Question

Imagine you are comparing dogs and cats with respect to their levels of affection with their owner(s). Draw two distributions, one for dogs and one for cats, that violate the assumption of homogeneity of variance. (2 points per distribution, 2 points for correct demonstration of violating this assumption)

Answer 1

This is a classical example of Non-parametric tests where the assumptions of parametric tests are not met such as the level of affections of cats and dogs with their owners, It is not always possible to correct for problems with the distribution of a data set with these types o f problems. The binomial test is useful for determining if the proportion of responses in one of two categories is different from a specified amount, for such purposes we use Chi-Square test to determine if a distribution of observed frequencies differs from the theoretical expected frequencies so for distribution of cats and dogs we have to assume the counts of for both cats and dogs with their respective level of affection with their owners, for that we can only assume and get a figurative distribution so a simple box-plot distribution can be made for both cats and dogs of their levels of affection towards their owners and can be compared with their distribution of means, median quartile ranges and even we can see and filter out the outliers