Cattell's Scree Test In Relation To Bartlett's Chi-Square Test And Other Observations On The Number Of Factors Problem.
Cattell's Scree Test In Relation To Bartlett's Chi-Square Test And Other Observations On The Number Of Factors Problem.
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Cattell 的 Scree 检验与 Bartlett 的卡方检验以及对因子数量问题的其他观察有关。
DOI：
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发表时间：
1979
影响因子：
3.8
通讯作者：
R. Engstrom
中科院分区：
文献类型：
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作者：
J. Horn;R. Engstrom
结果表明，Cattell的scree检验和Bartlett的卡方检验都是基于相同的理论基础，前者反映的是统计学（受试者抽样）的变异性，而后者通常涉及心理测量学（变量抽样）的影响。如果α水平（隐含在scree测试中）设置相同，则两个测试应得出相同的结论。一些例子的分析表明，如果Bartlett检验的α水平被（明确地）设置在100到150的样本Ns的.0003附近，则该检验的应用结果将表明与基于更大（N = 600）样本确定的scree检验估计的因子数量大致相同。以这种方式使用，巴特利特检验可以产生相当好的因子数量的“总体”估计。Bartlett测试，因此scree测试，和测试的一个共同的因素模型和相关矩阵的意义之间的关系进行了阐述。
It is demonstrated that Cattell's scree test and Bartlett's chi-square test for the number of factors are both based on the same rationale, so the former reflects statistical (subject sampling) variability and the latter usually involves psychometric (variable sampling) influences. If the alpha-level (implicit in the scree test) is set the same, the two tests should lead to the same conclusions. Analyses with some examples suggest that if the alpha-level for the Bartlett test is set (explicitly) in the neighborhood of .0003 for sample Ns of 100 to 150, the results from applications of this test will indicate approximately the same number of factors as estimated on the basis of a scree test determined on a much larger (N ≃ 600) sample. Used in this way, the Bartlett test may yield fairly good "population" estimates of the number of factors. Relationships between the Bartlett test, hence the scree test, and tests for a common factor model and for the significance of a correlation matrix are explicated.