Testing a correlation coefficient s significance Using H 0 0 is preferable to H 0 0
This paper proposes an alternative approach in correlation analysis to significance testing. It argues that testing the null hypotheses H0: 0 versus the H1: 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 for any 0 1 instead of the simple null hypothesis H0: 0. At best, the value of 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, 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 0.