CONSEQUENCES OF VIOLATING THE INDEPENDENCE ASSUMPTION IN ANALYSIS OF VARIANCE
CONSEQUENCES OF VIOLATING THE INDEPENDENCE ASSUMPTION IN ANALYSIS OF VARIANCE
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DOI：
10.1037/0033-2909.99.3.422
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发表时间：
1986-05-01
影响因子：
22.4
通讯作者：
JUDD, CM
中科院分区：
文献类型：
--
作者：
KENNY, DA;JUDD, CM
本文的目的是全面讨论观测值的非独立性对用于检验某些离散自变量效果的均方的偏差影响。我们首先定义观察的非独立性，并讨论三种常见的假设非独立模式：由于群体而导致的非独立性、由于序列而导致的非独立性以及由于空间而导致的非独立性。然后，我们展示了在分析离散自变量的影响时，当忽略三种非独立性模式中的每一种时，如何得出治疗均方和误差均方的偏差。在每种情况下，我们都表明引入的偏差可能相当大。此外，每个均方偏差的综合影响可能导致 F 比率太大或太小。我们简要讨论消除偏差的方法，包括在分析中包含非独立性的来源、转换数据以消除它或对其进行建模。最后，我们建议，观察的非独立性不应仅仅被视为统计上的麻烦，而应被视为心理学研究许多领域的核心实质性问题。
The purpose of this article is to present a comprehensive discussion of the biasing effects of nonindependence of observations on the mean squares used to test the effect of some discrete independent variable. We start by defining nonindependence of observations and discuss three commonly assumed patterns of nonindependence : nonindependence due to groups, nonindependence due to sequence, and nonindependence due to space. We then show how the bias in both the mean square for treatment and the mean square for error can be derived when each of the three patterns of nonindependence is ignored in analyzing the effect of a discrete independent variable. In each case we show that the bias introduced can be considerable. Further, the combined effects of the bias in each of the mean squares can lead to either too large or too small F ratios. We briefly discuss ways to eliminate the biases, either by including the source of nonindependence in the analysis, transforming the data to remove it, or modeling it. Finally, we suggest that nonindependence of observations should be looked at not simply as a statistical nuisance, but also as a substantive issue central to many areas of psychological research.