Corrigendum to “At what sample size do correlations stabilize?” [J. Res. Pers. 47 (2013) 609–612] (S0092656613000858) (10.1016/j.jrp.2013.05.009))

The authors regret that a software bug was detected in the reproducible R code that accompanied the paper. The authors thank Dean Eckles and André Kretzschmar who independently detected and reported the bug. Due to a misplaced parenthesis, the Fisher's r-to-Z conversion which was described in the text was not applied to the width w of the corridor of stability in the computations. Hence, in the actual computations the width of the corridor was in the r metric, not in the Z metric. For example, for a true value of r =.4 and w =.1, the corridor of stability in the computations actually went from.3 to.5, instead of from.31 to.48, as described in the original paper. From hindsight, the described r-to-Z transformation made Table 1 in the original publication difficult to interpret, as its column headers reported a mix of numbers in different scales: The true correlation in the r metric, and the corridor width in the Z metric. Readers would have had to manually compute a Z-to-r transformation to derive the correct corridor boundaries. For example, a true effect size of ρ =.7 and w =.2 translates to a corridor of stability in the r metric ranging from.65 to.75. Hence, as originally presented, Table 1 is hardly understandable for readers. Incidentally, if the r-to-Z transformation is applied in the computations, the main conclusion still stands: “in typical scenarios the sample size should approach 250 for stable estimates”. In the Z metric, confidence intervals around a correlation are only dependent on sample size and, likewise, the point of stability does not depend on the size of the true correlation. For all δs the point of stability for w =.1 and 80% confidence is around n = 260. To summarize, the coding error means that the computations did not match with the original text description. After some reflection, we think that the relevant textual descriptions in the manuscript should be changed whereas the numerical results as well as the tables in the manuscript should be kept as they are, because what the code did was actually a better approach. Hence, in this correction note we define the width w of the corridor of stability in the r metric, and not, as originally described, in the Z metric. The reported results in Table 1 of the original publication are therefore correct but they should be understood to refer to a corridor width in the r metric. The relevant text in the manuscript describing the procedure also should be understood as referring to a corridor width in the r metric. This correction gives also the opportunity to align the paper with the intuitive understanding of most readers: While the table was difficult to interpret with the original description, it is better interpretable with this corrected description. The authors are sorry for this error, apologise for any inconvenience caused, and highlight the usefulness and necessity of open reproducible code. The corrected simulation code can be found at https://osf.io/ydbwr/.