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标题：Testing a correlation coefficient’s significance: Using H0: 0 < ρ ≤ λ is preferable to H0: ρ = 0
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作者：KLAUS D. KUBINGER ; DIETER RASCH ; MARIE ŠIMECKOVA 等
期刊名称：Psychology Science
印刷版ISSN：1614-9947
出版年度：2007
卷号：49
期号：02
出版社：Pabst Science Publishers
摘要：This paper proposes an alternative approach in correlation analysis to significance testing. It argues that testing the null-hypotheses H0: ρ = 0 versus the H1: ρ > 0 is not an optimal strategy. This is because rejecting the null-hypothesis, as traditionally reported in social science papers – i.e. a significant correlation coefficient (regardless of how many asterisks it is adorned with) – very often has no practical meaning. Confirming a population’s correlation coefficient as being merely unequal to zero does not entail much gain of content information, unless this correlation coefficient is sufficiently large enough; and this in turn means that the correlation explains a relevant amount of variance. The alternative approach, however, tests the composite null-hypothesis H0: 0 < ρ ≤ λ for any 0 < λ < 1 instead of the simple null-hypothesis H0: ρ = 0. At best, the value of λ is chosen as the square root of the expected relative proportion of variance which is explained by a linear regression, the latter being the so-called coefficient of determination, ρ2. The respective test statistic is only asymptotically normally distributed: in this paper a simulation study is used to prove that the factual risk is hardly larger than the nominal risk with regard to the type-I-risk. An SPSS-syntax is given for this test, in order to fill the respective gap in the existing SPSS-menu. Furthermore it is demonstrated, how to calculate the sample size according to certain demands for precision. By applying the approach given here, no “use of asterisks” would lead a researcher astray – that is to say, would cause him/her to misinterpret the type-I-risk or, even worse, to overestimate the importance of a study because he/she has misjudged the content relevance of a given correlation coefficient ρ > 0.
关键词：null-hypotheses testing, correlation coefficient, coefficient of determination, linear dependency, sample size determination