Statistically Insignificant News

From the Duluth News Tribune:

The number of abortions performed in Duluth in 2008 increased about 3.5 percent from 2007 even as abortions across the state dropped about 6.5 percent and fell to the lowest level since the 1970s, according to a report released Wednesday by the state Department of Health.

THE PROBLEM:

I don't think a 3.5% increase of a few hundred cases is reason for concern.

THE HYPOTHESES:

The null hypothesis, H0, is that p1-p2=0. If this is true, there is no difference in the number of abortions per capita in Duluth from 2007 to 2008. (The difference reported in the DNT would be due to random variations rather than something explainable, such as the development of more favorable attitudes toward abortion.) The alternative hypothesis, H1, is that p1 does not equal p2. In other words, the number of abortions per capita changed from 2007 to 2008.

THE NECESSARY NUMBERS:

I looked up the report from the Minnesota Department of Health and it did not give the number of abortions in Duluth. I instead used the number of abortions in St. Louis county in 2007 (391) and added 3.5% to get the number for 2008 (404.685, but I rounded up to 405). I used the population in Duluth, not St. Louis county, so this is going to be an extremely conservative calculation. In 2007, according to the DNT, Duluth's population was 84281. The city gained 3 people in 2008. I adjusted the populations to include only 52% of the people, because if I remember correctly from the CPS benchmarks I've been working with lately, 52% of the population are women.

THE CALCULATIONS:

I'm going to skip the calculations here, but I did them in Excel. I got z= -.04745, and p=.4813.

THE CONCLUSION:

Fail to reject the null hypothesis. In other words, the increase in abortions from 2007 to 2008 is not significant. There is a 48% chance that the increase occurred by chance (e.g. a few extra condoms broke this year and those people happened to prefer abortion over the alternatives). There is no reason to worry at this point. Easier said than done: the DNT reports that "The increased number of abortions in Duluth worries Scott Fischbach, executive director of the Minnesota Citizens Concerned for Life. 'I don't have an answer [for why that is],' he said. 'We'll be working with our members up there to redouble our efforts to make sure that women in the area know they don't have to get an abortion.'"

I wonder how many people are going to panic over this reported increase...