Statisticians have devised three basic approaches to make conclusions about populations from samples of data:

The first method is to assume that parameter values for populations follow a special distribution, known as the Gaussian (bell shaped) distribution. Once you assume that a population is distributed in that manner, statistical tests let you make inferences about the mean (and other properties) of the population. Most commonly used statistical tests assume that the population is Gaussian. These tests are sometimes called parametric tests.

The second method is to rank all values from low to high and then compare the distributions of ranks. This is the principle behind most commonly used nonparametric tests, which are used to analyze data from non-Gaussian distributions.

The third method is known as resampling. With this method, you create a population of sorts by repeatedly sampling values from your sample. This is best understood by an example. Assume you have a single sample of five values, and want to know how close that sample mean is likely to be from the true population mean. Write each value on a card and place the cards in a hat. Create many pseudo samples by drawing a card from the hat, writing down that number, and then returning the card to the hat. Generate many samples of N=5 this way. Since you can draw the same value more than once, the samples won’t all be the same (but some might be). When randomly selecting cards gets tedious, use a computer program instead. The distribution of the means of these computer-generated samples gives you information about how accurately you know the mean of the entire population. The idea of resampling can be difficult to grasp. To learn about this approach to statistics, read the instructional material available at www.resample.com.  Prism does not perform any tests based on resampling. Resampling methods are closely linked to bootstrapping methods.