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The case of the suspicious husband
“The average gestation period is 266 days. Some babies come early. Others come late. Yours was late. In the United States there are about twelve thousand babies born this late each year. Yours is just one of them.”

It happened a good 40 years ago; in fact, this year (2013) we celebrate the 40th anniversary of this celebrated story that has made its way into statistic folklore. It’s worth recounting it here.

In 1973, a San Diego reader complained to a newspaper columnist:

“You wrote in your column that a women is pregnant for 266 days…. I carried my baby for ten months and five days… there is no doubt about it because I know the exact date my baby was conceived… My husband is in the Navy and it couldn’t have been conceived any other time because I saw him only once for an hour, and I didn’t see him again until the day the baby was born… there is no way this baby isn’t his baby… please print a retraction about that 266-day carrying time because otherwise I will be in a lot of trouble.”

The columnist wrote back saying: “Dear Reader: The average gestation period is 266 days. Some babies come early. Others come late. Yours was late.”

While the columnist was bang on, he could have been more quantitative. He should have marshaled math logic to provide greater assurance to the couple. This is what he could have done.

That the kid was born late is a fact. At approximately 310 days it was way above 266, which the columnist rightly says is the global average. The point is, what is the probability of this 310 happening. Meaning, what is the probability of a kid getting born 44 days behind the average? Meaning, is it so unusual that we could conclude that the woman was lying? This is where statistics comes in handy.

Let’s assume that the gestation period follows a normal distribution curve; that is, it is bell shaped. In that case it would be possible, by using the Z value table, to find the probability that a pregnancy would last at least 310 days. Now, current data says that the average gestation period is 266 days with a standard deviation (movement around the mean) of 16 days. This is an information to which the columnist was privy. Statistics’ normal distribution table suggests that under the circumstances (average = 310, standard deviation =16), the probability that a pregnancy would last at least 10 months and 5 days (about 300days or longer) is 0.003.

This means that three babies out of a thousand are born this late. With 40 lakh babies born each year in America,about twelve thousand babies are born this late. The columnist could have replied saying:“the average gestation period is 266 days. Some babies come early. Others come late. Yours was late. In the United States there are about twelve thousand babies born this late each year. Yours is just one of them.” This response would not only have been reassuring to the wife, but persuasive to her husband as well.

But just hold on. In hypothesis testing, the probability of 0.003 is extreme for the null hypothesis to be true. In our example, the null hypothesis is: “This baby is my husband’s.” In traditional hypothesis testing, you reject the null hypothesis if the P-value is smaller than the levels of significance. Mathematically, a P-value of 0.003 would reject the null hypothesis. So, we normally would reject the hypothesis that this baby is San Diego reader’s husband’s baby. So, if it was really the husband’s baby, how do we explain our wrong test result? Simple. At times, life falls outside the predictions of probability theory! In short, life is not all math.

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