How different variances are?

In measuring separation, if F is much greater than one null hypothesis is rejected, hence we conclude that the means of the population treatments differ. We take account of magnitude of skewedness in F test. Exercise No 5: I have F= 1.889 ???

If the variances are not all equal ANOVA will produce an anti-conservative p-value yielding an increase in the probability of a type I error. Therefore, it is important to test, either formally or informally, whether the homogeneity of variance assumption is satisfied.

In two tailed p value (hypocrite) relationships, when the only aspect of interest is the trend above or below the chosen value, we can apply Mann-Whitney test for matched pair to identify the magnitude of differences, to trace the trends and reveal the power of suspects!

If there were no difference on average between the sample values and the hypothesized specific value we would expect an equal number of observation above and below the specific value. We thus use the Binomial distribution to evaluate the probability of the observed frequencies when the true probability of p is ½.