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| 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. | Following Rosenthal (1987) the sum of z values divided by the square root of the number of terms being summed follows a Normal distribution. |
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| 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. |
Rosenthal also shows how t statistics may be summed to obtain a combined t value. |
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| Howell DC (2002) Statistical methods for psychologists. Duxbury Pess: Pacific Gove,CA | Rosenthal R (1987) Judgement studies design analysis and meta-analysis. CUP:Cambridge. |
Combining z values and t values with large numbers of degrees of freedom
Following Rosenthal (1987) the sum of z values divided by the square root of the number of terms being summed follows a Normal distribution.
Rosenthal also shows how t statistics may be summed to obtain a combined t value.
Reference
Rosenthal R (1987) Judgement studies design analysis and meta-analysis. CUP:Cambridge.