In Exercise?, ?use the following listed chest deceleration measurements (in g, where g? ?is the force of gravity) from samples of small, midsize, and large cars. (These values are from Data Set 13 in Appendix B.) Also shown (on the next page) are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different size categories have the same mean chest deceleration in the standard crash test. Chest Deceleration Measurements ?(g)? from a Standard Crash Test S m a l l M i d s i z e L a r g e ANOVA a.? What characteristic of the data above indicates that we should use ?one-way analysis of variance? b.? If the objective is to test the claim that the three size categories have the same mean? chest deceleration, why is the method referred to as analysis of ?variance??
Solution 1BSC Step 1 a) What characteristic of the data above indicates that we should use one-way analysis of variance b) If the objective is to test the claim that the three size categories have the same mean, chest declaration, why is the method referred to as analysis of variance a) We have to use one-way analysis of variance, five assumptions should be met with. These are: 1. The populations should follow normal distribution: SPSS results (Analyze-Descriptives-Explore-All variables in DV-plots-normality tests with plots-OK) in table 1 are given normality. For a normal data, the Shapiro-Wilk statistics should be greater than 0.05. then we look at table1. we can conclude that the given data is normally distributed. S h ap Kolmog ir orov-Sm o- irnov a W il k S t S a S t i d i Statistic df i g f g s . . t i c S . . . m 1 8 1 a .267 7 7 4 5 4 l 1 8 4 l M . e . . 2 d 9 5 .204 7 0 7 i 3 6 0 u 1 1 * m . . L . 9 7 a .189 7 2 7 5 5 r 0 3 2 g 0 e * Step 2 2. Standard deviations of populations should not differ significantly from each other: Here 3 populations of the standard deviations are 5.64, 6.30 and 4.46 for small, midsized and large cars respectively. Then the standard deviations are not significantly different from each other. 3.Based on random sampling the samples have been drawn as no no other sampling method has been specified and data is quantitative in nature. 4. There are three independent categories of cars : First one is small ,second one is midsized and third one is large . 5. On the basis of one parameter the samples have been categorized . Thatis chest declaration measurements.