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#### Analysis of Variance (ANOVA) HOMEWORK Statistics for the Behavioral Sciences On a separate piece of paper, show all of your work and be neat

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Analysis of Variance (ANOVA) HOMEWORK Statistics for the Behavioral Sciences On a separate piece of paper, show all of your work and be neat. 1. When do you use an analysis of variance? What is the difference between a one-factor ANOVA and a two-factor ANOVA? 2. A psychotherapist asks a sample of violent and nonviolent criminals from a low SES (socioeconomic status), middle SES, or upper SES background to indicate how accountable they feel they are for their crimes. Identify each factor and the levels of each factor in this example. Factor B Level 1 Level 2 FACTOR A Level 1 Level 2 5 5 10 10 Factor B Level 1 Level 2 FACTOR A Level 1 Level 2 10 5 10 5 Factor B Level 1 Level 2 FACTOR A Level 1 Level 2 5 5 5 10 3. Which table represents a main effect of A? A main effect of B? An interaction of A X B? 4. When looking at a graph of an A X B interaction, describe the pattern that indicates that the interaction is possibly significant. 5. In a one-way ANOVA, what are two sources of variation that can contribute to the between-groups population variance estimate? If H0 is true, what should the F ratio equal or be close to? If H0 is not true, should the F ratio be greater than, less than, or equal to 1? Why? 6. Why is the F test always nondirectional? How are differences between specific pairs of population means determined? (Once you reject the null hypothesis, what do you do?) 7. In a study on the effects of stress on illness, a researcher tallied the number of colds people contracted during a six-month period as a function of the amount of stress they reported during the same time period. There were three stress levels: minimal, moderate, and high stress, with four participants in each group. An ANOVA summary table is below. Fill in the missing data and determine if the null hypothesis should be rejected at the .05 level of significance. Source Between groups Within groups Total df SS 22.17 MS F 1.64 36.92 8. Emile Durkheim (1858-1917), a founder of sociology, believed that modernization produced social problems such as suicide. On variables such as electricity consumption, newspaper circulation, and gross national product, 13 countries were classified as to their degree of modernization (low, medium, or high). The numbers below are suicide rates per 100,000 persons. Test the null hypothesis at the .01 level of significance. Degree of Modernization: Low 4 8 7 5 Medium 17 10 9 12 High 20 22 19 9 14 9. Bandura, Blanchard, and Ritter (1969) conducted an experiment that provided individuals with one of four treatments for their intense fear of snakes. One group worked with a model – a person who handled a 4-foot king snake and encouraged others to imitate her. One group watched a film of adults and children who enjoyed progressively closer contact with a king snake. A third group received desensitization therapy, and a fourth group served as a control, receiving no treatment. The numbers of the snake-approach responses after treatment are listed below. Test the null hypothesis at the .05 level of significance. Type of Treatment: Model 29 27 27 21 Film 22 18 17 15 Desensitization 21 17 16 14 Control 13 12 9 6 10. Common sense says that a valuable goal is worth suffering for. Is that the way it works? In a classic experiment in social psychology (Aronson and Mills, 1959), college women had to “qualify” to be in an experiment. The qualification activity caused severe embarrassment, mild embarrassment, or no embarrassment. After qualifying, the women listened to a recorded discussion, which was, according to the experimenters, “one of the most worthless and uninteresting discussions imaginable.” The dependent variable was the women’s ratings of the discussion (higher scores indicate more favorable ratings). Determine if the amount of embarrassment the women experienced influenced their ratings of the discussion, using a significance level of .05. Looking at the group means (and without doing a post hoc test), indicate whether the data suggest common sense is correct… or incorrect. (That is, will suffering make you value something NOT valuable?). Degree of Embarrassment: Severe 18 23 14 20 25 Mild 18 12 14 15 10 None 17 15 9 12 13

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