Summary The most widely used measure of segregation is the so‐called dissimilarity index. It is now well understood that this measure also reflects randomness in the allocation of individuals to units (i.e. it measures deviations from evenness, not deviations from randomness). This leads to potentially large values of the segregation index when unit sizes and/or minority proportions are small, even if there is no underlying systematic segregation. Our response to this is to produce adjustments to the index, based on an underlying statistical model. We specify the assignment problem in a very general way, with differences in conditional assignment probabilities underlying the resulting segregation. From this, we derive a likelihood ratio test for the presence of any systematic segregation, and bias adjustments to the dissimilarity index. We further develop the asymptotic distribution theory for testing hypotheses concerning the magnitude of the segregation index and show that the use of bootstrap methods can improve the size and power properties of test procedures considerably. We illustrate these methods by comparing dissimilarity indices across school districts in England to measure social segregation.

中文翻译：

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对于分离的不相似指数的更可靠的推断。

总结隔离度最广泛使用的度量是所谓的相似性指数。现在众所周知，该度量还反映了个人对单位分配的随机性（即，它测量的是均匀性的偏差，而不是随机性的偏差）。即使没有潜在的系统隔离，当单位大小和/或少数群体比例较小时，这也会导致隔离索引的值较大。我们对此的回应是基于基础的统计模型对指数进行调整。我们以一种非常笼统的方式来指定分配问题，其中有条件的分配概率存在差异，这是所导致的隔离的基础。由此，我们推导了对任何系统隔离的存在进行似然比检验，并对相异指数进行偏差调整。我们进一步发展了渐近分布理论，以测试有关偏析指数幅度的假设，并表明使用自举方法可以显着改善测试程序的大小和功效。我们通过比较英格兰各个学区的相异指数来衡量社会隔离来说明这些方法。