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DON’T YET NAME YOUR CHILD P.I.G.: REPLY TO MORRISON AND SMITH

RESPONSE

Department of Economics; Pomona College; Claremont, CA (Smith)
New York, NY (Morrison)

The ideal data set would have complete mortality data for everyone with positive and negative initials in several birth cohorts. For a less-than-ideal data set with incomplete mortality data for some birth cohorts, there is still a valid statistical test with a well-defined p value.

There is no compelling reason to look instead at death cohorts comprised of people with different birth years; there is a persuasive disadvantage in that death cohorts can be misleading if the popularity of initials varies from birth year to birth year. Christenfeld et al. tried to cope with this problem by choosing control groups whose initials had similar trends in popularity. Their original paper suggested that they calculated trends by comparing the popularity of initials for those who died at the beginning and end of their sample period, which Christenfeld acknowledges would be "hopelessly noisy." Christenfeld says that the trends were actually calculated from regression lines, but this procedure, too, is hopelessly noisy for the very same reasons given in our paper. First, there are many possible patterns around a trend line that have different implications for longevity. Second, a trend line for decedents grouped by death year is a flawed measure of changes in the popularity of initials for birth cohorts and an unreliable measure of the effects of changes in the popularity of initials on the average age at death (AAD).

It is true that there are combinations of incomplete mortality data and creative mortality patterns for which the AAD of decedents grouped by birth year will incorrectly fail to reject the null hypothesis. However, this is also true if decedents are grouped by death year. (Indeed, every statistical test has some chance of Type II error!)

Suppose, for example, that we have data for people who died between 1970 and 1990 and that, conveniently, the initials P.I.G. were first given to newborns in 1970 and were given to the same number of newborns every year thereafter. Suppose further that deaths are constant between the ages of 0 and 20, but that mortality rates are consistently higher for people with the initials P.I.G. than for others during the first 20 years of life. For every birth cohort and for every death cohort for which we have data, the average age at death (AAD) is the same for those with the initials P.I.G. as for other groups even though the initials P.I.G. are deadly. The fundamental problem is the incompleteness of the mortality data.

So, p values are well-defined for birth cohorts and hopelessly noisy for death cohorts, and there is no persuasive way of telling which design has more power. We are left with our original question, why group decedents by year of death? Why not use the most complete mortality data that is available with data grouped by year of birth?

Our study used data for people who died during the years 1905 through 2003. Restricting our study to birth years where there were at least five decedents with positive initials and five decedents with negative initials, we had birth cohorts back to the 1850s. For some birth years (like 1860) many people died too young to be included in our study; for other birth years (like 1960) many people died (or will die) too old to be included. The fact that there is no difference in AAD for either type of truncated birth cohort suggests that a very clever mortality pattern is needed for our tests to be misleading. Even more tellingly, there are several birth cohorts for which we have age-at-death data for a very high percentage of the cohort. Specifically, the 1905 to 1923 birth cohorts should give us reliably long horizons because more than 80% of the people born in each of these years died by age 80. We have data for 2,576 male and 2,789 female decedents with positive or negative initials in these cohorts and, if there are effects on mortality of the magnitude reported by Christenfeld, these effects should reveal themselves.

For male decedents, those with positive initials had a higher AAD for 10 of these birth cohorts and a lower AAD for 9 cohorts, with an overall average difference in AADs of 0.08 years. For female decedents, those with positive initials had a higher AAD for 9 birth cohorts and a lower AAD for 10 cohorts, with an overall average difference in AADs of –0.01 years.

This exchange nicely illustrates why researchers generally focus on Type I errors: (a) Type II errors are difficult to assess; and (b) surprising claims should be viewed skeptically unless the evidence is very persuasive.

DOI:10.1097/01.psy.0000296501.22504.02

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