7.2.9 - Summary of Advanced Material

In this lesson we learned about:

• Profile analysis for one-sample mean and how to carry it out in SAS
• Computing simultaneous and Bonferroni confidence intervals for the differences between sample means for each variable;
• Drawing conclusions from those confidence intervals (make sure that you indicate which population has the larger mean for each significant variable); 
• Profile plots for two-sample means
• Methods for diagnosing the assumptions of the two-sample Hotelling's T-square test.

In practice, the data analyses should proceed as follows:

1. Step 1. For small samples, use histograms, scatterplots, and rotating scatterplots to assess the multivariate normality of the data. If the data do not appear to be normally distributed, apply appropriate normalizing transformations.

2. Step 2. Use Bartlett's test to assess the assumption that the population variance-covariance matrices are homogeneous.

3. Step 3. Carry out the two-sample Hotelling's T-square test for equality of the population mean vectors. If Bartlett's test in Step 2 is significant, use the modified two-sample Hotelling's T-square test. If the two-sample Hotelling's T-square test is not significant, conclude that there is no statistically significant evidence that the two populations have different mean vectors and stop. Otherwise, go to Step 4.

4. Step 4. Compute either simultaneous or Bonferroni confidence intervals. For the significant variables, draw conclusions regarding which population has the larger mean.