12.48 Skepticism, self-interest, and two-way ANOVA: A study on motivated skepticism examined whether participants were more likely to be skeptical when it served their self-interest (Ditto & Lopez, 1992). Ninety-three participants completed a fictitious medical test that told them they had high levels of a certain enzyme, TAA. Participants were randomly assigned to be told either that high levels of TAA had potentially unhealthy consequences or potentially healthy consequences. They were also randomly assigned to complete a dependent measure before or after the TAA test. The dependent measure assessed their perception of the accuracy of the TAA test on a scale of 1 (very inaccurate) to 9 (very accurate). Ditto and Lopez found the following means for those who completed the dependent measure before taking the TAA test: unhealthy result, 6.6; healthy result, 6.9. They found the following means for those who completed the dependent measure after taking the TAA test: unhealthy result, 5.6; healthy result, 7.3. From their ANOVA, they reported statistics for two findings. For the main effect of test outcome, they reported the following statistic: F(1, 73) = 7.74, p < 0.01. For the interaction of test outcome and timing of the dependent measure, they reported the following statistic: F(1, 73) = 4.01, p < 0.05.

a. State the independent variables and their levels. State the dependent variable.

b. Which kind of ANOVA would be used to analyze these data? State the name using the original language as well as the more specific language.

c. Use the more specific language of ANOVA to calculate the number of cells in this research design.

d. Create a table of cell means, marginal means, and the grand mean. Assume that equal numbers of participants were assigned to each cell (even though this was not the case in the actual study).

e. Describe the significant main effect in your own words.

f. Draw a bar graph that depicts the main effect. g. Why is the main effect misleading by itself? h. Is the main effect qualified by a statistically significant interaction? Explain. Describe the interaction in your own words. i. Draw a bar graph that depicts the interaction. Include lines that connect the tops of the bars and show the pattern of the interaction. j. Is this a quantitative or qualitative interaction? Explain. k. Change the cell mean for the participants who had a healthy test outcome and completed the dependent measure before the TAA test so that this is now a qualitative interaction. l. Draw a bar graph depicting the pattern that includes the new cell mean. m. Change the cell mean for the participants who had a healthy test outcome and completed the dependent measure before the TAA test so that there is now no interaction. n. Draw a bar graph that depicts the pattern that includes the new cell mean.