Simpson’s paradox

Back in November, I posted about the fact that I was going to be more bullish about the fact that I am a physicist but that I do educational research. As I try to build my confidence to say some of things that follow from that in my own voice, I’ll start by quoting some more articles I have read in the past few months.

To start with, there was a piece in New Scientist back in February (Issue number 3062, 27th February 2016, pg 35-37), by Michael Brooks and entitled “Thinking 2.0”. This article starts by pointing out Newton’s genius in recognising the hidden variable (gravity) that connects a falling apple and the rising sun. He goes on to explain that “we know that correlation does not equal causation, but we don’t grasp the depth of it” – and to point out that our sloppy understanding of ¬†statistics can lead us into deep water.

Brooks gives a powerful hypothetical example of Simpson’s paradox, defined by Wikipedia as a paradox “in which a trend appears in different groups of data but disappears or reverses when these groups are combined” (the Wikipedia article gives some more examples and is worth reading). The example in the New Scientist article is about a clinical trial involving 400 men and 400 women that apparently shows that a new drug is effective in treating an illness – for both the men and the women. However, if you look at the 800 participants as a whole, it becomes apparent that more of those who were NOT given the drug recovered than those who received the drug. How so? Well, although the sample was nicely balanced between men and women, and half of the participants received the drug whilst half didn’t, it turns out that far more men were given the drug in this particular study, and men are much more likely to recover, whether or not they receive the drug. The men’s higher overall recovery rate masked the drug’s negative effect. This is a hypothetical example, and in a structured environment such as a clinical trial, such potential pitfalls can generally be circumnavigated. But medical – and educational – research often operates in what Brooks rightly describes as muddy waters. Controls may not be possible and we can be led astray by irrelevant, confusing or missing data.

Although I was aware of Simpson’s paradox and thought I had a reasonable understanding of ‘lies, damned lies and statistics’ it took me some time to get my head around what is going on here. We need to be really careful.

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2 Responses to Simpson’s paradox

  1. i agree we need to be careful in this matter

  2. in conclusion the drug doesn’t have great rates of recovery

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