### T distributions

A t-distribution is the sampling distribution if many t-values are produced from samples from the same population. It is a probability distribution that resembles the normal distribution but has an additional parameter known as “degrees of freedom”. How the distribution compares to the normal curve depends on how close the mean is to 0 and the standard deviation to 1.

The degrees of freedom are roughly equal to the number of observations in the test. The more degrees of freedom the more confident we can be that the results resemble the true full population distribution.

A t-statistic (or t-value) is the ratio of the observed coefficient to the standard error, which can be evaluated against the t-distribution appropriate for the size of the data sample.

A hypothesis test may use a t-distribution to calculate a p-value as to whether the results could be due to chance. If the p-value is low enough, with a large enough t-statistic we can reject the null hypothesis at some level of statistical significance. The fewer the degrees of freedom and therefore the fatter the tails of the relevant t-distribution, the higher the t-statistic will need to be in order for us to reject the null hypothesis.