634 CHAPTER 12 Analysis of Variance Statistical Literacy and Critical Thinking 1.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? Small Midsize Large SUV Left Femur 8.0 7.0 2.5 1.0 2.0 0.4 0.7 1.1 0.7 0.5 0.6 1.8 0.3 1.3 1.1 0.4 0.4 0.6 0.2 0.2 Right Femur 2.8 1.0 0.3 0.3 0.2 0.6 0.8 1.3 0.5 1.1 1.5 1.7 0.2 0.6 0.9 0.7 0.7 3.0 0.2 0.2 2.Two-Way ANOVA If we have a goal of using the data given in Exercise 1 to (1) determine whether the femur side (left, right) has an effect on the crash force measurements and (2) to determine whether the vehicle size has an effect on the crash force measurements, should we use one-way analysis of variance for the two individual tests? Why or why not? 3. Interaction a. What is an interaction between two factors? b. In general, when using two-way analysis of variance, if we find that there is an interaction effect, how does that affect the procedure? c. Shown below is an interaction graph constructed from the data in Exercise 1. What does the graph suggest? 4.Balanced Design Does the table given in Exercise 1 constitute a balanced design? Why or why not? 5.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? 12-2 Basic Skills and Concepts Statdisk
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