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If you are reporting a correlation matrix in APA style, are you supposed to report r as in corr.test() or R^2 as in lm()$r.squared? Which one is correct, and what does the other one represent?

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APA publication manual does not explicitly say weather you should choose $R^2$ or $r$ for your results. They say however:

Page 38 of APA Manual:

When reporting the results of inferential statistical tests or when providing estimates of parameters or effect sizes, include sufficient information to help the reader fully understand the analyses conducted and possible alternative explanations for the outcomes of those analyses. Because each analytic technique depends on different aspects of the data and assumptions, it is impossible to specify what constitutes a "sufficient set of statistics" for every analysis. However, such a set usually includes at least the following: the per-cell sample sizes; the observed cell means (or frequencies of cases in each category for a categorical variable); and the cell standard deviations, or the pooled within-cell variance. In the case of multivariable analytic systems, such as multivariate analyses of variance, regression analyses, structural equation modeling analyses, and hierarchical linear modeling, the associated means, sample sizes, and variance-covariance (or correlation) matrix or matrices often represent a sufficient set of statistics. At times, the amount of information that constitutes a sufficient set of statistics can be extensive; when this is the case, this information could be supplied in a supplementary data set or appendix.

The only place with a correlation table is page 136 with this example:

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That being said, I would report Person rs with p values for showing correlation results and leave $R^2s$ for regression results

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