Testing Claims about Homogeneity (Equality of Several Proportions) Reference Page

**Purpose:** To test whether two or more population
proportions are the same. (Note: If there are only two proportions to compare,
we recommend using the test of two proportions, once you’ve learned about it.)

**Requirements:** Set up a two-way table of observed
counts. One way is for the populations; the other is for "success" / "failure". Use
the table to compute the expected counts for each cell in the table, thus:.
The required conditions for the test are

1) The data are from simple random samples, one from each population.

2) The samples are independent of each other.

3) All expected counts are greater than 1.

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

**Hypotheses:**

, where is the number of groups. This hypothesis means, “All proportions are the same.”

The alternative hypothesis is
*At
least one of the proportions is different from at least one of the others*.
(Hopefully, this reminds you of the ANOVA hypotheses.)

**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__. (Note: There will either be two rows and
columns
or rows
and 2 columns. Either way, there will be
degrees
of freedom.)

**WARNING: The test
statistic is very sensitive to round-off errors made during calculation. **We
recommend using the above formula instead of the one usually found in textbooks,
as it suffers less from this problem. Also, we recommend entering the entire
calculation in your calculator all at once, rather than computing each term
separately, to help minimize round-off error.

** **

**SPSS instructions for testing claims about several
proportions:** Click here.

**Examples of testing claims about several proportions: **Click here.

**Related topics:**

Chi-squared tests master reference page

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

**Statistics Reference Pages page:**
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.**