What Studentize is
Studentize is a method of adjusting the standard errors of an estimator for greater accuracy. It is named after William Sealy Gosset, who developed the method in 1908.
Studentize consists of several steps:
- Calculate the sample mean and sample standard deviation of the data set.
- Calculate the difference between each observation and the sample mean.
- Divide each difference by the sample standard deviation. This will give you the standardized scores.
- Take the square root of the sample size and divide each standardized score by it. This will give you the studentized scores.
- Calculate the studentized residuals for each observation by subtracting the predicted value from the observed value, and then dividing by the estimated standard error of the prediction.
- Compare the studentized residuals to a standard normal distribution to identify outliers.
Examples
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Studentize can be used to compare the performance of different students in a class. By measuring the mean and standard deviation of each student’s test scores, the instructor can determine which students are excelling and which are struggling.
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Studentize can also be used to measure the overall performance of a class. By collecting data on the class’s average test score, the instructor can determine how the class is doing as a whole.
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Studentize can also be used to identify outliers in a class. By collecting data on the class’s highest and lowest test scores, the instructor can determine which students may need additional help.