We don’t just observe this for the most extreme events, but in general if we select an above or below average event then the adjacent events will tend to be more average. If we had selected his slowest sprint, we would find the same thing reversed – the adjacent sprints would now be a bit faster. That is because we deliberately selected the fastest sprint and then looked at what happened on other sprints. It will probably be slightly slower, and his previous sprint will be slower as well. You then look at how fast he ran on his next sprint. For instance, imagine that you look at all the sprints made by Usain Bolt, and find his personal best. This might seem mystical when stated like this, but if we think of everyday examples it is obviously true. When this is done we will find that, on average, the extreme measurements that we selected will be accompanied by less extreme measurements at another time. The second measure can be taken before, after, or at the same time as the first. In this example, we select students that score high or low on a test at one time, and then compare those scores to ones taken at another time. Regression toward the mean (abbreviated from now on as RTTM) occurs whenever measurements are selected for their extremeness (e.g., the high or low scores are chosen for further analysis), and then compared to other measurements of the same quantity. While I do not wish to comment on the proposals themselves, I suggest that this Figure illustrates a a statistical artifact called “regression toward the mean,” and that the apparently shocking pattern of results is simply what we would expect when we have two populations of differing ability, and several imperfect measurements of that ability. I will refer to this is Figure 2, following Feinstein’s own labelling. Below we see a figure that has been widely circulated in the media (from Feinstein, 2003). A policy proposal recently put forward by Nick Clegg has been supported by apparent evidence that children from poor families of high ability massively underachieve relative to children from wealthy families of similar ability, and that conversely children from wealthy families of low ability massively overachieve relative to children from poor families matched on ability.
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