Eating Breakfast Cereal and Conceiving Boys Newscientist.com ran the headline "Breakfast Cereals Boost Chances of Conceiving Boys," based on an article which found that women who eat breakfast cereal before becoming pregnant are significantly more likely to conceive boys. \( { }^{1} \) The study used a significance level of \( \alpha=0.01 \). The researchers kept track of 133 foods, and for each food, tested whether there was a difference in the proportion conceiving boys between women who ate the food and women who didn't. Of all the foods, only breakfast cereal showed a significant difference. If none of the 133 foods actually have an effect on the gender of a conceived child, how many (if any) of the individual tests would you expect to show a significant result just by random chance? test(s)
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In this scenario, the significance level is set at \( \alpha = 0.01 \). This means that, if there is no actual effect, we would expect \( 1\% \) of the tests to yield significant results purely by chance. With 133 foods tested, we would calculate the expected number of tests showing a significant result as follows: \[ \text{Expected significant results} = 133 \times 0.01 = 1.33 \] Therefore, we would expect about 1 to 2 of the individual tests to show a significant result just by random chance. It's a classic case of the multiple testing problem, where testing numerous hypotheses increases the likelihood of encountering false positives. In research, this underscores the importance of adjusting for multiple comparisons, like using a Bonferroni correction, to maintain the integrity of findings!
