In statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

, a studentized residual is the quotient resulting from the division of a residual

Errors and residuals in statistics

In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...

 by an estimate

Estimator

In statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule and its result are distinguished....

 of its standard deviation

Standard deviation

Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

. Typically the standard deviations of residuals in a sample vary greatly from one data point

Data point

In statistics, a data point is a set of measurements on a single member of a statistical population, or a subset of those measurements for a given individual...

 to another even when the errors

Errors and residuals in statistics

In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...

 all have the same standard deviation, particularly in regression analysis

Regression analysis

In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...

; thus it does not make sense to compare residuals at different data points without first studentizing. It is a form of a Student's t-statistic

Student's t-statistic

In statistics, the t-statistic is a ratio of the departure of an estimated parameter from its notional value and its standard error. It is used in hypothesis testing, for example in the Student's t-test, in the augmented Dickey–Fuller test, and in bootstrapping.-Definition:Let \scriptstyle\hat\beta...

, with the estimate of error varying between points.

This is an important technique in the detection of outlier

Outlier

In statistics, an outlier is an observation that is numerically distant from the rest of the data. Grubbs defined an outlier as: An outlying observation, or outlier, is one that appears to deviate markedly from other members of the sample in which it occurs....

s.