When using a t-test of significance it is assumed that the observations come from a population which follows a Normal distribution. This is often true for data that is influenced by random fluctuations in environmental conditions or random measurement errors. The t-distribution is essentially a corrected version of the normal distribution in which the population variance is unknown and hence is estimated by the sample standard deviation.

One should always use care when interpreting the results of a statistical test. For a simple example we look at the hypothetical results of John and Jane measuring the mean mass of 20 pennies from the millions of pennies in circulation. Unknown to either of them, they are given the same 20 pennies but John's scale is biased by +0.2 grams relative to Jane's. A statistical test shows that there is a significant difference between the two sample means. We know this can't be true. The point here is that biases or other nonrandom (non normally distributed) influences on the data can make statistical tests worthless. Also, it is important to realize that we may never be completely certain that all such biases have been eliminated from our observations. Students should always be careful when stating and interpreting the results of statistical tests. Dana Krempels of the University of Miami give a somewhat humorous WARNING on her interactive t-Tester page.