In statistics and in applications of statistics, normalization can have a range of meanings.
Case: 1 In the simplest cases, normalization of ratings means adjusting values measured on different scales to a notionally common scale, often prior to averaging.
Case: 2 In more complicated cases, normalization may refer to more sophisticated adjustments where the intention is to bring the entire probability distributions of adjusted values into alignment.
In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization, where the quantiles of the different measures are brought into alignment.
In another form of usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in a way that eliminates the effects of certain gross influences, as in an anomaly time series. Some types of normalization involve only a rescaling, to arrive at values relative to some size variable. In terms of levels of measurement, such ratios only make sense for ratio measurements - where ratios of measurements are meaningful, not interval measurements - where only distances are meaningful, but not ratios.