Statistics 250 Honors, Spring 2003Lab assignment #10, Apr. 4

Your Name(s):

Type or copy/paste your answers to the following questions. Do not erase the questions. When you finish, print this document and hand it in.

1. Using Minitab's capability to produce a graph of residuals versus fits in one-way ANOVA, create separate residual plots using both the original (untransformed) survival time data and the log-transformed survival time data as the response. For each plot, naturally, you should use Organ as the explanatory factor. Copy and paste the plots below.

2. Based on the necessary conditions for an ANOVA F-test (p. 492), explain why, based on the plots in question 1, it appears wise to use the log-transformed survival time data as the response when using ANOVA.

3. In last week's lab, you established strong evidence that the null hypothesis is not true; in other words, not all five types of cancer have the same mean survival times. However, this answer alone is unsatisfactory from a scientific perspective; if there are differences, we should attempt to describe these differences! One way to explore this question is to consider all the possible pairwise comparisons between two of the five groups. How many such comparisons are possible? (Another way to look at it: How many handshakes are possible in a group of five people?) Explain your answer.

4. It is NOT a good idea to run one t-test for each of the pairwise comparisons. The reason is subtle: Even if H0 is really true, with so many tests being performed simultaneously, there is a pretty good chance that one or more of the p-values will happen to fall below 5%. Thus, the type-I error probability will actually be greater than 5% if H0 is true. To correct for this fact, we should choose a method that controls the family error rate, defined on p. 496. The most common such method is called Tukey's method.

In your one-way ANOVA for the log-transformed survival data, have Minitab generate Tukey comparison confidence intervals with a family error rate of 5% (click "Comparisons" in the ANOVA window). Copy and paste below the resulting matrix of confidence intervals.

5. Interpret the results of question 4: Which differences are significant? (i.e., which intervals don't contain zero?) By considering the signs of the confidence intervals, tell which mean survival times are significantly greater than which other mean survival times.

6. Using ANOVA followed by a Tukey procedure if necessary, answer the question posed in the lab regarding the physical handicap data: Do subjects systematically evaluate qualifications differently according to the candidate's handicap, and if so, which handicaps produce the different evaluations? Include any output you deem necessary to make your point.