Testing Claims about the Independence of Two Variables

**Purpose:** To test whether two variables are
independent of each other.

**Conditions:** Set up a two-way table of observed
counts. One way will be for the values of one of the random variables you’re
using. The other will be for values of the other random variable. Use it to
compute the expected counts for each cell in the table, thus:.
The conditions for the test are

(1) All the data in the two-way table come from a single (simple) random sample.

(2) All expected counts are higher than 1.

(3) No more than 20% of the expected counts are less than 5.

**Hypotheses:**

*Neither
of the variables depends the other*.
Many people say it this way: *
There is no
association between the two variables*.
The alternative hypothesis is
*At
least one of the variables depends on at least one of the others*, or,
*There is an
association between some of the variables.*

**Test Statistic:** We recommend using software such as
SPSS to calculate the
test
statistic, the degrees of freedom, and the p-value. However, you __can__ use
the formula
,
with degrees
of freedom, and get the p-value from a
table
such as

Table F in Moore & McCabe’s __The Practice of Business
Statistics__.

** **

**SPSS instructions for testing claims about independence:**
Click here.

**Examples of testing claims about independence: **
Click here.

**Related topics:**

Chi-squared tests master reference page

Tests of homogeneity (several proportions)

Goodness-of-fit (comparing populations when one population is “known”)

**Statistics Reference Pages:**
Click here

BYU-Idaho mailto:brownd@byui.edu

232 Ricks Building 208-496-1839 voice

Rexburg, ID 83460 208-496-2005 fax

**Please
do not call me at home.**