A test of independence determines whether a contingency table's two variables are independent.

In this case, independence means that the probability of any event involving both variables can be directly obtained by multiplying their individual probabilities.

For example, to understand the relationship between alcohol consumption and road accident fatality, arrange the data in a two-by-two contingency table. The  rows represent the subjects' sobriety or intoxication, while the columns represent the fatality or nonfatality of road accidents.

Data from randomly selected samples represent the observed frequencies arranged in the two-way table.

Here, E represents the expected frequency, r indicates the number of rows, and c indicates the number of columns. The expected frequency for each cell must be atleast 5.

The chi-square test statistic is calculated using these expected and observed frequencies. The critical value and P-values are calculated using suitable degrees of freedom from the chi-square table or software.

Finally, a hypothesis test is performed to determine whether alcohol consumption and road accident fatality are independent events.