CHAPTER 3 Getting Statistical: A Short Review of Basic Statistics 39

Confidence intervals

An important application of statistical estimation theory in biostatistics is calculat-

ing confidence 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 confi-

dence 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, propor-

tions, 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 sub-

topics. It encompasses all the famous (and many not-so-famous) statistical tests

of significance, including the Student t tests and the analysis of variance (other-

wise known as ANOVA). Both t tests and ANOVAs are covered in Chapter 11. Statis-

tical 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 differ-

ent 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 hyperten-

sive 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.