ABSTRACT
This chapter introduces sampling theory and applications to statistical inference. The chapter begins with an example of drawing very small samples from a small finite population of six fish. The small population size permits listing of each possible sample mean of size n along with the probability of each sample mean. The result is the sampling distribution, a central concept in sampling theory. This small example illustrates the tendency of the sample means to cluster around the population mean and serves to introduce the central limit theorem, which shows that the distribution of sample means or sums converge into a normal distribution as the sample size increases, irrespective of the distribution of the population. The population of the six fish is flat, but the sample means start to cluster even with small samples of n = 2 and n = 3.
Other sampling distributions include the t-distribution and the F-distribution. An example using the F-distribution illustrates the use of statistical tests. The remaining sections of the chapter summarize different types of probability samples and non-probability samples. Probability samples include simple random sample (SRS), systematic sample, stratified sample, and cluster sample. Non-probability samples include quota sample, purposive sample, and snowball sample.
