Do "old" people snore more than young? A random sample of 995 people were surveyed and categorized by whether they were "young" (184 people under 30) or "old" (811 people over 30).

> prop.test(x=c(318,48), n=c(811,184), conf.level=0.95) 2-sample test for equality of proportions with continuity correction data: c(318, 48) out of c(811, 184) X-squared = 10.5513, df = 1, p-value = 0.001161 alternative hypothesis: two.sided 95 percent confidence interval: 0.05610974 0.20636815 sample estimates: prop 1 prop 2 0.3921085 0.2608696

The *x* counts are for what we might call "success."
Here success is snorin; 318 old people and 48 young people did it.. The
order in which these are entered is the same as the order of subtraction
for computing the difference, so the confidence interval is for the
difference old-young. We are comparing two age groups so the sizes of the
age groups go in as *n*. Note that you get both a hypothesis test
and a confidence interval. The results may not exactly agree with what you
get using textbook formulae because R is making some tweaks ("continuity
correction") that are not worth the effort if you are doing things by
hand.

If you do not have the counts, but you have the data in variables in R,
you can use the R `table` command to get the counts. This also
checks for some types of gross errors, such as an 11 in a column that is
supposed to be 0-1. We will use the heart attack data as an example. You
have to reattach the table each time you open R.

> table(SEX,DIED) Error in table(SEX, DIED) : object "SEX" not found > attach(heartatk) > table(SEX,DIED) DIED SEX 0 1 F 4298 767 M 7136 643

R is being mean and not returning the row and column totals. We can get
those with repeated use of `table` and `length`.

> table(SEX) SEX F M 5065 7779 > table(DIED) DIED 0 1 11434 1410 > length(SEX) [1] 12844

It would make a good exercise to put these totals in their proper place in the original table. Page layout is no guide to what is statistically correct!

We will compare the mortality rates of males and females. This amounts
to labeling death as "success". We need the numbers who died in
each group for *x* and the total number of people in each group
(total males and total females) for *n*. Make sure you enter these
in consistent order. We are very old and followed the old-fashioned rule
of "ladies first" -- for both *x* and *n*.

> prop.test(x=c(767,643),n=c(5065,7779)) 2-sample test for equality of proportions with continuity correction data: c(767, 643) out of c(5065, 7779) X-squared = 147.7612, df = 1, p-value < 2.2e-16 alternative hypothesis: two.sided 95 percent confidence interval: 0.05699518 0.08055073 sample estimates: prop 1 prop 2 0.15143139 0.08265844

"Ladies first" means we subtracted *F-M* so the positive
numbers in the confidence interval mean the mortality rate was higher for
women. The fact that it does not include zero means that the difference is
unlikely to be due to sampling error. (Bear in mind that this is not a
random sample so we need to be very cautious in extrapolating to other
states or years.) The tiny *p*-value confirms this.

© 2006 Robert W. Hayden