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Sampling Distribution of a Statistic

The term sampling distribution of a statistic refers to the distribution of some sample statistic, over many samples drawn from the same population. Much of classical statistics is concerned with making inferences from (small) samples to (very large) populations.

Key Terms

Sample statistic

A metric calculated for a sample of data drawn from a larger population

Data distribution

The frequency distribution of individual values in a data set

Sampling distribution

The frequency distribution of a sample statistic over many samples or resamples

Central Limit Theorem

The tendency of the sampling distribution to take on a normal shape as sample size rises

Standard error

The variability (standard deviation) of a sample statistic over many samples (not to be confused with standard deviation, which, by itself, refers to variability of individual data values)

Typically, a sample is drawn with the goal of measuring something (with a sample statistic) or modeling something (with a statistical or machine learning model). Since our estimate or model is based on a sample, it might be in error—it might be different if we were to draw a different sample. We are therefore interested in how different it might be—a key concern is sampling variability. If we had lots of data, we could draw additional samples and observe the distribution of a sample statistic directly. Typically, we will calculate ...