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| MSE = $$\frac{\sum_text{i} (N_text{i}-1) SD_text{i}^text{2}}{(\sum_text{i}N_text{i})-G } $$ | MSE = $$\sum$$ over i [$$(N(i)-1) SD(i)^2 ^]/ [($$\sum$$ over i)N(i)) - G ] $$ |
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| which equals $$\frac{\sum_text{i} SD_text{i}^text{2}}{G} $$ in the special case of equal group sizes. | which equals ($$\sum$$ over i $$SD(i)^2 ^ )/G $$ in the special case of equal group sizes. |
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))