Question: A group of researchers would like to conduct a study of the effect of marital status (married vs. not married) on the Center for Epidemiologic Studies Depression Scale scores. Previous studies have shown that the standard deviation of scores is approximately 11.5, and the researchers assume this value is the same for married and not married participants. The researchers believe a 7-point difference in scores would be clinically meaningful.

1. Assuming an equal number of participants in both groups and a type I error rate of 5%, how many participants would the researchers need in their study to achieve 80% power?
2. Suppose the researchers conduct the study and produce significant results that indicate that CES-D scores are higher (i.e. depressive symptoms are more severe) among individuals who are not married. In their conclusion, they claim that their study provides evidence that countries with fewer married individuals are more depressed, on average. Do you agree with this claim? Why or why not? If not, what type of fallacy have the researchers committed?

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