CHAPTER 11 Comparing Average Values between Groups 149

Interpreting the output from a t test

Listing 11-1 is the output from a one-sample t-test, where we tested the mean

fasting glucose in the NHANES participants against the hypothesized mean of 100

mg/dL:

LISTING 11-1:

R Output from a One-Sample Student t Test

> t.test(GLUCOSE$LBXGLU, mu = 100)

One Sample t-test

data: GLUCOSE$LBXGLU

t = 21.209, df = 4743, p-value < 2.2e-16

alternative hypothesis: true mean is not equal to 100

95 percent confidence interval:

110.1485 112.2158

sample estimates:

mean of x

111.1821

The R output starts by stating what test was run and what data were used, and

then reports the t statistic (21.209), the df (4743), and the p value, which is writ-

ten in scientific notation: < 2.2e–16. If you have trouble interpreting this notation,

just remove the < and then copy and paste the rest of the number into a cell in

Microsoft Excel. If you do that, you will see in the formula bar that the number

resolves to 0.00000000000000022 — which is a very low p value! The shorthand

used for this in biostatistics is p < 0.0001, meaning it is sufficiently small. Because

of this small p value, we reject the null hypothesis and say that the mean glucose

of NHANES participants is statistically significantly different from 100 mg/dL.

But in what direction? For that, it is necessary to read down further in the R out-

put, under 95 percent confidence interval. It says the interval is 110.1485 mg/dL to

112.2158 mg/dL (if you need a refresher on confidence intervals, read Chapter 10).

Because the entire interval is greater than 100 mg/dL, you can conclude that the

NHANES mean is statistically significantly greater than 100 mg/dL.

Now, let’s examine the output from the paired t test of SBP measured two times

in the same participant, which is shown in Listing 11-2.