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Why does H contain a “>” sign and not a “<” sign? H represents the scenario
a
a
in which those taking Adderall experience more vomiting than those on the
placebo — that’s something the FDA (and any candidate for the drug) would
want to know about. But the order of the groups is important, too. You want
to set it up so the Adderall group is first, so that when you take the Adderall
proportion minus the placebo proportion, you get a positive number if H is
true. If you switch the groups, the sign would have been negative.
Now calculate the test statistic:
1. First, determine that
The sample sizes are n = 374 and n = 210, respectively.
2
1
2. Take the difference between these sample proportions to get
.
Part IV: Guesstimating and Hypothesizing with Confidence . a
3. Calculate the overall sample proportion to get
4. The standard error is .
5. Finally, the test statistic is 0.032 ÷ 0.020 = 1.60. Whew!
The p-value is the percentage chance of being at or beyond (in this case to
the right of) 1.60, which is 1 – 0.9452 = 0.0548. This p-value is just slightly
greater than 0.05, so, technically, you don’t have quite enough evidence to
reject H . That means that according to your data, vomiting is not experi-
o
enced any more by those taking this drug when compared to a placebo.
A p-value that’s very close to that magical but somewhat arbitrary significance
level of 0.05 is what statisticians call a marginal result. In the preceding exam-
ple, because the p-value of 0.0548 is close to the borderline between accept-
ing and rejecting H , it’s generally viewed as a marginal result and should be
o
reported as such.
The beauty of reporting a p-value is that you can look at it and decide for
yourself what you should conclude. The smaller the p-value, the more evi-
dence you have against H , but how much evidence is enough evidence? Each
o
person is different. If you come across a report from a study in which some-
one found a statistically significant result, and that result is important to you,
ask for the p-value so that you can make your own decision. (See Chapter 14
for more.)

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