Data Analysis with R, Second Edition - Second Edition

Smaller samples

Remember when I said that the sampling distribution of sample means is approximately normal for a large enough sample size? This caveat means that for smaller sample sizes (usually considered to be below 30), the sampling distribution of the sample means is not well approximated by a normal distribution. It is, however, well approximated by another distribution: the t-distribution.

A bit of history... The t-distribution is also known as the Student's t-distribution. It gets its name from the 1908 paper that introduces it, by William Sealy Gosset writing under the pen name Student. Gosset worked as a statistician at the Guinness Brewery and used the t-distribution and the related t-test to study small samples of the quality ...