PS296 Chapter Notes - Chapter 16: Null Hypothesis
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3 major assumptions: normality, homogeneity of variance, independence of observations. This average value of the 5 sample variances (s j) is one estimate of the population variance ( e) and is referred to as mswithin/mserror (mean square within, mean square error) If the null hypothesis is true, then the sample means have been drawn from the same population (or identical populations), and therefore: Equal sign with . is read as is estimated by . We can reverse this, so that instead of estimating the variance of means from the variance of the population, we can estimate the variance of the population from the variance of the sample means: This is known as msbetweengroups or msgroups or mstreatment. Now the common population variance is estimated by the variance of means, so long as the null is true. If the null is false, the variance of means will overestimate the common population variance.
