Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

t Distribution

W.S. Gosset demonstrated in 1908 that the ratio t between the difference of the sample mean and the population mean, and the standard error of the mean, is not normally distributed if the population parameters are unknown:

This ratio follows a special distribution, called t-distribution. The t-distribution is broader than the normal distribution for small sample numbers, and approaches the normal distribution for large sample sizes. Below the t-distribution is given for 1, 3, and 10 degrees of freedom.

Hinweis: The t distribution having one degree of freedom is equal to the standard Cauchy distribution.