# Quick Introduction to T distribution #1 ## What is T distribution?

The Student’s T distribution which is commonly known as T distribution is used when the sample size of a statistical study is small and the population variance is not known. The T distribution curve looks very similar to a normal distribution at first glance, however the curve may be narrower or fatter depending on the Degrees of freedom of the sample size and the distribution of the data. Usually the sample sizes for T distribution tests are n < 30.

## Degrees of Freedom

The form of the T distribution is usually defined by the degrees of Freedom of the sample size. The DF can be easily calculated by the formula

DF = n – 1
where n = sample size of the data.

The form becomes narrower as the T Distribution DOF increases. The figure below shows the changes in the distribution.

The distribution curve when the DoF is 1000 is very similar to Normal Distribution and can be approximated without significant error.

## T Score

Z score is used in normal distribution when the population variance is known and the data is known to follow normal distribution. When the population variance is unknown and sample size is smaller than 30 ( n< 30), we cannot approximate it with a normal distribution. This means we need to use the T score formula which is given below.

Note the similarities of the T score and Z score Formulae.

## Uses of T distribution

This distribution is commonly used in statistical experiments where the population of the experiment subject is known to be normally distributed, but the sample size for the experiment may be skewed due to data collection method or if the sample size n < 30.

A major field that uses T distribution is wildlife studies, where it is difficult to acquire data of wildlife flora and fauna in large sample sizes. The experiments are done with T distribution and the results are then extrapolated to encompass the population.