14. ANOVA

Interaction

a. What is an interaction between two factors?

"Using Technology to Perform a Two-Way ANOVA Test In Exercises 15–18, use technology and the block design to perform a two-way ANOVA test. Use α=0.10. Interpret the results. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.

[APPLET] Advertising A study was conducted in which a sample of 20 adults was asked to rate the effectiveness of advertisements. Each adult rated a radio or television advertisement that lasted 30 or 60 seconds. The block design shows these ratings (on a scale of 1 to 5, with 5 being extremely effective).

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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?

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.

Pulse Rates Shown below are pulse rates from Data Set 1 “Body Data” in Appendix B, and the StatCrunch display from two-way analysis of variance of these data. In analyzing these data, what important feature is addressed with two-way analysis of variance that is not addressed with two separate tests of (1) difference between mean pulse rates based on gender, or (2) differences among the mean pulse rates in the different age brackets?

"Using Technology to Perform a Two-Way ANOVA Test In Exercises 15–18, use technology and the block design to perform a two-way ANOVA test. Use α=0.10. Interpret the results. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.

[APPLET] Vehicle Sales The owner of a car dealership wants to determine whether the gender of a salesperson and the type of vehicle sold affect the number of vehicles sold in a month. The block design shows the numbers of vehicles, listed by type, sold in a month by a sample of eight salespeople.

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?

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?

In Exercises 21 and 22, (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal.

[APPLET] The table shows the monthly electric bills (in dollars) for a sample of households from four regions of the United States. At α=0.10, can you conclude that the mean monthly electric bill is different in at least one of the regions? (Adapted from U.S. Energy Information Administration)

Which of the following interaction plots best indicates no interaction between the two factors?

A university surveys how study group size (solo, duo, group) and study environment (quiet, noisy) affect test performance. Which of the following conclusions most clearly suggests an interaction effect between the 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.

One vs. Two What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?

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?

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?