Loglinear analysis has gained wide acceptance in sociology as the method of choice for the analysis of categorical data. Three alternatives which define interactions and deal with sampling variability in a different manner are developed here. Loglinear analysis and the three alternatives are applied to data on racial prejudice in the United States in 1946 and in 1963. Conventional loglinear analysis leads to the conclusion that the effect of time was the same in the North and the South, whereas the alternative approaches support a contrary conclusion that the time effect was greater in the South than in the North. For the analysis of interaction in the 2×2×2 table, two of the alternatives are simpler to apply and easier to comprehend than loglinear analysis. The third alternative clarifies the useful distinction between estimating the characteristics of the population and describing that population.