Page 331 - Statistics for Dummies

Chapter 19: Two-Way Tables and Independence
I analyzed the data from the aspirin/polyps study using a hypothesis test for
the difference of two proportions (found in Chapter 15). The proportions being
compared were the proportion of patients taking aspirin who developed subse-
quent polyps and the proportion of patients not taking aspirin who developed
subsequent polyps. Looking at these results, my p-value is less than 0.0024.
(A p-value measures how likely you were to have gotten the results from your
sample if the populations really had no difference; see Chapter 14 to get the
scoop on p-values.)
Because this p-value is so small, the difference in proportions between the
aspirin and non-aspirin groups is declared to be statistically significant, and
I conclude that a relationship exists between taking aspirin and developing
fewer subsequent polyps.
You can’t make conclusions about relationships between variables in a popu-
lation based only on the sample results in a two-way table. You must take into
account the fact that results change from sample to sample. A hypothesis test
gives limits for how different the sample results can be to still say the vari- 315
ables are independent. Beware of conclusions based only on sample data from
a two-way table.
Making prudent predictions
A common goal of research (especially medical studies) is to make predic-
tions, recommendations, and decisions after a relationship between two
categorical variables is found. However, as a consumer of information, you
have to be very careful when interpreting results; some studies are better
designed than others.
The colon-cancer study from the previous section shows that patients who
took aspirin daily had a lower chance of developing subsequent polyps
(17% compared to 27% for the non-aspirin group). Because this was a well-
designed experiment and the hypothesis test for generalizing to the popu-
lation was significant, making predictions and recommendations for the
population of colon-cancer patients based on these sample results is appro-
priate. They’ve indeed earned the headline of their press release: “Aspirin
Prevents Polyps in Colon-Cancer Patients.”
Resisting the urge to jump to conclusions
Try not to jump to conclusions when you hear or see a relationship being
reported regarding two categorical variables. Take a minute to figure out
what’s really going on, even when the media wants to sweep you away with a
dramatic result.

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