What effects appear to be present in your plots?
In the exercises for Chapters 6 and 7, we considered a study investigating how parent-infant play changes as infants grow older. This exercise uses the same data, but adds the parent’s gender as a third factor. Specifically, mothers of four girls and of four boys at each of three ages (7, 10, and 13 months) were videotaped during toy-play interactions with their infants. An equal number of fathers from different families were also observed. The dependent variable to be considered here was the proportion of time parents encouraged pretend play in their children. Suppose the following hypothetical data were obtained: a. Test the statistical significance of the three main effects, the three two-way interactions, and the three-way interaction. Also calculate corresponding measures of association strength for each effect. b. Plot the cell means in a manner similar to that shown in Specifically, draw one plot for girls and a second plot for boys. Place Age on the x-axis for each plot. c. What effects appear to be present in your plots? Is the visual impression consistent with the results of the significance tests from part a? d. What additional tests involving the factor of the child’s gender should be performed, based on your results from part a? e. According to the flowchart in what additional tests of effects involving the parent’s gender and the child’s age might be performed here? f. Perform any and all appropriate tests of simple effects of parent’s gender within levels of the child’s age. g. Find corresponding confidence intervals for each of the effects you tested in part f. h. Perform any and all appropriate tests of simple effects of the child’s age separately for mothers and fathers. i. Test the linear trend of child’s age, separately for mothers and fathers. j. Find corresponding confidence intervals for each linear trend you tested in part i. In particular, define the slope in terms of a 1-month change in age. k. Summarize the nature of your findings for these data.
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