A contingency table, also known as a cross-tabulation (crosstab), is a type of table used in statistics to display the relationship between two categorical variables. It helps in analyzing patterns, dependencies, and associations between variables.
Structure of a Contingency Table
A contingency table consists of:
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Rows → Represent categories of one variable.
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Columns → Represent categories of another variable.
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Cells → Contain the frequency (count) of occurrences for the combination of both variables.
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Marginal Totals → The sum of each row and column.
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Grand Total → The overall total of all observations.
Example: Contingency Table for Gender and Preferred Mode of Transport
A survey was conducted among 100 people to study the relationship between gender and preferred mode of transport.
| Mode of Transport | Male | Female | Total |
|---|---|---|---|
| Car | 25 | 20 | 45 |
| Bike | 30 | 10 | 40 |
| Public Transport | 5 | 10 | 15 |
| Total | 60 | 40 | 100 |
Uses of Contingency Tables:
✔ Chi-Square Test for Independence – Used to check if there is a significant relationship between two categorical variables.
✔ Probability Calculations – Used in probability and decision-making.
✔ Market Research & Surveys – Helps in understanding customer preferences.