Normal probability plots and sample sizes for data obtained

Normal probability plots and sample sizes for data obtained by two studies (A and B) are given below. For each study, state whether the F-test or the Levene test is more appropriate to test the hypothesis of equal population variances. Explain your answers. n1 = 20 n2 = 20 Which test is most appropriate? Explanation n1 = 100 n2 = 100 Which test is most appropriate? Explanation:

Solution

Generally, You could use an F test to assess the variance of two groups, but the using F to test for differences in variance strictly requires that the distributions are normal. Using Levene\'s test (i.e., absolute values of the deviations from the mean) is more robust.

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a)

As it can be seen from the probability plot of the A1 and A2, the two distributions are almost normal as they lie along the standard normal distribution straight line. This means that in this case, the data are normally distributed for A1 and A2.

So, an F-test would be more appropriate in this case.

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b)

In this case, the two distributions are highly skewed from the standard normal distribution line, so we can say that the distributions are not normal.

Hence, in this case a Levene\'s test would be more appropriate.