# 4.1 - Sampling Distributions

Sample statistics are random variables because they vary from sample to sample. As a result, sample statistics have a distribution called the sampling distribution. The video below demonstrates the construction of a sampling distribution for a known population proportion using StatKey (http://www.lock5stat.com/StatKey/index.html). StatKey is a free online application that we will be using throughout the course.

An important aspect of a sampling distribution is the standard error (SE). The standard error is the standard deviation of a sampling distribution.  For a single categorical variable this may be referred to as the standard error of the proportion. For a single quantitative variable this may be referred to as the standard error of the mean. If a sampling distribution is constructed using data from a population, the mean of the sampling distribution will be approximately equal to the population parameter.

Sampling Distribution
Distribution of sample statistics with a mean approximately equal to the mean in the original distribution and a standard deviation known as the standard error
Standard Error
Standard deviation of a sampling distribution
Using StatKey to Construct a Sampling Distribution Given a Known Population Proportion

Note that this method of constructing a sampling distribution requires that we have population data. In most cases we do not know all of the population values. If we did, then we wouldn't need to construct a confidence interval to estimate the population parameter! In those cases we can use bootstrapping methods which you will see in the next section.

As you look through the following examples, note that when the sample size is large the sampling distribution is approximately symmetrical and centered at the population parameter.