Question

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. The study used a significance level of α = 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. a. If none of the 133 foods actually have an effect on the sex of a conceived child, how many (if any) of the individual tests would you expect to show a significant result just by random chance? Explain. (Hint: Pay attention to the significance level.) b. Do you think the researchers made a Type I error? Why or why not? c. Even if you could somehow ascertain that the researchers did not make a Type I error, that is, women who eat breakfast cereals are actually more likely to give birth to boys, should you believe the headline "Breakfast Cereals Boost Chances of Conceiving Boys"? Why or why not?

Answer 1

In statistical tests with a significance level of α = 0.01, about 1 or 2 foods out of 133 might show significant results by chance. There is the possibility of a Type I error considering the multiple tests were conducted. Even without a Type I error, skepticism towards the headline is warranted as correlation does not imply causation.

Step-by-step explanation:

The question pertains to statistics, particularly the interpretation of results from multiple hypothesis tests and understanding the concepts of Type I errors (false positives) and the implications of correlation versus causation.

a. Expected Significant Results by Random Chance

If none of the 133 foods actually affect the sex of a conceived child, we would expect some to show a significant result simply by chance due to the significance level set at α = 0.01. With 133 independent tests, if there are no actual effects, we would anticipate 1% of these to yield a significant result due to random variation, which equates to approximately 1.33 or roughly 1 or 2 foods.

b. Possibility of a Type I Error

Considering that multiple tests were conducted, and only breakfast cereal was found to be significant, there is a possibility that the researchers made a Type I error. This means they could have incorrectly rejected the null hypothesis for this one food item, taking what is actually a random variation as an effect.

c. Believability of the Headline

Even if we assumed there was no Type I error, it would still be prudent to be skeptical about the headline. Correlation does not imply causation, and multiple external factors might contribute to this observed correlation. Claims of causation require controlled experimental evidence, which is not provided simply by statistical association