Exercise 33 1. Do the data meet criteria for homogeneity of variance? Provide a rationale for your answer. The data meet criteria for homogeneity of variance because the Test of Homogeneity of Variance was not significant, p = 0.455 Test of Homogeneity of Variances HoursWorked Levene Statistic df1 df2 Sig. .840 2 12 .455 2. If calculating by hand, draw the frequency distribution of the dependent variable, hours worked at a job. What is the shape of the distribution? If using SPSS, what is the result of the Shapiro- Wilk test of normality for the dependent variable?
The shape of the distribution is roughly normal. There may be a slight skew to the right. The Shapiro-Wilk test of normality shows that it is a normal distribution with p = 0.314. Tests of Normality Kolmogorov-Smirnov a Shapiro-Wilk Statist ic df Sig. Statist ic df Sig. HoursWor ked .206 15 .085 .934 15 .314 a. Lilliefors Significance Correction 3. What are the means for three groups’ hours worked on a job? The means for the three groups are Supported M = 14.6, TAU Observational M = 15.2, TAU Randomized M = 26.6. Descriptives HoursWorked N Me an Std. Deviat ion Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound Supported 5 14. 60 6.504 2.90 9 6.52 22.68 8 24 TAU Observational 5 15. 20 3.701 1.65 5 10.60 19.80 9 18 TAU Randomized 5 26. 60 7.436 3.32 6 17.37 35.83 15 35 Total 1 5 18. 80 8.029 2.07 3 14.35 23.25 8 35
4. What are the F value and the group and error df for this set of data? The F = 6.162, error df = 2, and group df = 12. ANOVA HoursWorked Sum of Squares df Mean Square F Sig. Between Groups 457.200 2 228.600 6.162 .014 Within Groups 445.200 12 37.100 Total 902.400 14 5. Is the F significant at α = 0.05? Specify how you arrived at your answer. The F is significant at an alpha of 0.05 because the test statistic shows a p value of 0.014, well below the alpha for type 1 error. 6. If using SPSS, what is the exact likelihood of obtaining an F value at least as extreme as or as close to the one that was actually observed, assuming that the null hypothesis is true? The likelihood of obtaining an F value at least as extreme is considered type 1 error and is equal to the p value of the observed statistic, which is 1.4% 7. Which group worked the most weekly job hours post-treatment? Provide a rationale for your answer.
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- Spring '14