tdistribution:
A continuous distribution, with single peaked probability density symmetrical around the null value and a bellcurve shape. Tdistribution is specified completely by one parameter  the number of degrees of freedom.
If X and Y are independent random variables, X has the standard normal distribution and Y  chisquare distribution with N degrees of freedom, then the random variable

has tdistribution with N degrees of freedom.
It was found by W. S. Gossett, a statistician working for Guiness (the Irish brewery), to be a good approximation to the distribution of the means of randomly drawn samples from a fixed population. Gossett published his findings in 1908 under the name "Student," hence the distribution is often called the "Student´s t." In the 1930´s, the tdistribution was also found to be a good approximation to the distribution of the difference in means of two randomlydrawn samples. (Note: the exact distribution of these differences can be derived by permuting the two samples. Before computers, when the derivation of this exact distribution was difficult or impossible to determine, the tdistribution was universally used as a substitute for the exact permutation distribution. With computer intensive methods now widely available, exact tests are increasingly used in preference to the tdistribution.)
See also: tstatistic and ttest
If the symbols do not display properly, try
the graphic version of this page