Lab 9 Objectives:

In lab 8, we investigated the assumptions underlying the parametric procedures that we've been using (t-tests, ANOVA). We focused on the departure from the normality assumption. In this lab, we discuss the use of nonparametric procedures (chap 13) in S-Plus when our data suggest the parametric assumptions are violated.

Nonparametric Tests

Let's proceed using the data for exercise 15. Read in the data lowbwt (since you have used it before, you may only need to restore your previous workspace; if not download it and read it in again)

By default, S-plus will read in the data as double precision; in this case we want to treat sex as a categorical factor. Go to the Data menu, and select Change Data Type. Select the column for sex, and then under the New Type field select Factor. Click on OK.

The apgar5 score is on ordinal variable that takes on the values between 0 and 10. What does this imply about the normality assumption? Would the CLT be useful if our sample size was much larger?

To run the Wilcoxon test, go to the Statistics menu and select Compare samples. For two independent samples (obvious, right?), select 2 samples, then Wilcoxon Rank test. Specify the outcome variable and the grouping variable in this case. (If there are equal sample sizes, variable 1 and variable 2 may refer to the two groups wihtout having a grouping variable)

For paired data, repeat the above, enter the two outcomes as Variable 1 and Variable 2, but do not check the grouping variable box. Select Signed Rank instead of Rank Sum.

What is the intepretation of the p-value?

Repeat these steps/questions for exercise 13 (data bed), 14 (data program), and 16 (data insure). Be careful to check whether the variable is ordinal! Be sure you can recognize a paired situation versus an independent samples situation. Also, make sure you are able to interpret the S-Plus output (see examples in lecture notes, too)