Chapter 10

Having Confidence in Your Results

IN THIS CHAPTER

Investigating the basics of confidence intervals

Calculating confidence intervals for several different statistics

Linking significance testing to confidence intervals

In Chapter 3, we describe how statistical inference relies on both accuracy and precision when making

estimates from your sample. We also discuss how the standard error (SE) is a way to indicate the level

of precision of your sample statistic, but that SE is only one way of expressing the preciseness of your

statistic. In this chapter, we focus on another way — through the use of a confidence interval (CI).

We assume that you’re familiar with the concepts of populations, samples, and statistical

estimation theory (see Chapters 3 and 6 if you’re not), and that you know what SEs are (read

Chapter 3 if you don’t). Keep in mind that when you conduct a human research study, you’re

typically enrolling a sample of study participants drawn from a hypothetical population. For

example, you may enroll a sample of 50 adult diabetic patients who agree to be in your study as

participants, but they represent the hypothetical population of all adults with diabetes (for details

about sampling, turn to Chapter 6). Any numerical estimate you observe from your sample is a

sample statistic. A statistic is a valid but imperfect estimate of the corresponding population

parameter, which is the true value of that quantity in the population.

Feeling Confident about Confidence Interval

Basics

The main part of this chapter is about how to calculate confidence intervals (Cis) around the sample

statistics you get from research samples. But first, it’s important for you to be comfortable with the

basic concepts and terminology related to CIs.

Defining confidence intervals

Informally, a confidence interval indicates a range (or interval) of numerical values that’s

likely to encompass the true value. More formally, the CI around your sample statistic is

calculated in such a way that it has a specified likelihood of including or containing the value of

the corresponding population parameter.