Chapter 2 Probability Models: How Do I Get a Sampling Distribution?

Key concepts: bootstrapping/bootstrap sample, sampling with replacement, exact approach, approximation with a theoretical probability distribution, binomial distribution, (standard) normal distribution, (Student) t distribution, F distribution, chi-squared distribution, condition checks for theoretical probability distributions, sample size, equal population variances, independent samples, dependent/paired samples.

Watch this micro lecture on probability models for an overview of the chapter.

Summary

How do we get a sampling distribution without drawing many samples ourselves?

In the previous chapter, we drew a large number of samples from a population to obtain the sampling distribution of a sample statistic, for instance, the proportion of yellow candies or average candy weight in the sample. The procedure is quite simple: Draw a sample, calculate the desired sample statistic, add the sample statistic value to the sampling distribution, and repeat this thousands of times.

Although this procedure is simple, it is not practical. In a research project, we would have to draw thousands of samples and administer a survey to each sample or collect data on the sample in some other way. This requires too much time and money to be of any practical value. So how do we create a sampling distribution, if we only collect data for a single sample? This chapter presents three ways of doing this: bootstrapping, exact approaches, and theoretical approximations.

After studying this chapter, you should know the limitations of the three methods of creating a sampling distribution, when to use which method, and how to check the conditions for using a method.