Page 270 - Statistics II for Dummies

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

However, because Chi-square tables in general only give a few values for each
Chi-square distribution, the best you can say using this table is that your
p-value for this test is less than 0.005.

Here’s the big news: Because your p-value is less than 0.05, you can conclude
based on this data that gender and house paint color preference are likely to
be related in the population (dependent), like the American Demographics
Survey said (quoted at the beginning of this chapter). Only now, you have
a formal statistical analysis that says this result found in the sample is also
likely to occur in the entire population. This statement is much stronger!
If your data shows you can reject Ho, you only know at that point that the two
variables have some relationship. The Chi-square test statistic doesn’t tell you
what that relationship is. In order to explore the relationship between the two
variables, you find the conditional probabilities in your two-way table (see
Chapter 13). You can use those results to give you some ideas as to what may
be happening in the population.

For the gender and house paint color preference example, because paint
color preference is related to gender, you can examine the relationship
further by comparing the male versus female paint color preferences and
describing how they’re different. Start by finding the percentage of men that
prefer white houses, which comes out to 180 ÷ 500 = 0.36, or 36 percent,
calculated from Table 14-1. Now compare this result to the percentage of
women who prefer white houses: 125 ÷ 500 = 0.25, or 25 percent. You can
now conclude that in this population (not just the sample) men prefer white
houses more than women do. Hence, gender and house paint color prefer-
ence are dependent.

Dependent variables affect each other’s outcomes, or cell counts. If the cell
counts you actually observe from the sample data won’t match the expected
cell counts under Ho: The variables are independent, you conclude that the
dependence relationship you found in the sample data carries over to the pop-
ulation. In other words, big differences between observed and expected cell
counts mean that the variables are dependent.

Extracting the p-value from computer output
After Minitab calculates the test statistic for you, it reports the exact p-value
for your hypothesis test. The p-value measures the likelihood that your
results were found just by chance while Ho is still true. It tells you how much
strength you have against Ho. If the p-value is 0.001, for example, you have
much more strength against Ho than if the p-value, say, is 0.10.

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