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

When you find probabilities based on a sample, as you do in this chapter, you
have to realize that those probabilities pertain to that sample only. They don’t
transfer automatically to the population being studied. For example, if you
take a random sample of 1,000 adults and find that 55 percent of them watch
reality TV, this study doesn’t mean that 55 percent of all adults in the entire
population watch reality TV. (The media makes this mistake every day.) You
need to take into account the fact that sample results vary; in Chapters 14 and
15, you do just that. But this chapter zeros in on summarizing the information
in your sample, which is the first step toward that end (but not the last step in
terms of making conclusions about your corresponding population).

Marginal probabilities

A marginal probability makes a probability out of the marginal total, for either
the rows or the columns. A marginal probability represents the proportion
of the entire group that belongs in that single row or column category. Each
marginal probability represents only one category for only one variable — it
doesn’t consider the other variable at all. In the cellphone example, you have
four possible marginal probabilities (refer to Table 13-3):

✓ Marginal probability of female , meaning that 50 percent of
all the cellphone users in this sample were females
✓ Marginal probability of male , meaning that 50 percent of
all the cellphone users in this sample were males
✓ Marginal probability of using a cellphone for personal calls ,
meaning that 74 percent of all cellphone users in this sample make per-
sonal calls with their cellphones
✓ Marginal probability of not using a cellphone for personal calls
, meaning that 26 percent of all the cellphone users in this
sample don’t make personal calls with their cellphones

Statisticians use shorthand notation for all probabilities. If you let M = male,
F = female, Yes = personal cellphone use, and No = no personal cellphone use,
then the preceding marginal probabilities are written as follows:
✓ P(F) = 0.50
✓ P(M) = 0.50
✓ P(Yes) = 0.74
✓ P(No) = 0.26

Notice that P(F) and P(M) add up to 1.00. This result is no coincidence
because these two categories make up the entire gender variable. Similarly,
P(Yes) and P(No) sum up to 1.00 because those choices are the only two

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