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| \mbox{Combined Z } = \frac{ \sum_{K} Z_{k}}{\sqrt{K}} | Combined Z = \frac{ \sum_text{K} Z_text{k}}{\sqrt{K}} |
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| \mbox{Combined t } =\frac{\sum t_{k}} {\Sqrt{ \frac{ \sum_{k} df_{k}} ]{df_{k}-2} } | Combined t = \frac{\sum t_text{k}} {\Sqrt{ \frac{ \sum_text{k} df_text{k}} ]{df_text{k}-2} } |
Combining z values and t values with large numbers of degrees of freedom
Following Winer (1971) and Rosenthal (1987) the sum of z values divided by the square root of the number of terms being summed follows a Normal distribution. This approach known as Stouffer's method may be computed using this [attachment:combineZ.xls spreadsheet].
$$ Combined Z = \frac{ \sum_text{K} Z_text{k}}{\sqrt{K}} $$
Mosteller and Bush(1954) and Rosenthal (1987) also show how t statistics (each with degrees of freedom over 2) may be summed to obtain a combined t value. These computations may be performed using this [attachment:combineT.xls spreadsheet].
$$ Combined t = \frac{\sum t_text{k}} {\Sqrt{ \frac{ \sum_text{k} df_text{k}} ]{df_text{k}-2} } $$
References
Mosteller F, Bush RR (1954). Selected quantitative techniques. In: Lindzey G, ed. Handbook of Social Psychology, Cambridge, Mass: Addison-Wesley, pp 289-334.
Rosenthal R (1987) Judgement studies design analysis and meta-analysis. CUP:Cambridge. The requisite chapter may be viewed [http://books.google.co.uk/books?id=zLCv3Ca2BJoC&pg=PA212&lpg=PA212&dq=lancaster+%26+1961+%26+%22p+values%22&source=web&ots=dj1zMMHTM3&sig=A8QbbKGJCmc0F7C2JH7F_NfCqkk&hl=en#PPA211,M1 here]
Winer, B.J. (1971). Statistical principles in experimental design (2nd ed.). New York: McGraw-Hill. (1991 edition available in CBU library)