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?

c. The format of the table is transposed so that the row and column factors are interchanged.

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?

Sitting Heights The sitting height of a person is the vertical distance between the sitting surface and the top of the head. The following table lists sitting heights (mm) of randomly selected U.S. Army personnel collected as part of the ANSUR II study. Using the data with a 0.05 significance level, what do you conclude? Are the results as you would expect?

Weights from ANSUR I and ANSUR II The following table lists weights (kg) of randomly selected U.S. Army personnel obtained from the ANSUR I study conducted in 1988 and the ANSUR II study conducted in 2012. If we use the data with two-way analysis of variance and a 0.05 significance level, we get the accompanying display. What do you conclude?

Pancake Experiment Listed below are ratings of pancakes made by experts (based on data from Minitab). Different pancakes were made with and without a supplement and with different amounts of whey. The results from two-way analysis of variance are shown. Use the displayed results and a 0.05 significance level. What do you conclude?

One-Way ANOVA In general, what is one-way analysis of variance used for?