intervals. Confidence intervals provide another way to indicate the precision of an estimate or

measurement from a sample. A confidence interval (CI) is an interval placed around an estimated

value to represent the range in which you strongly believe the true value for that variable lies. How

wide you make this interval is dependent on a numeric expression of how strongly you believe the true

value lie within it, which is called the confidence level (CL). If calculated properly, your stated

confidence interval should encompass the true value a percentage of the time at least equal to the stated

confidence level. In fact, if you are indeed making an estimate, it is best practices to report that

estimate along with confidence intervals. As an example, you could express the 95 percent CI of the

mean ages of a sample of graduating master’s degree students from a university this way: 32 years (95

percent CI 28 – 34 years).

At this point, you may be wondering how to calculate CIs. If so, turn to Chapter 10, where we describe

how to calculate confidence intervals around means, proportions, event rates, regression coefficients,

and other quantities you measure, count, or calculate.

Statistical decision theory

Statistical decision theory is a large branch of statistics that includes many subtopics. It encompasses

all the famous (and many not-so-famous) statistical tests of significance, including the Student t tests

and the analysis of variance (otherwise known as ANOVA). Both t tests and ANOVAs are covered in

Chapter 11. Statistical decision theory also includes chi-square tests (explained in Chapter 12) and

Pearson correlation tests (included in Chapter 16), to name a few.

In its most basic form, statistical decision theory deals with using a sample to make a decision

as to whether a real effect is taking place in the background population. We use the word effect

throughout this book, which can refer to different concepts in different circumstances. Examples

of effects include the following:

The average value of a measurement may be different in one group compared to another. For

example, obese patients may have higher systolic blood pressure (SBP) measurements on average

compared to non-obese patients. Another example is that the mean SBP of two groups of

hypertensive patients may be different because each group is using a different drug — Drug A

compared to Drug B. The difference between means in these groups is considered the effect size.

The average value of a measurement may be different from zero (or from some other

specified value). For example, the average reduction in pain level measurement in surgery patients

from post-surgery compared to 30 days later may have an effect that is different from zero (or so

we would hope)!

Two numerical variables may be associated (also called correlated). For example, the taller

people are on average, the more they weigh. When two variables like height and weight are

associated in this way, the effect is called correlation, and is typically quantified by the Pearson

correlation coefficient (described in Chapter 15).

Honing In on Hypothesis Testing