Definition§
A contingency table, also known as a cross-tabulation or crosstab, is a data table used in statistics to display the frequency distribution of variables. Typically, it categorizes survey or observational data into a matrix format, allowing for the comparison of multiple characteristics or attributes. Each cell in a contingency table shows the count or frequency of occurrences for specific pairs of variable combinations, facilitating the analysis of relationships between the variables.
Examples§
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Gender and Age Groups: A condominium project surveys the gender and age range of its homeowners. The contingency table might look like this:
20-30 31-40 41 and above Male 15 20 12 Female 18 22 10 -
Smoking Status and Exercise Frequency: A health study might categorize people by whether they smoke and how frequently they exercise:
Rarely/Never Exercise Sometimes Exercise Regularly Exercise Smoker 30 20 5 Non-Smoker 40 30 25
Frequently Asked Questions (FAQ)§
What is the purpose of a contingency table?§
Contingency tables are used to study the relationship between categorical variables and to perform a variety of statistical tests, including chi-square tests for independence or association.
How do you interpret a contingency table?§
Interpreting a contingency table involves examining the frequencies in each cell, row, and column to identify patterns and relationships between the variables. It can also involve computing marginal totals and relative frequencies.
Can contingency tables be used for more than two variables?§
Yes, while two-dimensional (2D) tables are most common, contingency tables can be expanded to three or more dimensions, though they become harder to represent visually.
What statistical tests are used with contingency tables?§
Common tests include the chi-square test for independence, Fisher’s exact test (for small sample sizes), and various measures of association like Cramer’s V or phi coefficient.
What is a marginal total in a contingency table?§
A marginal total is the sum of frequencies along any row or column, representing the total occurrences of that characteristic across all categories of the other variable.
Related Terms§
- Cross-tabulation: The process of creating a contingency table.
- Marginal Distribution: The totals of rows and/or columns in a contingency table.
- Chi-square Test: A test used to determine if there is a significant association between categorical variables in a contingency table.
- Cramer’s V: A measure of association between two nominal variables, ranging between 0 (no association) and 1 (perfect association).
- Phi Coefficient: Another measure of association for binary variables.
Online References§
Suggested Books for Further Studies§
- “Statistics for Business and Economics” by Paul Newbold, William L. Carlson, and Betty Thorne - Covers a comprehensive range of statistical methods, including the use of contingency tables.
- “An Introduction to Categorical Data Analysis” by Alan Agresti - A detailed guide focused on methods for categorical data analysis, including contingency tables.
- “Statistics in Plain English” by Timothy C. Urdan - Provides clear explanations of basic statistical concepts, suitable for beginners.
Fundamentals of Contingency Table: Statistics Basics Quiz§
Thank you for exploring the intricacies of contingency tables with me and engaging in our comprehensive quiz to solidify your understanding!
