Question: Seasonal Dyslexia. Researchers at the University of Arkansas theorize that exposure to influenza and other viral diseases in the second trimester of pregnancy may be a factor increasing the odds that the child will be dyslexic. (Dyslexia is a reading disability, defined as a reading score on standard tests falling at least two years behind the expected level, despite a normal IQ.) One piece of evidence that could support this would be a high rate of dyslexia in children born in the summer months, because the second trimester would have fallen in the influenza season.
Design an observational study to examine this conclusion. Assume that this will be a case-control study with a random sample of dyslexic boys compared to an equally sized random sample of nondyslexic boys. Compare the frequency of births in June, July, and August with the frequency of births in December, January, and February. Ignore births in the other months. In the control group, you expect about 50% to be born in the summer months. How large should each sample be if you wish to detect a twofold difference in the odds?