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Fisher transformation
About: Fisher transformation is a research topic. Over the lifetime, 836 publications have been published within this topic receiving 38087 citations.
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TL;DR: In this paper, the 100th anniversary of Galton's first discussion of regression and correlation is celebrated, and 13 different formulas representing a different computational and conceptual definition of Pearson's r are presented.
Abstract: In 1885, Sir Francis Galton first defined the term “regression” and completed the theory of bivariate correlation. A decade later, Karl Pearson developed the index that we still use to measure correlation, Pearson's r. Our article is written in recognition of the 100th anniversary of Galton's first discussion of regression and correlation. We begin with a brief history. Then we present 13 different formulas, each of which represents a different computational and conceptual definition of r. Each formula suggests a different way of thinking about this index, from algebraic, geometric, and trigonometric settings. We show that Pearson's r (or simple functions of r) may variously be thought of as a special type of mean, a special type of variance, the ratio of two means, the ratio of two variances, the slope of a line, the cosine of an angle, and the tangent to an ellipse, and may be looked at from several other interesting perspectives.
3,251 citations
TL;DR: The use of kappa implicitly assumes that all disagreements are equally serious as discussed by the authors, which is not the case, and hence the use of the kappa scale implicitly implies that not all disagreements will be equally serious.
Abstract: or weighted kappa (Spitzer, Cohen, Fleiss and Endicott, 1967; Cohen, 1968a). Kappa is the proportion of agreement corrected for chance, and scaled to vary from -1 to +1 so that a negative value indicates poorer than chance agreement, zero indicates exactly chance agreement, and a positive value indicates better than chance agreement. A value of unity indicates perfect agreement. The use of kappa implicitly assumes that all disagreements are equally serious. When the investigator can specify the relative seriousness of each kind of disagreement, he may employ weighted kappa, the proportion of weighted agreement corrected for chance. For measuring the reliability of quantitative scales, the product-moment and intraclass correlation coefficients are widely
2,986 citations
TL;DR: In this paper, the authors provide simple but accurate methods for comparing correlation coefficients between a dependent variable and a set of independent variables using the Fisher z transformation and include a test and confidence interval for comparing two correlated correlations, a test for heterogeneity, and a contrast among k ≥ 2 correlated correlations.
Abstract: The purpose of this article is to provide simple but accurate methods for comparing correlation coefficients between a dependent variable and a set of independent variables. The methods are simple extensions of Dunn & Clark's (1969) work using the Fisher z transformation and include a test and confidence interval for comparing two correlated correlations, a test for heterogeneity, and a test and confidence interval for a contrast among k (>2) correlated correlations. Also briefly discussed is why the traditional Hotelling's t test for comparing correlated correlations is generally not appropriate in practice
2,300 citations
2,001 citations
TL;DR: In this article, a procedure for estimating the reliability of sets of ratings in terms of the intraclass correlation coefficient is discussed, based upon the analysis of variance and the estimatio
Abstract: A procedure for estimating the reliability of sets of ratings in terms of the intraclass correlation coefficient is discussed The procedure is based upon the analysis of variance and the estimatio
1,982 citations