The Median Is A Powerful And Neglected Statistic

The median is so neglected that Microsoft Excel’s pivot tables which are designed to display statistical summary data don’t even give the option of displaying medians.  The arithmetic mean was independently invented several times for reducing measurement error including by Isaac Newton and it has been the dominant measure of central tendency since the beginning of modern statistics in the late 1800s.  But the median is the best measure for ordinal data such as measures of economic wellbeing and the median is often better for data that has unreliable outliers such as political polls.  Sam Wang is a biologist at Princeton who created a very simple model for aggregating political polls as a hobby in his spare time which has been more accurate than almost all of the professional pollsters who stake their careers on predicting election outcomes.  His relatively simple technique uses the median of polls for aggregating them rather than the mean of poll results.

[Wang’s] Analysis relies entirely on the well-established principle that the median of multiple state polls is an excellent predictor of actual voter behavior. [One reason is because] median-based statistics correct for outliers.

Using the median poll result is a simple protocol for reducing the bias that individual polls have rather than engaging in motivated reasoning to weigh the relative biases of different polls.  Sam Wang has many rivals in predicting election outcomes like HuffPollsterThe Upshot, and FiveThirtyEight (Nate Silver).  They use much more complex models based on mean poll results, but so far Wang’s model has worked just as well or better with much less complexity.  I do have some qualms about some of Wang’s assumptions and conclusions, but his use of median poll results has proven itself in the last few elections.  I’ll look forward to seeing how it does in the next election.  Currently, he is predicting that the Republican party will take over the Senate.

Posted in Medianism

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