I was in charge of the Bureau of Labor Statistics. So I had some of the most brilliant mathematical statistical minds in the country , who would put together the modern technology, if you like, of understanding the economy and tracking it and trying to influence it. by Daniel Patrick Moynihan, Politician, Sociologist and Diplomat
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| Source: thechiefstoryteller.com |
What is Contingency Table ?
Contingency table is a useful tool for examining relationships between categorical variables. It is a special type of frequency distribution table, where variables are shown simultaneously. It is also called as cross-classification table.
A contingency table can summarize three probability distributions - joint, marginal and conditional.
Joint Distributions
When we need to consider relationship between two or more events. It allows us to reason about the relationship between multiple events. Like: It is cloudy and raining. The sum of joint distribution is 1.
Marginal Distributions
A marginal distribution is where you are only interested in one of random variables, either X or Y. When may only be interested in a subset of the events. The row and column totals of the contingency table provide the marginal distributions. The sum of marginal distribution is 1.
Conditional Distributions
Sometimes, we know an event has already happened and we want to model what will happen next. It allows us to reason about causality. Like: It is cloudy and it might rain. It describe the distribution of one variable given the levels of the other variable. The sum of conditional distribution is 1.
Implementation of One-Way Table
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| One Way Table |
Implementation of Two-Way Table
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| Two Way Table |
Add Margins and CrossTable
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| Marginal Distribution |
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| CrossTable |
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