Objectives for Unit Nine

Chi Square Analysis

**1. Know situations when it is
appropriate for chi square analysis.**

Chi square analysis is appropriate
when it is desired to test whether two or more distributions are identical.
The actual test is whether the frequencies for each category in the distributions
being compared are in the same proportions (or are the corresponding percentages
in each distribution equal). Chi square is most commonly used with nominal
and ordinal variables when frequency distribution on a variable of interest
are compared for two or more groups. For example, you might want to compare
whether freshmen, sophomores, juniors, and seniors differed in their preferences
for president of the student body in a school. The preferences for each
class would be a frequency distribution. Preference would be a nominal
variable and class in school an ordinal variable.

It is possible to compare two or more distributions of observed values or to compare one distribution of observed values with a hypothesized distribution such as the normal curve or a distribution of equal frequencies.

**2. Know the minimum expected
frequencies needed for a chi square test.**

A common rule-of-thumb for proper
interpretation of chi square tests is to have no cell with an expected
frequency less than 1 and no more than 20% of the cells with an expected
frequency less than 5.

**3. Know what to do when minimum
expected frequency requirements are not met.**

If minimum expected frequency requirements
are not met it is recommended to consider combining rows or columns so
that the requirements are met. Rows and columns should only be combined
if meaningful interpretation can be made of the new row or column.

**4. Be able to interpret frequency
tables exhibiting significant chi square values.**

To interpret a chi square table,
it is necessary to compare the row or column percentages and subjectively
determine their differences.