Contingency Tables

Planning Analysis:
Contingency Tables

Crosstab/Contingency Tables

Contingency tables provide an easy method to determine relationships between two variables. Following is one example.

If you are using contingency tables for a cause/effect analysis, you need to initially develop a hypothesis for the analysis. This will allow you to consider is which direction to analyze the data.

The Cause & Effect Rule

The cause and effect rule provides some guidelines for determining how to proceed with the analysis. The rule states that whenever one factor can be considered the cause, and the other the effect, the percents should be computed in the direction of the causal factor, provided the sample is representative in that direction.

In this example, residence is hypothesized as the causal factor in determining support for annexation. Keep in mind that percentages should not, and cannot take the place of measures of association, but can provide key insights in a first pass or "basic" analysis.

Table 1 shows the base data. The table provides the results of a sample survey of county residents on the issue of annexation. In addition to asking whether respondents favored annexation, the survey also asked respondents whether they lived in the City or County.

Table 1. Results of Annexation Voting Poll

	Favor Annexation
Location	Yes	No	Total
City Resident	550	500	1,050
County Resident	375	650	1,025
Total	925	1,150	2,075

Thus, the question: Are respondents' more likely to favor or oppose annexation based on location of residence? In other words, residence is hypothesized as the causal factor in determining support for annexation.

An analysis of this data using percentages could be conducted in three ways:

(1). Annexation by residence (i.e., by columns)

(2). Residence by annexation (i.e., by rows)

(3). By total response

I briefly mentioned the "Cause & Effect rule" in class. This rule basically states that whenever one factor can be considered the cause, and the other the effect, the percents should be computed in the direction of the causal factor, provided the sample is representative in that direction.

In the above example, we will assume that the sample is representative in both directions. Thus, the following analyses:

Table 2. Annexation by Residence

	Favor Annexation
Location	Yes	No
City Resident	59%	43%
County Resident	41%	57%
Total	100%	100%

Table 3. Residence by Annexation

	Favor Annexation
Location	City	County
Yes	52%	37%
No	48%	63%
Total	100%	100%

Based on the "cause and effect" rule, Table 3 would be the proper way to calculate the percentages.

And the conclusions:

1. Analysis of residence by annexation (Table 3), shows that city residents are split on the topic (52% favor, 48% oppose), while county residents strongly oppose annexation (37% favor, 63% oppose). Thus, we can conclude that residence has an impact on support for annexation.

2. Although, support is not a causal factor, analysis by support (Table 2) shows a different picture. City residents are more likely than county residents to support annexation. Table 2 (annexation by residence) shows that, of those respondents that support annexation, a much higher percentage of city residents (59%) support annexation, compared to county residents (41%). The opposite impact is seen by analysis of the "no" column.

Thus, both analyses yield insights. However, the analysis of residence by annexation clearly shows the causal relationship between residence and support for annexation.

A third way to calculate the percentages is as a percent of all respondents. Table 4 shows this analysis.

Table 4. Support for Annexation, all Respondents

	Favor Annexation
Location	Yes	No	Total
City Resident	27%	24%	51%
County Resident	18%	31%	49%
Total	45%	55%	100%

This table also provides some key information. First it shows that the percentage of respondents was nearly equal for city residents (51%) and county residents (49%). If this distribution is reflective of the entire county population, it helps to verify the reliability of the data set. Second, it shows that overall, residents oppose annexation 55% to 45%. Note that the most valuable information from this analysis is provided in the total columns--the percentages in the interior of the table yield little useful information.