You are working with the text-only light edition of "H.Lohninger: Teach/Me Data Analysis, Springer-Verlag, Berlin-New York-Tokyo, 1999. ISBN 3-540-14743-8". Click here for further information.

## One-Sample t-TestSmall Samples

For small sample sizes, the mean shows a t-distribution (compare the case for large samples: in this case the means are distributed according to a normal distribution). The reason for this is that the estimate s of the standard deviation is not accurate enough. But again the assumption is that the distribution of the data is approximately normal. The only difference from the derivation for the large sample case is that, instead of the z-scores, we will use the t-scores, which we can obtain from statistical tables, or by using the Teach/Me distribution calculator. The t-distribution depends on the number of samples. Its parameter is called degree of freedom, and it is equal to the number of samples minus 1: df = n - 1.

For a detailed description of how to perform a t-test, please have a look at the z-test section.

Last Update: 2005-Jul-16