Contingency tables – A Level Further Mathematics OCR Revision

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.

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.

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.

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.