= Summing z values and summing t values =
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]]. For, 1 $$\leq$$ k $$\leq$$ K and k-th z value, $$z_text{k}$$
Combined z = sum over k z(k)/sqrt(K)
Also, note that since chi-square(1) = z^2^ a sum of chi-squares ''each having one degree of freedom (df)'' may be obtained by square rooting each chi-square(1) and entering as a z-value.
Mosteller and Bush(1954) and Rosenthal (1987) also use the formula presented [[https://stats.stackexchange.com/questions/136415/is-there-a-t-test-equivalent-to-stouffers-z-test | here]] to 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]]. For 1 $$\leq$$ k $$\leq$$ K we have the k-th t ratio, t(k), with degree of freedom df(k)
Combined t = sum over k t(k) / Sqrt [ Sum over k df(k)/(df(k)-2) ]
Also, note that since F(1,df) = t^2^(df) a sum of F statistics whose ''first degree of freedom is one'' may be evaluated by square rooting and treating as a t statistic shose degrees of freedom equal the second F statistic degree of freedom.
t statistics with more than 30 degrees of freedom closely resemble z values so there will be little difference in results summing t statistics with over 30 degrees of freedom and summing z values.
__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.
Winer, B.J. (1971) Statistical principles in experimental design (2nd ed.). New York: McGraw-Hill.
(1971 and 1991 editions of this book are available in the CBU library)