Page 249 - Statistics II for Dummies

Chapter 13: Forming Associations with Two-Way Tables 233

What should you divide by? That is the question!

To get the correct answer for any probability in ✓ If you want the percentage of personal-
a two-way table, here’s the trick: Always iden- call makers who are male, you take 325
tify the group being examined. What’s the prob- divided by 752, the total number of people
ability “out of”? In the cellphone example (refer who make personal calls with their cell-
to Table 13-3), phones.
✓ If you want the percentage of all users who In each of these three cases, the numerator is
are males using their phones for personal the same but the denominators are different,
calls, you take the cell count 325 divided by leading you to very different answers. Deciding
1,016, the grand total. which number to divide by is a very common
source of confusion for people, and this trick
✓ If you want the percentage of males who
are using their cellphones for personal can really give you an edge on keeping it
calls, you take 325 divided by 508, the total straight.
number of males.

Trying To Be Independent

Independence is a big deal in statistics. The term generally means that two
items have outcomes whose probabilities don’t affect each other. The items
could be events A and B, variables x and y, survey results from two people
selected at random from a population, and so on. If the outcomes of the two
items do affect each other, statisticians call those two items dependent (or
not independent). In this section, you check for and interpret independence
of individual categories, one from each categorical variable in a sample, and
you check for and interpret independence of two categorical variables in a
sample.

Checking for independence

between two categories

Statistics instructors often have students check to see whether two catego-
ries (one from a categorical variable x and the other from a categorical vari-
able y) are independent. I prefer to just compare the two groups and talk
about how similar or different the percentages are, broken down by

20_466469-ch13.indd 233 7/24/09 9:47:59 AM