This article is concerned with paradoxes in 2×2×n contingency tables, suchas Simpson's paradox, in which the association in the 2 × 2 marginal table is quite different from the associations in the 2 × 2 partial tables. We prove that if the relative number of observations in each row of each partial table or in each column of each partial table is constant, then Simpson's paradox cannot occur. We also prove that under a certain condition, the paradox cannot occur if the odds ratios in the partial tables are uniformly greater than a lower bound (e.g. ＞ 1.125) or uniformly less than some upper bound.Finally, we show that Simpson's paradox and an amalgamation paradox cannot occur if certain ratios of cell counts are constant in the partial tables.