FAQ/mse142018-03-12 11:11:06PeterWatson132013-03-08 10:17:56localhostconverted to 1.6 markup122011-03-21 12:45:29PeterWatson112011-03-21 12:37:51PeterWatson102011-03-21 12:37:32PeterWatson92011-03-21 12:29:06PeterWatson82011-03-21 12:27:42PeterWatson72011-03-21 12:27:15PeterWatson62011-03-21 12:25:48PeterWatson52011-03-21 12:25:27PeterWatson42011-03-21 12:25:10PeterWatson32011-03-21 12:24:36PeterWatson22011-03-21 12:23:45PeterWatson12011-03-21 12:21:50PeterWatson
How do I compute Mean Square Error (MSE) in EXCEL or SPSS?Mean square error or MSE is frequently requested by journals as a companion statistic for ANOVA and, especially, t-tests. MSE is the average intra-group variance. MSE is outputted in ANOVA tables but can be computed using a weighted average of the group variances. Fo G groups with the i-th an SD, $$SD_text{i}$$ and sample size $$N_text{i}$$, MSE = $$\sum$$ over i [$$(N(i)-1) SD(i)2 ]/ [($$\sum$$over i)N(i)) - G ]$$ which equals ($$\sum$$ over i $$SD(i)2 )/G$$ in the special case of equal group sizes. MSE is also useful for computing Cohen's d effect size, the number of standard deviations between a pair of group means, because d = (difference in a pair of group means) divided by the square root of the MSE In EXCEL, suppose we have two groups (A and B ) in cells A1:A100 and B1:B100 respectively, Cohen's d can then be computed using COHENSD =(SQRT(((COUNT(A1:A100)-1)+(COUNT(B1:B100)-1)))*(AVERAGE(A1:A100)-AVERAGE(B1:B100)))/(SQRT((COUNT(A1:A100)-1)*POWER(STDEV(A1:A100),2)+(COUNT(B1:B100)-1)*POWER(STDEV(B1:B100),2))) and the mean square error in EXCEL is computed by MSE = ((COUNT(A1:A100)-1)*POWER(STDEV(A1:A100),2)+(COUNT(B1:B100)-1)*POWER(STDEV(B1:B100),2))/((COUNT(A1:A100)-1)+(COUNT(B1:B100)-1))