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Contingency Tables

Posted on February 16, 2021February 16, 2021 by financialeducation

Contingency tables display the frequency distributions of two or more variables at once. They are useful for finding patterns among the variables. They are made by listing all of the categories of one variable as columns and the categories of the other as rows.

In a previous post we created frequency distributions for the 30 companies in the Dow Jones Industrial Average by sector and by size. We can now create a contingency table for both variables.

<250B250-500B500-750B750B-1T>1TTotal
Information Technology410027
Industrials400004
Healthcare220004
Financials310004
Consumer Staples220004
Consumer Discretionary210003
Communication Services110002
Materials100001
Energy100001
Total20800230

The total for each row or column is the marginal frequency for that category. For example, the information technology sector has a marginal frequency of 7 and stocks with a market cap between 250 and 500 billion have a marginal frequency of 8.

We also see that there are 4 information technology companies with a market cap below 250 billion. This is the joint frequency of the 2 variables.

As with frequency distributions, contingency tables can be presented on a relative (percentage) basis, as shown below.

<250B250-500B500-750B750B-1T>1TTotal
Information Technology13%3%0%0%7%23%
Industrials13%0%0%0%0%13%
Healthcare7%7%0%0%0%13%
Financials10%3%0%0%0%13%
Consumer Staples7%7%0%0%0%13%
Consumer Discretionary7%3%0%0%0%10%
Communication Services3%3%0%0%0%7%
Materials3%0%0%0%0%3%
Energy3%0%0%0%0%3%
Total67%27%0%0%7%100%

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