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Chapter 13: Forming Associations with Two-Way Tables 231

But first, you need to bring conditional probabilities into the mix. In the cell-
phone example, if you want the percentage of females who use their cellphones
for personal calls, you take 427 divided by the total number of females (508) to
get 84 percent. Similarly, to get the percentage of males who use their cellphones
for personal calls, take the cell count (325) and divide it by that row total for
males (508), which gives you 64 percent. This percentage is the conditional
probability of using a cellphone for personal calls, given the person is male.

Now you’re ready to compare the males and females by using conditional prob-
abilities. Take the percentage of females who use their cellphones for personal
calls and compare it to the percentage of males who use their cellphones for
personal calls. By finding these conditional probabilities, you can easily com-
pare the two groups and say that in this sample at least, more females use their
cellphones (84 percent) for personal calls than men (64 percent).

Using graphs to display conditional probabilities
One way to highlight conditional probabilities as a tool for comparing two
groups is to use graphs, such as a pie chart comparing the results of the
other variable for each group or a bar chart comparing the results of the
other variable for each group. (For more info on pie charts and bar charts,
see my book Statistics For Dummies (Wiley) or your Stats I textbook.)
You may be wondering how close the two pie charts need to look (in terms
of how close the slice amounts are for one pie compared to the other) in
order to say the variables are independent. This question isn’t one you can
answer completely until you conduct a hypothesis test for the proportions
themselves (see the Chi-square test in Chapter 14). For now, with respect to
your sample data, if the difference in the appearance of the slices for the two
graphs is enough that you would write a newspaper article about it, then go
for dependence. Otherwise, conclude independence.

Figures 13-1a and 13-1b use two pie charts to compare cellphone use of males
and females. Figure 13-1a shows the conditional distribution of cellphone
use for (given) males. Figure 13-1b shows the conditional distribution of
cellphone use for (given) females. A comparison of Figures 13-1a and 13-1b
reveals that the slices for cellphone use aren’t equal (or even close) for males
compared to females, meaning that gender and cellphone use for personal
calls are dependent in this sample. This confirms the previous conclusions.

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