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Given that the totals of six values in each of $5$ groups are $360,246,420,336,306$ and the estimated variance of a group mean is $6.2$ ,compute the analysis of variance.

I am not understanding only the fact that "What is estimated variance of a group mean?"

I know estimated of error variance,$\hat\sigma^2=MSE$

where $MSE=$Mean Square Error

ABC
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1 Answers1

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The variance of a group mean is the variance of the means across the groups. For the numbers you provided, the mean of each group is just: $\frac{360}{6},\frac{246}{6},\frac{420}{6},...$ etc. You want to calculate the sample variance of these 5 means that you now have and compare that to the $6.2$ that the problem has provided.

Patrick
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  • Is that the estimated variance of a group mean is Mean Square Error? And is the sample variance of those 5 means Mean square treatment? – ABC Aug 15 '13 at 13:42
  • Do you know the formula for MSE in terms of an estimators variance and its bias? What is the estimator in this case and its corresponding bias? Answering these questions will tell you if the estimated variance of the group mean is in fact equal to its MSE. – Patrick Aug 15 '13 at 16:32
  • No, i don't know. Can you please explain ? – ABC Aug 16 '13 at 04:10
  • Sure, the estimator here is the sample mean, or $\bar{X}$, which is an unbiased estimator for the population mean $\mu$. The MSE of any estimator $\hat{\theta}$ can be written as: $MSE = Var(\hat{\theta})+bias(\hat{\theta})^2$. Since the bias is $0$ for the sample mean the MSE and variance are equal here. – Patrick Aug 16 '13 at 11:15