MathLiveRegression toward the mean
For two repeated measurements of the same quantity, the group selected for an extreme first measurement will have a second measurement that lies closer to the overall mean. It describes why extreme results tend to be followed by less extreme ones.
\forall c\colon\mathbb{E}[X_1 \mid X_1 < c] < \mathbb{E}[X_2 \mid X_1 < c] \le \mathbb{E}[X_1] = \mathbb{E}[X_2] \le \mathbb{E}[X_2 \mid X_1 > c] < \mathbb{E}[X_1 \mid X_1 > c]What the symbols mean
| first measurement of the quantity | |
| second, repeated measurement of the same quantity | |
| threshold value used to select extreme first measurements | |
| expected value | |
| conditional expected value given the stated event |
About this formula
- FieldStatistics
- TopicStatistical phenomena
- LevelUniversity
- Also calledregression to the mean, reversion to the mean, mean regression, reversion to mediocrity, regression to mean formula
- SourceWikidata Q1135405
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