The estimate of the common variance given by (i)is unbiased under the null hypothesis, but (ii) estimates the common variance under the alternative hypothesis. The estimate of the common variance given by (iii) is always (iv), whether or not there is a population/treatment effect.

HI your question is incomplete attached to the answer is an image of the complete question

i) MSG

II) OVER

III) MSE

IV) UNBIASED

Explanation:

MSG ( ) : this is calculated by taking the sample variance of the sample distribution of the mean for every group involved with the test and it unbiased under the null hypothesis alone

while MSE is gotten from using the sample mean of the sample variances of each group involved with the test  and it is always unbiased whether or not there is a population / treatment effect

you so !

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