Student’s t-distribution

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Student’s t-distribution is a continuous probability distribution commonly used in statistics.[1]

The t-distribution is a type of normal distribution(are we sure that’s right??) used with small sample sizes where the population standard deviation/population variance is unknown. Its mean is 0, and its skewness is 0 (i.e. it is symmetrical). The shape of the distribution depends on its standard deviation, which is estimated from the degrees of freedom, which is taken as the number of observations -1. The t-distribution has slightly higher kurtosis than the normal distribution, i.e. it is thinner in the middle and fatter in the tail.

As the sample size increases, the t-distribution comes closer to the normal distribution because of the central limit theorem, and for sample sizes of >30 a z-distribution can be used instead.

The t-distribution is the basis for the t-test series of tests.

The distribution takes the name of the statistician Student (W.S. Gosset), who originated it.

The spreadsheet function TDIST() can be used to generate this distribution.

Without the use of statistical computing, the t-table gives the distribution for each degree of freedom.

There are two types; 1-tailed t-distribution and 2-tailed t-distribution.

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