Chapter 9

# The Confidence Game: Estimation

IN THIS CHAPTER

Introducing sampling distributions

Understanding standard error

Simulating the sampling distribution of the mean

Attaching confidence limits to estimates

Populations and samples are pretty straightforward ideas. A *population* is a huge collection of individuals, from which you draw a sample. Assess the members of the sample on some trait or attribute, calculate statistics that summarize that sample, and you’re in business.

In addition to summarizing the scores in the sample, you can use the statistics to create estimates of the population parameters. This is no small accomplishment. On the basis of a small percentage of individuals from the population, you can draw a picture of the population.

A question emerges, however: How much confidence can you have in the estimates you create? In order to answer this, you have to have a context in which to place your estimates. How probable are they? How likely is the true value of a parameter to be within a particular lower bound and upper bound?

In this chapter, I introduce the context for estimates, show how that plays into confidence in those estimates, and describe an Excel function that enables you to calculate your confidence level.

## Understanding Sampling Distributions

Imagine that you have a population and you draw a sample from this population. You measure the individuals of the sample on a particular attribute and calculate the sample mean. Return the sample members ...