Unrepeatable repeatabilities: a common mistake

TLDR: The correct calculation of repeatability is outlined, a common mistake is pointed out, how the incorrectly calculated value relates to repeatable values is shown, and a method for checking published values and calculating approximate repeatability values from the F ratio is provided.

Abstract: -Repeatability is a useful tool for the population geneticist or genetical ecologist, but several papers have carried errors in its calculation We outline the correct calculation of repeatability, point out the common mistake, show how the incorrectly calculated value relates to repeatability, and provide a method for checking published values and calculating approximate repeatability values from the F ratio (mean squares among groups/ mean squares within groups) Received 6 February 1986, accepted 25 August 1986 REPEATABILITY is a measure used in quantitative genetics to describe the proportion of variance in a character that occurs among rather than within individuals Repeatability, r, is given by: r = (VG + VEg)/ VP, (1) where VG is the genotypic variance, VEg the general environmental variance, and Vp the phenotypic variance (Falconer 1960, 1981) In addition to its use in assessing the reliability of multiple measurements on the same individual, repeatability may be used to set an upper limit to the value of heritability (Falconer 1960, 1981) and to separate, for instance, the effects of "self" and "mate" on a character such as clutch size (van Noordwijk et al 1980) Repeatability is therefore a useful statistic for population geneticists and genetical ecologists Recently, we have noticed an increasing number of published papers and unpublished manuscripts in which repeatability was miscalculated Our purpose is fivefold: (1) to outline the correct method of calculating repeatability; (2) to point out a common mistake in calculating repeatability; (3) to show how much this mistake affects values of repeatability; (4) to provide a quick way of checking published estimates, and to calculate an approximate value of repeatability from published F ratios and degrees of freedom; and (5) to make recommendations for authors, referees, editors, and readers to prevent the promulgation and propagation of incorrect repeatability values in the literature CALCULATION OF REPEATABILITY Repeatability is the intraclass correlation coefficient (Sokal and Rohlf 1981), which is based on variance components derived from a one-way analysis of variance (ANOVA) The intraclass correlation coefficient is given by some statistical packages; otherwise it can be calculated from an ANOVA ANOVA is described in most statistics textbooks (eg Sokal and Rohlf 1981; Kirk 1968 gives a detailed treatment of more complex designs of ANOVA), so we will not repeat it here, but give the general form of the results from such an analysis in Table 1 Repeatability, r, is given by r = sA / (S + SA)' (2) where S2A is the among-groups variance component and s2 is the within-group variance component These variance components are calculated from the mean squares in the analysis of variance as: