Page 260 - Statistics II for Dummies

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

The marginal row totals represent the total number in each row; the marginal
column totals represent the total number in each column. (See Chapter 13 for
more information on row and column marginal totals.)

Notice that of the males, the percentage that wants to paint the house white
is 180 ÷ 500 = 0.36, or 36 percent, as stated previously. And the percentage of
females that wants to paint the house white is 125 ÷ 500 = 0.25, or 25 percent.
(Both of these percentages represent conditional probabilities as explained
in Chapter 13.)

The American Demographics report concluded from this data that “. . . men
and women generally agree on exterior house paint colors; the main excep-
tion being the top male choice, white (36 percent would paint their next
house white versus 25 percent of women).” This type of conclusion is com-
monly formed, but it’s an overgeneralization of the results at this point.

You know that in this sample, more men wanted to paint their houses white
than women, but is 180 really that different from 125 when you’re dealing
with a sample size of 1,000 people whose results will vary the next time you
do the survey? How do you know these results carry over to the population
of all men and women? That question can’t be answered without a formal
statistical procedure called a hypothesis test (see Chapter 3 for the basics of
hypothesis tests).

To show that men and women in the population differ according to favorite
house color, first note that you have two categorical variables:
✓ Gender (male or female)
✓ Paint color (white or nonwhite)

Making conclusions about the population based on the sample (observed)
data in a two-way table is taking too big of a leap. You need to conduct a Chi-
square test in order to broaden your conclusions to the entire population. The
media, and even some researchers, can get into trouble by ignoring the fact
that sample results vary. Stopping with the sample results only and going mer-
rily on your way can lead to conclusions that others can’t confirm when they
take new samples.

You keep the connection between the two pieces of information by organizing
the data into one two-way table versus two individual tables — one for gender
and one for house-paint preference. With one two-way table, you can look at
the relationship between the two variables. (For the full details on organizing
and interpreting the results from a two-way table, see Chapter 13.)

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