Question

if objective is to find an unbiased estimator of class size effect, why you shouldn't look at measures of fit?

Answer 1

In statistical inference, we deal with two major steps: 1.estimation 2. Testing.

To find an unbiased estimator of a parameter is step involved in estimation while goodness of fit is a testing procedure. Unbiased estimator is defined as the estimate whose expection is equal to the parameter. Goodness of fit is defined as the measure to test how well the sample data fit to the distribution which is drawn from the population belonging to normal distribution. So, in finding the unbiased estimator we simply estimate the parameter by its unbiased estimate, there is no steps involved of testing nor we test about how well this unbiased estimator is estimating the population parameter. In measures of fit, we don't estimate any particular parameter but we fit certain sample data to certain population and check how well the sample values fit to it.

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