When evaluating the relationship between two or more different items or variables from an experiment, use a contingency table. This table allows for an at-a-glance analysis of observations between the variables. The most common type of contingency table is commonly referred to as the 2x2 or 2 row and 2 column contingency table, but can have as many rows and columns as needed for variables to be evaluated.
Start with two outcomes. In this example, we will use pass versus fail. These are the columns in the table.
Define the group variables. In our example, these will be the classes. They will be the rows for the table.
Class 1 A B Class 2 C D
Input the numbers. Instead of A, B, C and D in our example, we'll use some fictional numbers of students who passed and failed tests. In a real contingency table, numbers will be used, not variables.
Class 1 13 7 Class 2 19 1
Tally both ends. This is called "two-tallied."
Pass Fail Total
Class 1 13 7 20 Class 2 19 1 20 Total 32 8 40
Compute the P-value. The formula is A/(A+B) - C/(C+D).
If the P-value is very small, it is statistically significant and not randomly occurring.