# Statistics Dictionary

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### T Distribution

The t distribution (aka, Student t distribution) is the sampling distribution of the t statistic. The values of the t statistic are given by:

t = [ x - μ ] / [ s / sqrt( n ) ]

where x is the sample mean, μ is the population mean, s is the standard deviation of the sample, and n is the sample size.

The t distribution can be used whenever samples are drawn from populations possessing a bell-shaped distribution (i.e., approximately normal).

The distribution of the t statistic is similar to the distribution of a standard score . Both distributions are symmetrical with a mean of zero. Also, both distributions are bell-shaped, although the t distribution has a bigger variance.

To evaluate probabilities associated with the t distribution, we need to recognize that there are actually many different t distributions. The particular form of the t distribution is determined by its degrees of freedom .