T Distribution and Stanines

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Less common ways to standardize a distribution are by using a T distribution or Stanine. Like the z scores, each of these standardizations give the distribution a new mean and standard deviation. Different from the z scores is that the goal is to make all of the values positive.

The goal of the T distribution and Stanine is to create an artificial floor and ceiling. This means that it sqeezes the distribution together so that it does not continue infinitely like the normal curve.

T Distribution
In this distribution, the new mean is a relatively large number (depending on your data) and the standard deviation is a relatively large divisor of the mean.


 * An example of a T distribution is the SAT scores. For the SAT, the mean is 500 and a standard deviation is 100. You cannot have an SAT score below 200 so all of the values are positive.

Stanine
Short for "the standard nine," this divides a distribution into nine intervals or "stanines." For all Stanine scales, the mean is 5 and the standard deviation is 2. All of the intervals, except the 5th interval, are half of a standard deviation.

The purpose of the Statnine was to convert a test score into a single digit number.