# 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 = $$\frac{\sum_text{i} (N_text{i}-1) SD_text{i}^text{2}}{(\sum_text{i}N_text{i})-G } $$

which equals $$\frac{\sum_text{i} SD_text{i}^text{2}}{G} $$ 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))