What is a t-distribution?

What is a t-distribution?

The t-distribution is a type of normal distribution that is used for smaller sample sizes. Normally-distributed data form a bell shape when plotted on a graph, with more observations near the mean and fewer observations in the tails.

The t-distribution is used when data are approximately normally distributed, which means the data follow a bell shape but the population variance is unknown. The variance in a t-distribution is estimated based on the degrees of freedom of the data set (total number of observations minus 1).

It is a more conservative form of the standard normal distribution, also known as the z-distribution. This means that it gives a lower probability to the center and a higher probability to the tails than the standard normal distribution.

Example: t-distribution vs z-distribution
If you measure the average test score from a sample of only 20 students, you should use the t-distribution to estimate the confidence interval around the mean. If you use the z-distribution, your confidence interval will be artificially precise. 

 

T-distribution and the standard normal distribution