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# Contingency Table

last edited by 6 years, 7 months ago

A contingency table is a chart which helps determine the relationship between two categorical variables. Contingency tables are useful because they show how one variable is contingent upon the other. Within the table are cells which display the count, or number of times a variable combination appears. Cells running horizontally compose rows. Cells running vertically compose columns. On the border of the rows and columns are the marginal distributions, shown as counts or percentages, which display how frequently each combination of categorical variable appears in the data. Another way to examine the data, is to look at the conditional distribution, which shows the frequency of one type of outcome or condition for a single variable. This format allows for the relationship between explanatory and response variable to be clear by comparing percentages, but you should be careful to make sure to use the right percentage depending on the what a particular question is asking.

Here is a contingency table displaying the data of the results of weather forecasting for rain in a particular city. 97.5% of the time when no rain is forecasted, the forecast is correct. Comparatively, 2.5% of the time when no rain is forecasted, the forecast is incorrect and it rains. Together, the forecast for no rain adds up to 100% for the marginal distribution, which accounts for all forecasts of no rain. The conditional distribution will help us conclude why forecasters are more likely to incorrectly predict rain than no rain. The reason that rain is more often incorrectly forecasted (30.0%) than forecasts for rain (2.5%) may be because meteorologists will see a weather system, and predict rain, but in reality the system will pass without raining (70%). In the opposite case, meteorologists can see there is no weather system and are therefore more likely to correctly forecast no rain (97.5%).

How to Create a Contingency Table using SPSS:

• Select "Analyze" in the menu and Click on "Descriptive Statistics" then, click on "Crosstabs".
• Put the explanatory variable in the row box, and the response variable in the column box.
• Select on the "Statistics" button.
• Select on "Cells" box.
• Check the "Rows" box and click continue.
• Finally, select "OK" in the "Crosstabs" window and the table will appear in the SPSS statistics view window.