If samples are drawn from the population with replacement, then any number of samples of a given size, N, can be drawn. The moments of these samples themselves form distributions. Consider, for example, the means of the samples drawn from the population. One could prepare a frequency distribution of these means. A distribution of a sample statistic is referred to as a sampling distribution of that statistic. The middle distribution in the figure above is the sampling distribution of the mean. It is possible to prepare a sampling distribution of any statistic that can be calculated from sample data. For example, one could prepare a sampling distribution of the sample standard deviations.
Sampling distributions are important because they can be used to calculate the probabilities of experimental outcomes under the null hypothesis.
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