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230 Part IV: Building Strong Connections with Chi-Square Tests

You can see that P(Yes|M) + P(No|M) = 1.00 because you’re breaking all males
into two groups: those using cellphones for personal calls (Y) and those not (N).
Notice, however, that P(Yes|M) + P(Yes|F) doesn’t sum to 1.00. In the first case,
you’re looking only at the males, and in the second case, only at the females.

Comparing two groups with conditional probabilities
One of the most common questions regarding two categorical variables is
this: Are they related? To answer this question, you compare their condi-
tional probabilities.

To compare the conditional probabilities, follow these steps:
1. Take one variable and find the conditional probabilities based on the
other variable.
2. Repeat step one for each category of the first variable.
3. Compare those conditional probabilities (you can even graph them for
the two groups) and see whether they’re the same or different.
If the conditional probabilities are the same for each group, the variables
aren’t related in the sample. If they’re different, the variables are related
in the sample.
4. Generalize the results to the entire population by using the sample
results to draw a conclusion from the overall population involved by
doing a Chi-square test (see Chapter 14).

Revisiting the cellphone example from the previous section, you can ask spe-
cifically: Is personal use related to gender? You know that you want to com-
pare cellphone use for males and females to find out whether use is related
to gender. However, it’s very difficult to compare cell counts; for example, 325
males use their phones for personal calls, compared to 427 females. In fact,
it’s impossible to compare these numbers without using some total for per-
spective. 325 out of what?

You have no way of comparing the cell counts in two groups without creating
percentages (achieved by dividing each cell count by the appropriate total).
Percentages give you a means of comparing two numbers on equal terms. For
example, suppose you gave a one-question opinion survey (yes, no, and no
opinion) to a random sample of 1,099 people; 465 respondents said yes, 357
said no, and 277 had no opinion. To truly interpret this information, you’re
probably trying to compare these numbers to each other in your head. That’s
what percentages do for you. Showing the percentage in each group in a side-
by-side fashion gives you a relative comparison of the groups with each other.

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