7 0.3 0.1]; >> pfast(pvals)
ans =
- 0.0021
I.e. the combined p-value is 0.0021 for this array of 6 $$p$$-values..