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| MSE = $$\frac{\sum_text{i} (N_text{i}-1) SD^text{2}_{i}}{\sum_text{i} (N_text{i}-G) } $$ | MSE = $$\frac{\sum_text{i} (N_text{i}-1) SD_text{i}^text{2}}{\sum_text{i} (N_text{i}-G) } $$ |
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| which equals $$\frac{\sum_text{i} SD^text{2}_text{i}}{G} $$ in the special case of equal group sizes. | which equals $$\frac{\sum_text{i} SD_text{i}^text{2}}{G} $$ in the special case of equal group sizes. |
How do I compute Mean Square Error (MSE)?
Mean square error or MSE is frequently requested by journals as a companion statistic for ANOVA and, especially, t-tests. It 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.
In EXCEL, for two groups (A and B ) in cells A1:A100 and B1:B100 respectively this corresponds to
MSE =(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)))