Studentization

Article summary

In statistics, Studentization, named after William Sealy Gosset, who wrote under the pseudonym Student, is the process of dividing a statistic derived from a sample (such as sample mean) by a sample-based estimate of a population standard deviation. Unlike "normalization", where only the numerator is uncertain, Studentization has both numerator and denominator uncertain, typically (that is, under Gaussian assumptions) following a Student-T distribution. The term is also used for the standardisation of a higher-degree statistic by another statistic of the same degree: for example, an estimate of the third central moment would be standardised by dividing by the cube of the sample standard deviation. While standardization typically involves dividing a centered variable by the known population standard deviation ( \sigma ), studentization is required when \sigma is unknown. A simple example is the process of dividing a sample mean by the sample standard deviation when data arise from a location-scale family. The consequence of "Studentization" is that the complication of treating the probability distribution of the mean, which depends on both the location and scale parameters, has been reduced to considering a distribution which depends only on the location parameter.…

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