# Normalized gain score

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## Definition

The term normalized gain score is used for a variation of the gain score that normalizes it against the maximum gain possible. Explicitly, consider a pretest score and a posttest score, both normalized as scores out of 1. In this case, the normalized gain score is: $\mbox{Normalized gain score } = \frac{\mbox{Posttest score (out of 1)} - \mbox{Pretest score (out of 1)}}{1 - \mbox{Pretest score (out of 1)}}$

If the scores are not normalized to 1, then the normalized gain score can be computed as follows: $\mbox{Normalized gain score } = \frac{\mbox{Posttest score} - \mbox{Pretest score}}{\mbox{Maximum score possible} - \mbox{Pretest score}}$

In order for the normalized gain score to make conceptual sense, the "Maximum score possible" should be the score that it is possible for experts in the domain to achieve reliably. In other words, the test should be designed so that experts should reliably be able to obtain a full score. If this is not the case, then we should take "Maximum score possible" as the mean of the scores that experts would achieve in the test, not as the theoretical maximum score possible.