Page 257 - Statistics for Dummies

Chapter 15: Commonly Used Hypothesis Tests: Formulas and Examples

1. Calculate the sample proportions and for each sample. Let n and
1
n represent the two sample sizes (they don’t need to be equal).
2
.

2. Find the difference between the two sample proportions,
3. Calculate the overall sample proportion , the total number of indi-

viduals from both samples who have the characteristic of interest (for
example, the total number of smokers, male or female, in the sample),
divided by the total number of individuals from both samples (n + n ).
2
1
4. Calculate the standard error:

5. Divide your result from Step 2 by your result from Step 4. This answer
is your test statistic.
To interpret the test statistic, look up your test statistic on the standard
normal (Z-) distribution (the Z-table in the appendix) and calculate the p-value, 241
then make decisions as usual (see Chapter 14 for more on p-values).
Consider those drug ads that pharmaceutical companies put in magazines. The
front page of an ad shows a serene picture of the sun shining, flowers bloom-
ing, people smiling — their lives changed by the drug. The company claims
that its drugs can reduce allergy symptoms, help people sleep better, lower
blood pressure, or fix whichever other ailment it’s targeted to help. The claims
may sound too good to be true, but when you turn the page to the back of the
ad, you see all the fine print where the drug company justifies how it’s able to
make its claims. (This is typically where statistics are buried!) Somewhere in
the tiny print, you’ll likely find a table that shows adverse effects of the drug
when compared to a control group (subjects who take a fake drug), for fair
comparison to those who actually took the real drug (the treatment group; see
Chapter 17 for more on this).
For example, Adderall, a drug for attention deficit hyperactivity disorder
(ADHD), reported that 26 of the 374 subjects (7%) who took the drug experi-
enced vomiting as a side effect, compared to 8 of the 210 subjects (4%) who
were on a placebo (fake drug). Note that patients didn’t know which treat-
ment they were given. In the sample, more people on the drug experienced
vomiting, but is this percentage enough to say that the entire population on
the drug would experience more vomiting? You can test it to see.
In this example, you have H : p – p = 0 versus H : p – p > 0, where p repre-
o 1 2 o 1 2 1
sents the proportion of subjects who vomited using Adderall, and p repre-
2
sents the proportion of subjects who vomited using the placebo.

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