Pleased with your responses, you get the job. Your research assistant compares f
ID: 3333871 • Letter: P
Question
Pleased with your responses, you get the job. Your research assistant compares four groups of youths (college degrees, n = 220; some college, n = 190; high school diploma, n = 200; and some high school, n = 185) on the combined DVs: academic self-concept, academic motivation, and perception of college. Based on the literature, she expects to find moderate differences in perception among the group. She reports Box’s M = 178.54, p < .001 and a Wilks’ Lambda of .409, p < .01. She is worried that (a), the group sizes are not equal and (b) her sample size might be too small. She has asked you to review her statistics. What advice would you give?
Explanation / Answer
Box's M tests the assumption that the variance/covariance matrices are equal across two or more groups. Here we are using the test to find if there are difference in perception among the 4 different groups using Dependent variables academic self-concept, academic motivation, and perception of college. Naturally doing a test of equivalence on group with unequal sample size would lead to a false significance level. However the sample problem does not arise using Box's M. Box's M looks at the sample sizes and sizes of the variances and covariances for each group cell and if groups with larger samples have larger variances and covariances, then the alpha level (significance level) is conservative and the null hypothesis can be rejected confidently. But if groups with smaller samples produce larger variances than the significant test is too liberal. If there is a non-significant result, the null hypothesis can be confidently retained. However in our case we can be certain since we have a significant result since we are given that p < 0.001. Also remember that Box's M is a powerful statistic and if we have large sample say(N = 2000), so even small differences in these determinants will be statistically significant. This could lead to some large groups with small varianvces and small groups with large variances. It will be more difficult to reject the null hypothesis in this case. However if our sample is large and we can reject the null hypothesis you can do so with confidence as p would always be less than 0.001