Consider a contingency table with two variables: alcohol consumption, and road accident fatality, with corresponding observed frequencies.

Suppose a researcher wants to conduct a test of independence, which requires both the observed and expected frequencies of the dataset.

But how will the researcher determine the expected frequency? First, the researcher assumes that the two variables are independent. So, the probability of any event involving both variables can be calculated using the multiplication rule for independent events.

The product of the probability value and the table's grand total gives the expected frequency for the first cell. From this, a general formula for the expected frequency is obtained, which can be further simplified.

This simplified formula is then used to calculate the expected frequencies of the other cells.

Once all the expected frequencies are calculated, the researcher can proceed to determine the chi-square test statistic and conduct the hypothesis test.