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Regression to the mean

First 3 6 2 5 3 2 5 6 3 4
Second 5 6 6 2 6 3 4 4 2 3
Delta +2 0 +4 -3 +3 +1 -1 -2 -1 -1

Repeated measurements vary about an average value, so that an initial value is not a representative value that can be easily reproduced, unlike the mean. You can easily check for yourself, by throwing dices, the relationship between initial value and change, i.e. the difference between subsequent and initial value. Let us assume that you have thrown dices 20 times (do by all means repeat this experiment) and recorded them in pairs, as in the table.Regression to the mean

We subsequently plot the change (Delta) as a function of the initial value, and observe a clear negative correlation between the two: the lowest values are usually followed by an increase, after high values the next observation tends to be lower. We are dealing with an artifact which is known as regression to the mean.

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