Divorced From Reality

Saturday, September 29th, 2007

Divorced From Reality reports on some truly awful statistical work:

The story of ever-increasing divorce is a powerful narrative. It is also wrong. In fact, the divorce rate has been falling continuously over the past quarter-century, and is now at its lowest level since 1970. While marriage rates are also declining, those marriages that do occur are increasingly more stable. For instance, marriages that began in the 1990s were more likely to celebrate a 10th anniversary than those that started in the 1980s, which, in turn, were also more likely to last than marriages that began back in the 1970s.

Why were so many analysts led astray by the recent data? Understanding this puzzle requires digging deeper into some rather complex statistics.

The Census Bureau reported that slightly more than half of all marriages occurring between 1975 and 1979 had not made it to their 25th anniversary. This breakup rate is not only alarmingly high, but also represents a rise of about 8 percent when compared with those marriages occurring in the preceding five-year period.

But here’s the rub: The census data come from a survey conducted in mid-2004, and at that time, it had not yet been 25 years since the wedding day of around 1 in 10 of those whose marriages they surveyed. And if your wedding was in late 1979, it was simply impossible to have celebrated a 25th anniversary when asked about your marriage in mid-2004.

The social scientists running the numbers should have read up on survival/failure time analysis:

Imagine that you are a researcher in a hospital who is studying the effectiveness of a new treatment for a generally terminal disease. The major variable of interest is the number of days that the respective patients survive. In principle, one could use the standard parametric and nonparametric statistics for describing the average survival, and for comparing the new treatment with traditional methods (see Basic Statistics and Nonparametrics and Distribution Fitting). However, at the end of the study there will be patients who survived over the entire study period, in particular among those patients who entered the hospital (and the research project) late in the study; there will be other patients with whom we will have lost contact. Surely, one would not want to exclude all of those patients from the study by declaring them to be missing data (since most of them are “survivors” and, therefore, they reflect on the success of the new treatment method). Those observations, which contain only partial information are called censored observations (e.g., “patient A survived at least 4 months before he moved away and we lost contact;” the term censoring was first used by Hald, 1949).

In general, censored observations arise whenever the dependent variable of interest represents the time to a terminal event, and the duration of the study is limited in time. Censored observations may occur in a number of different areas of research. For example, in the social sciences we may study the “survival” of marriages, high school drop-out rates (time to drop-out), turnover in organizations, etc. In each case, by the end of the study period, some subjects will still be married, will not have dropped out, or are still working at the same company; thus, those subjects represent censored observations.

In economics we may study the “survival” of new businesses or the “survival” times of products such as automobiles. In quality control research, it is common practice to study the “survival” of parts under stress (failure time analysis).

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