14. ANOVA

Interaction

a. What is an interaction between two factors?

Transformations of Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3. How are the results affected in each of the following cases?

b. Each sample value is multiplied by the same nonzero constant.

Transformations of Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3. How are the results affected in each of the following cases?

a. The same constant is added to each sample value.

Transformations of Data Example 1 illustrated the use of two-way ANOVA to analyze the sample data in Table 12-3. How are the results affected in each of the following cases?

d. The first sample value in the first cell is changed so that it becomes an outlier.

Two-Way Anova The measurements of crash test forces on the femur in Table 12-3 from Example 1 are reproduced below with fabricated measurement data (in red) used for the left femur in a small car. What characteristic of the data suggests that the appropriate method of analysis is two-way analysis of variance? That is, what is “two-way” about the data entered in this table?

c. Shown below is an interaction graph constructed from the data in Exercise 1. What does the graph suggest?

Balanced Design Does the table given in Exercise 1 constitute a balanced design? Why or why not?

Car Crash Test Measurements If we use the data given in Exercise 1 with two-way analysis of variance and a 0.05 significance level, we get the accompanying display. What do you conclude?

Distance Between Pupils The following table lists distances (mm) between pupils of randomly selected U.S. Army personnel collected as part of the ANSUR II study. Results from two-way analysis of variance are also shown. Use the displayed results and use a 0.05 significance level. What do you conclude? Are the results as you would expect?

Cola Weights The displayed results from Exercise 1 are from one-way analysis of variance. What is it about this test that characterizes it as one-way analysis of variance instead of two-way analysis of variance?