130 PART 3 Getting Down and Dirty with Data

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 sam-

ple statistic is calculated in such a way that it has a specified likelihood of includ-

ing or containing the value of the corresponding population parameter.

The SE is usually written after a sample mean with a ± (read “plus or minus”)

symbol followed by the number representing the SE.  As an example, you may

express a mean and SE blood glucose level measurement from a sample of adult

diabetics as 120 ± 3 mg/dL. By contrast, the CI is written as a pair of numbers —

known as confidence limits (CLs) — separated by a dash. The CI for the sample

mean and SE blood glucose could be expressed like this: 114 – 126 mg/dL. Notice

that 120 mg/dL — the mean — falls in the middle of the CI. Also, note that the

lower confidence limit (LCL) is 114 mg/dL, and the upper confidence limit (UCL) is

126 mg/dL. Instead of LCL and UCL, sometimes abbreviations are used, and are

written with a subscript L or U (as in CLL or CLU) indicating the lower and upper

confidence limits, respectively.

Although SEs and CIs are both used as indicators of the precision of a numerical

quantity, they differ in what they are intending to describe (the sample or the

population):»

» ^{A SE indicates how much your observed sample statistic may fluctuate if the}

same study is repeated a large number of times, so the SE intends to describe

the sample.»

» ^{A CI indicates the range that’s likely to contain the true population parameter,}

so the CI intends to describe the population.