442022-06-23 08:31:04PeterWatson432022-06-23 08:19:43PeterWatson422022-06-23 08:18:56PeterWatson412022-06-23 08:14:41PeterWatson402022-06-23 08:14:10PeterWatson392022-06-23 08:10:13PeterWatson382022-06-23 07:49:15PeterWatson372013-03-08 10:17:39localhostconverted to 1.6 markup362008-04-24 15:47:28PeterWatson352008-04-24 15:46:26PeterWatson342008-04-24 15:45:29PeterWatson332008-04-24 15:45:02PeterWatson322008-04-24 15:44:08PeterWatson312008-04-24 15:43:45PeterWatson302008-04-24 15:43:13PeterWatson292008-04-24 15:42:24PeterWatson282008-04-24 15:15:33PeterWatson272008-04-24 15:14:21PeterWatson262008-04-24 15:07:16PeterWatson252008-04-24 15:06:34PeterWatson242008-04-24 15:05:49PeterWatson232008-04-24 15:02:02PeterWatson222008-04-24 15:00:52PeterWatson212008-04-24 14:59:08PeterWatson202008-04-24 14:54:15PeterWatson192008-04-24 14:53:25PeterWatson182008-04-24 14:52:54PeterWatson172008-04-24 14:52:03PeterWatson162008-04-24 14:50:01PeterWatson152008-04-24 11:49:51PeterWatson142008-04-24 11:48:32PeterWatson132008-04-24 11:48:22PeterWatson122008-04-24 11:47:46PeterWatson112008-04-24 11:47:28PeterWatson102008-04-24 11:44:16PeterWatson92008-04-24 11:17:14PeterWatson82008-04-24 11:15:16PeterWatson72008-04-24 11:13:55PeterWatson62008-04-24 10:56:55PeterWatson52008-04-23 09:30:07PeterWatson42008-04-23 09:28:16PeterWatson32008-04-23 09:27:48PeterWatson22008-04-23 09:24:27PeterWatson12008-04-23 09:21:03PeterWatson

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 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) = z2 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 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 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) = t2(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)