PSYCHOLOGY 300B (A01)

Transcription

1 PSYCHOLOGY 00B (A01) Assignment February, 019 t = n M i M j + n SS R = nc (M R GM ) SS C = nr (M C GM ) SS error = (X M) = s (n 1) SS RC = n (M GM ) SS R SS C SS total = (X GM ) df total = rcn 1 df R = r 1 df C = c 1 df RC = rc df R df C 1= (r 1)(c 1) df error = rc(n 1) MS C = SS C df C F C = MS C SS = n (M M R1 ) df = c 1 SS = n (M M R1 ) df = c 1 F = MS η R = SS R η C = SS C η RC = SS RC 1. A developmental psychologist studying theory of mind among normally developing and mildly autistic young children selects a sample of children of each type. Within each of these two groups of children, half are years old and the other half are years old. Each child is given a test measuring how well his or her theory of mind has developed. The resulting data are analyzed using a two-factor analysis of variance. What are the two independent variables and what are the levels of each variable? What is the dependent variable?. For each of the two plots of data below (representing two different sets of data), indicate which effects are significant (main effect of factor A, main effect of factor B, and interaction). A difference between means (or a difference between differences) of or more is deemed significant.

2 1 B A 1 B A. Construct a table of means for a x design in which the row main effect is significant, the column main effect is significant, and the interaction is not significant. A difference between means (or a difference between differences) of or more is deemed significant. The row factor has levels and the column factor has levels.. Construct a bar graph for a x design in which one main effect is significant, the other main effect is not significant, and the interaction is not significant. A difference between means (or a difference between differences) of or more is deemed significant.. The following table presents the mean and standard deviation for each condition in a x design. There were 1 subjects in each condition. Compute the two-factor ANOVA for this data set and provide the resulting ANOVA summary table. You should find that the interaction is significant with a =.0. Examine this interaction by computing simple effects for the factor with levels (column factor) at each level of the other factor (row factor). You should also find that the row factor does not have a main effect. Is it safe to conclude, considering the results of your analyses, that you have no evidence for the claim that the row factor affects the dependent variable? Report the effect size for each main effect and for the interaction using h. Means and standard deviations (in parentheses) for each condition: C1 C C R1 1 () () 7 () R () 9 () 11 (). Use the cell means in the table below (based on a x factorial design) to compute the sum of squares, degrees of freedom, and the mean square for the interaction effect only. The values in the table are cell means based on n =. C1 C R1.0. R..0 R.. 7. The data from a x factorial design, in which young children were randomly assigned to conditions, are shown below as cell means. The row variable is type of television character (human vs. cartoon characters) that subjects viewed just prior to being tested,

3 and the column variable is amount of violence expressed in the program (low, medium, high). The dependent variable is amount of aggressive behavior displayed by a subject during a one-hour play session held after the television program had been viewed. A twofactor ANOVA indicated that there was a significant main effect of level of violence and a significant interaction. The main effect of type of character was not significant. What do these results, along with the pattern of means, allow you to conclude concerning the influence of type of television character and amount of violence on aggressive behavior among children? Level of violence Type of character Low Medium High Human Cartoon In each of the plots shown below, means from two conditions of a x design are shown. These two conditions represent level 1 of Factor B. In each plot, add two more means, representing level of Factor B to produce the pattern of effects specified for each plot. In all cases, a difference between means or a difference between differences of at least points is deemed significant. Draw a line connecting the points that you add. (a) Factor A main effect and interaction are significant, but not the Factor B main effect. 1 A (b) Factor A main effect is significant, but Factor B main effect and interaction are not. 1 A

4 (c) Factor B main effect and interaction are significant, but not Factor A main effect. 1 A 9. Each of the plots below shows the means from a factorial design. For each plot, indicate which effects are significant. In all cases, a difference between means or a difference between differences of at least points is deemed significant. (a) (b) 7 A B 7 B A. A researcher is studying driving ability in younger and older adults. She wants to test the hypothesis that older adults can operate a vehicle as safely as younger drivers as long as they are free of distraction. When a distraction is present, however, it is expected that older adults will drive less safely than younger adults. The researcher tests this idea by randomly assigning a group of younger and older adults to perform a driving test in a driving simulator under conditions of no distraction or moderate distraction. Notice that the researcher's hypothesis leads to the prediction that this x design should produce an interaction effect. Assuming that an interaction is found, what simple effects tests should be done to evaluate her hypothesis? 11. In a social psychology study of persuasion, a researcher manipulated the credibility of the message source and the degree of discrepancy between the message and the subjects' original opinions. The researcher first had subjects rank their preferences for nine obscure modern poems. Then they read an essay expressing a favorable opinion for a poem that they had ranked next to the bottom. One group was told that the favorable opinion was written by T. S. Eliot (highly credible source, being a well-known poet and literary expert). Another group was told that the favorable opinion was written by a college student who was training to become a high-school English teacher (a low credibility source). Degree of

5 discrepancy was manipulated by varying the strength of the favorable opinion that subjects read: (a) "best example" of a certain poetic style (large discrepancy), (b) "superior to all but two of the others" (medium discrepancy), and (c) "just average" (small discrepancy). One third of the subjects in each credibility group (high vs. low) were assigned to each of the discrepancy conditions. The researcher measured the amount of change in subjects' opinions that occurred after receiving the persuasive message. The change score for each subject (0 subjects in each of the six groups in the design) is provided in the cred.txt data file that is posted on the course web site. Note that these are hypothetical, but realistic, data. (a) Use R to compute an ANOVA for these data. (b) Compute by hand a simple effects test to determine whether there is a significant effect of the discrepancy variable for subjects exposed to a low credibility source. Use a =.0. (c) Compute by hand a pairwise t test to determine whether in the main effect of discrepancy there is a significant difference between the medium and large discrepancy conditions. Use a =.0. (d) Compute by hand a test to determine whether there is an effect of credibility when the message conveys a large degree of discrepancy. Use a =.0.