A–8 APPENDIXThe larger a sample we have, the more confident we can be about the estimates
we make about the population. This is seen in FIGURE A.10, which shows samples
of heights drawn from the distributions for females and males shown in Figure
A.2. With only five individuals of each sex, it is not clear whether the difference in
their means is because males really are taller than females, or because by chance
we happened to measure women who are shorter and men who are taller than
average. But with 250 individuals of each sex, it’s obvious that the difference is real.Testing Hypotheses
White-tailed deer (Odocoileus virginianus) live north to Alaska and south to Peru.
Like many other mammals, deer tend to be larger the farther they are from the
equator, a pattern known as Bergmann’s rule (see Chapter 8). One hypothesis to
explain this pattern is that populations in colder climates have evolved larger body
sizes as a way to conserve heat.
To test that hypothesis, we might see if the body size of deer also varies with
elevation. The heat conservation hypothesis predicts that deer populations at high
elevations should be larger than those at low elevations because temperature tends
to decrease with elevation. Imagine that you have a friend in Colorado who reports
that the weight of a single adult male deer living at 1600 m above sea level is 75 kg.
Another friend living near sea level in Texas reports that a single adult male there
weights 60 kg. Are those data strong support for the hypothesis? No, because there
is a plausible alternative hypothesis. Perhaps on average there is no difference
between deer in Colorado and Texas, but by chance the deer that was weighed in
Texas happened to be smaller than the one weighed in Colorado. After requesting
that your friends each weigh a total of 20 deer, you find that all but 1 of the deer
weighed in Colorado are heavier than the deer weighed in Texas. You would now
be very confident that the deer living in Colorado are heavier, which is consistent
with the heat conservation hypothesis.Futuyma Kirkpatrick Evolution, 4e
Sinauer Associates
Troutt Visual Services
Evolution4e_A.10.ai Date 01-08-2017 03-01-2017150160170180190n = 250Height (cm)FIGURE A.10 Our confidence in detecting a difference between n = 5 n = 25
two populations grows with the size of the samples. The three
panels show sample sizes (n) of 5, 25, and 250 females and males
drawn from the distributions shown in Figure A.2. The horizontal
lines show the means of the samples.23_EVOL4E_APP.indd 8 3/22/17 1:52 PM