FAQ/CombiningZandT - CBU statistics Wiki

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Combining z values and t values with large numbers of degrees of freedom

Following (for example Howell (2002) p.144) the square of a z value follows a chi-square distribution on 1 degree of freedom. Moreover the sum of N z values follows a chi-square distribution on N degrees of freedom.

Since a t value with a large number of degrees of freedom (say df > 30) closely follows a standard Normal distribution the sum of the squares of N t statistics with a large numbers of degrees of freedom will also yield a chi-square distribution with N degrees of freedom .

Both these approaches are useful in combining results from multiple testing e.g. t statistics assessing brain activities at different time points.