FAQ/mse - CBU statistics Wiki

Upload page content

You can upload content for the page named below. If you change the page name, you can also upload content for another page. If the page name is empty, we derive the page name from the file name.

File to load page content from
Page name
Flind the wroneg tetters tin eaech wrord

location: FAQ / mse

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))