Pulse Rate The following table lists pulse rates obtained from Data Set 1 in Appendix B

TwoWay ANOVA Data Set 13 in Appendix B lists results from car crash tests. Included in results from car crash tests are loads (pounds) on the left femur and right femur, and those values are shown in the table below. What characteristic of the data suggests that the appropriate method of analysis is twoway analysis of variance? That is, what is twoway about the data entered in the table? Small Midsize Large Left Femur 1188 399 215 289 317 1636 329 301 738 707 297 882 602 810 937 245 280 882 334 411 472 Right Femur 1261 844 752 324 713 1202 446 133 772 1048 236 554 1474 687 669 1046 905 554 455 547 290

TwoWay ANOVA If we have a goal of using the data described in Exercise 1 to (1) determine whether size of a car has an effect on the load measurements and (2) to determine whether the location of the femur (left or right) has an effect on the load measurements, should we use oneway analysis of variance for the two individual tests? Why or why not?

Interaction What is an interaction between two factors? In general, when using two way analysis of variance, if we find that there is an interaction effect, how does that affect the procedure?

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

Car Crash Tests If we use the data described in Exercise 1 with twoway analysis of variance, we get the accompanying display. What do you conclude? MINITAB d

Car Crash Tests The following table lists results from car crash tests. The listed values are measures of chest deceleration (in g) categorized by type (whether the car is foreign or domestic) and car size (small, midsize, large). Results from twoway analysis of variance are also displayed. Use the displayed results and use a 0.05 significance level. What do you conclude? Size of Car Small Medium Large Foreign 44 41 32 54 49 45 43 47 42 Domestic 43 43 37 44 37 38 42 34 33 MINITAB d

Verbal IQ Scores Example 1 in this section used performance IQ scores from Data Set 5 in Appendix B for twoway analysis of variance with the factors of sex (male, female) and measured blood lead level (low, medium, high). If we use the verbal IQ scores with those same factors, we get the accompanying results. Use the displayed results and use a 0.05 significance level. What do you conclude? MINITAB d

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 twoway analysis of variance are shown. Use the displayed results and a 0.05 significance level. What do you conclude? Whey 0% 10% 20% 30% No Supplement 4.4 4.5 4.3 4.6 4.5 4.8 4.5 4.8 4.8 4.6 4.7 5.1 Supplement 3.3 3.2 3.1 3.8 3.7 3.6 5.0 5.3 4.8 5.4 5.6 5.3 MINITAB d

SelfEsteem The following table lists measures of selfesteem obtained from a student project as supervised by Jannay Morrow at Vassar College (based on data from Richard Lowry). The objective of the project was to study how levels of selfesteem in subjects relate to their perceptions of selfesteem in other target people who were described in writing. Selfesteem levels were measured using the Coopersmith SelfEsteem Inventory, and the test here works well even though the data are at the ordinal level of measurement. Use a 0.05 significance level and apply the methods of twoway analysis of variance. What do you conclude? Subject's SelfEsteem Low Medium High Target's SelfEsteem Low 4 4 3 3 3 1 3 5 3 4 3 3 4 4 4 2 3 5 5 4 4 4 3 2 2 4 1 2 3 3 4 2 2 3 3 3 High 2 2 4 3 3 2 4 2 1 2 3 2 2 3 1 3 3 4 2 4 2 4 3 4 2 2 3 1 4 3 2 3 1 4 3 4

Pulse Rate The following table lists pulse rates obtained from Data Set 1 in Appendix B. Use a 0.05 significance level and apply the methods of twoway analysis of variance. What do you conclude? Under 30 Years of Age Over 30 Years of Age Female 78 104 78 64 60 98 82 98 90 96 76 76 72 66 72 78 62 72 74 56 Male 60 80 56 68 68 74 74 68 62 56 46 70 62 66 90 80 60 58 64 60

Transformations of Data Example 1 illustrated the use of twoway ANOVA to analyze the sample data in Table 123. How are the results affected in each of the following cases? a. The same constant is added to each sample value. b. Each sample value is multiplied by the same nonzero constant. c. The format of the table is transposed so that the row and column factors are interchanged. d. The first sample value in the first cell is changed so that it becomes an outlier.