Using the correct statistical test for the equality of regression coefficients
Using the correct statistical test for the equality of regression coefficients
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DOI：
10.1111/j.1745-9125.1998.tb01268.x
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发表时间：
1998-11-01
期刊：
影响因子：
5.8
通讯作者：
Piquero, A
中科院分区：
文献类型：
--
作者：
Paternoster, R;Brame, R;Piquero, A
犯罪学家通常对考察回归背景下的交互效应感兴趣。例如，在其他相关因素不变的情况下，犯罪同伴对自己犯罪行为的影响对男性和女性的影响是否相同？或者“某一特定治疗方案的效果在初犯和惯犯之间是否相当？”检验这种交互作用的一个常见策略是测试独立样本上两个回归系数之间的差异。也就是说，b(1)=b(2)吗？传统上，犯罪学家在进行这些系数比较时，会使用t检验或z检验来衡量不同斜率之间的差异。虽然对这一策略的适当性有相当大的共识，但在犯罪学文献中，对于t或z公式中差异的标准误差、系数差异的抽样分布的标准偏差的正确估计值，存在一些混乱。犯罪学家在他们的实证工作中使用了两种不同的标准偏差估计器。在这篇笔记中，我们指出这些估计器中的一个是正确的，而另一个是不正确的。不正确的估计量使一个人的假设检验偏向于拒绝b(1)=b(2)的零假设。不幸的是，这种对差异标准误差的错误估计在犯罪学中已经相当普遍。我们给出了正确的统计检验的公式，并用文献中的两个例子说明了有偏估计如何导致错误的结论。
Criminologists are often interested in examining interactive effects within a regression context. For example, "holding other relevant factors constant, is the effect of delinquent peers on one's own delinquent conduct the same for males and females?" or "is the effect of a given treatment program comparable between first-time and repeat offenders?" A frequent strategy in examining such interactive effects is to test for the difference between two regression coefficients across independent samples. That is, does b(1) = b(2)? Traditionally, criminologists have employed a t or z test for the difference between slopes in making these coefficient comparisons. While there is considerable consensus as to the appropriateness of this strategy, there has been some confusion in the criminological literature as to the correct estimator of the standard error of the difference, the standard deviation of the sampling distribution of coefficient differences, in the t or z formula. Criminologists have employed two different estimators of this standard deviation in their empirical work. In this note, we point out that one of these estimators is correct while the other is incorrect. The incorrect estimator biases one's hypothesis test in favor of rejecting the null hypothesis that b(1) = b(2). Unfortunately, the use of this incorrect estimator of the standard error of the difference has been fairly widespread in criminology. We provide the formula for the correct statistical test and illustrate with two examples from the literature how the biased estimator can lead to incorrect conclusions.