134 PART 3 Getting Down and Dirty with Data

As you can see, CI calculations include a k x SE component, which is both added to

and subtracted from the estimate to get the limits. This component is called the

margin of error (ME).

Confidence limits computed this way are often referred to as normal-based,

asymptotic, or central-limit-theorem (CLT) confidence limits. The value of k in the

formulas depends on the desired confidence level and can be obtained from a table

of critical values for the normal distribution. Table 10-1 lists the k values for some

commonly used confidence levels.

For the most commonly used confidence level, 95 percent, k is 1.96, or approxi-

mately 2. This leads to the very simple approximation that 95 percent upper con-

fidence limit is about two SEs above the value, and the lower confidence limit is

about two SEs below the value.

The confidence interval around a mean

Suppose that you enroll a sample of 25 adult diabetics (N = 25) as participants in

a study, and find that they have an average fasting blood glucose level of 130 mg/

dL with a standard deviation (SD) of ±40 mg/dL. What is the 95 percent confi-

dence interval around that 130 mg/dL estimated mean?

To calculate the confidence limits around a mean using the formulas in the pre-

ceding section, you first calculate the SE, which in this case is the standard error

of the mean (SEM). The formula for the SEM is SEM

SD

N

/

, where SD is the SD

of the sample values, and N is the number of values included in the calculation.

For the fasting blood glucose study sample, where your SD was 40 mg/dL and your

sample size was 25, the SEM is SEM

40

25

/

, which is equal to 40/5, or 8 mg/dL.

TABLE 10-1

Multipliers for Normal-Based Confidence Intervals

Confidence Level

Tail Probability

k Value

50%

0.50

0.67

80%

0.20

1.28

90%

0.10

1.64

95%

0.05

1.96

98%

0.02

2.33

99%

0.01

2.58