Variability assessment of qualitative data has an important role in diverse areas such as sociology, quality engineering, healthcare, decision making, genetics, metrology in chemistry and many others. To test the homogeneity hypothesis, we use two main categorical factors. Using a cross-balanced design, we provide a decomposition theorem of the sample total-variation into ‘intra’ (within) component and ‘inter’ (between) component for any scale. Building on this, we provide a way for decomposing the ‘inter’ component itself into variation components contributed by the two factors and their interaction (when we consider more than one replicated test in the cross-design). Moreover, focusing on an ordinal scale, we offer segregation power indices for testing the significate effects of the two factors and their interaction. A two-way ORDANOVA calculator is provided to display the empirical distributions of the segregation power indices and to find critical points of the test statistics distributions at the given confidence level. Some examples are given to demonstrate the proposed method.

定性数据的可变性评估在社会学，质量工程，医疗保健，决策，遗传学，化学计量学等许多领域都具有重要作用。为了检验同质性假设，我们使用两个主要的分类因素。使用交叉平衡设计，对于任何规模，我们都将样本总变化分解为“内部”  （内部）分量和“内部”  （中间）分量的分解定理。在此基础上，我们提供了一种分解“国际”的方式 组件本身变成变异组件，这是由两个因素及其相互作用共同作用的（当我们在交叉设计中考虑多个重复测试时）。此外，我们以序数尺度为重点，提供了隔离力指数，以测试这两个因素的显着影响以及它们之间的相互作用。提供了一个双向ORDANOVA计算器，以显示偏析强度指数的经验分布，并在给定的置信度下查找测试统计量分布的关键点。给出了一些例子来说明所提出的方法。