# Contingency tables

## Contingency Tables Fundamentals

• A Contingency table is a type of table that displays the frequency distribution of multiple categorical variables.
• They are often used in statistical analysis to establish the relationship between two categorical variables.
• It’s a vital tool in the Chi-Squared test, where it’s used to display the expected and observed frequencies.

## How to Construct a Contingency Table

• Identify the two variables you are focusing on; these will constitute the rows and columns of your table.
• Calculate the total frequency of each variable, which should be placed in the final row or column of the table.
• Each cell in the table represents the frequency of a particular combination of the two variables.
• The sum of the frequencies in any row or column should equate to the total frequency mentioned earlier.

## Contingency Tables in Chi-Squared Tests

• A contingency table can be used to carry out a Chi-Squared test of independence.
• The Chi-Squared test is used to determine if there is a significant association between the two categorical variables.
• The expected frequency for each cell in a Chi-Squared test is calculated as (Row Total x Column Total) / Grand Total.

## Interpreting Contingency Tables

• Contingency tables provide a basic visual representation of the relationship between variables.
• If there is a significant difference between the observed and expected frequencies in each cell of the table (i.e., your Chi-Squared test is significant), it suggests that the variables are not independent.
• Always remember to interpret statistical findings in context, considering the limitations and potential confounding variables of the study from which your data was collected.