NHANES$MARRIED).

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 written 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 output, 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.

LISTING 11-2 R Output from a Paired Student t Test

> t.test(BP$BPXOSY1, BP$BPXOSY2, paired = TRUE)

Paired t-test

data: BP$BPXOSY1 and BP$BPXOSY2

t = 4.3065, df = 10325, p-value = 1.674e–05

alternative hypothesis: true mean difference is not equal to 0

95 percent confidence interval:

0.1444651 0.3858467

sample estimates:

mean difference

0.2651559

Notice a difference between the output shown in Listings 11-1 and 11-2. In Listing 11-1, the third line

of output says, “alternative hypothesis: true mean is not equal to 100.” That is because we specified

the null hypothesis of 100 when we coded the one-sample t test. Because we did a paired t test in

Listing 11-2, this null hypothesis now concerns 0 because we are trying to see if there is a statistically

significant difference between the first SBP reading and the second in the same individuals. Why