How would you react to doing much worse on an exam than you expected? There is some evidence to suggest that most individuals believe that they can cope with this kind of problem better than their fellow students (Igou, 2008). In the study, participants read a scenario of a negative event and were asked to use a 10-point scale to rate how it would affect their immediate well-being (-5 strongly worsen to +5 strongly improve). Then they were asked to imagine the event from the perspective of an ordinary fellow student and rate how it would affect that person. The difference between the two ratings was recorded. Suppose that a sample of n = 25 participants produced a mean difference of MD = 1.28 points (self rated higher) with a standard deviation of s = 1.50 for the difference scores.
a. Is this result sufficient to conclude that there is a significant difference in the ratings for self versus others? Use a two-tailed test with α = .05.
b. Compute r2 and estimate Cohen's d to measure the size of the treatment effect.
c. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.