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Chapter 14: Being Independent Enough for the Chi-Square Test 245

Determining the hypotheses

Every hypothesis test (whether it be a Chi-square test or some other test)
has two hypotheses:

✓ Null hypothesis: You have to believe this unless someone shows you
otherwise. The notation for this hypothesis is Ho.
✓ Alternative hypothesis: You want to conclude this in the event that you
can’t support the null hypothesis anymore. The notation for this hypoth-
esis is Ha.

In the case where you’re testing for the independence of two categorical
variables, the null hypothesis is when no relationship exists between them.
In other words, they’re independent. The alternative hypothesis is when the
two variables are related, or dependent.

For the paint color preference example from the previous section, you write
Ho: Gender and paint color preference are independent versus Ha: Gender
and paint color preference are dependent. And there you have it — step two
of the Chi-square test.

For a quick review of hypothesis testing, turn to Chapter 3. For a full discus-
sion of the topic, see my other book Statistics For Dummies (Wiley) or your
Stats I textbook.

Figuring expected cell counts

When you’ve collected your data and set up your two-way table (for example,
see Table 14-1), you already know what the observed values are for each cell
in the table. Now you need something to compare them to. You’re ready for
step three of the Chi-square test — finding expected cell counts.

The null hypothesis says that the two variables x and y are independent.
That’s the same as saying x and y have no relationship. Assuming indepen-
dence, you can determine which numbers should be in each cell of the table
by using a formula for what’s called the expected cell counts. (Each individual
square in a two-way table is called a cell, and the number that falls into each
cell is called the cell count; see Chapter 13.)

Table 14-1 shows the observed cell counts from the gender and paint color
preference example. To find the expected cell counts you take the row total
times the column total divided by the grand total, and do this for each cell in
the table. Table 14-2 shows the calculations for the expected cell counts for
the gender and paint color preference data.

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