If the data form a "population sample", then the cell probabilities are interpreted as the frequencies of each of the four groups in the population as defined by their "X" and "Y" values. In many settings it is impractical to obtain a population sample, so a selected sample is used. For example, we may choose to sample units with with a given probability "f", regardless of their frequency in the population (which would necessitate sampling units with with probability ). In this situation, our data would follow the following joint probabilities: