# Rank-biserial correlation

@article{Cureton1956RankbiserialC, title={Rank-biserial correlation}, author={Edward E. Cureton}, journal={Psychometrika}, year={1956}, volume={21}, pages={287-290} }

A formula is developed for the correlation between a ranking (possibly including ties) and a dichotomy, with limits which are always ±1. This formula is shown to be equivalent both to Kendall'sτ and Spearman'sρ.

## 111 Citations

Rank-Biserial Correlation when Ties Are Present

- Mathematics
- 1968

GLASS (1966) presents an interesting simplification of the formula for the rank-biserial correlation, and shows that in the untied case it is algebraically equivalent to one given by the writer…

Note on Rank Biserial Correlation

- Mathematics
- 1966

variables, n consecutive ranks, a dichotomy, a trichotomy, etc. In this paper we shall be concerned with developing a measure of the correlation between one variable comprising n consecutive untied…

Modified biserial correlation coefficients

- Mathematics
- 1981

Asymptotic distribution theory of Brogden's form of biserial correlation coefficient is derived and large sample estimates of its standard error obtained. Its efficiency relative to the biserial…

Critical Values of the Rank-Biserial Correlation Coefficient

- Mathematics
- 1976

For data with observations on variable Y restricted to consecutive and untied ranks 1,2... n, and with observations on X restricted to nominal classification into group 1 or 2, the Mann-Whitney…

Point biserial correlation coefficient and its generalization

- Mathematics
- 1960

The problem of measuring the association between two characters, one quantitative and the other qualitative, is discussed. The formula for the large sample standard error of the point biserial…

Ordinal-Level Variables, II

- Mathematics
- 2018

This chapter examines measures of association designed for two ordinal-level variables that are based on pairwise comparisons of differences between rank scores. Included in Chap. 5 are Kendall’s τa…

The Simple Difference Formula: An Approach to Teaching Nonparametric Correlation1:

- Mathematics
- 2014

Although teaching effect sizes is important, many statistics texts omit the topic for the Mann-Whitney U test and the Wilcoxon signed-rank test. To address this omission, this paper introduces the ...

Bayesian rank-based hypothesis testing for the rank sum test, the signed rank test, and Spearman's ρ

- MathematicsJournal of Applied Statistics
- 2020

Bayesian inference for rank-order problems is frustrated by the absence of an explicit likelihood function. This hurdle can be overcome by assuming a latent normal representation that is consistent…

A RANKING VARIABLE ANALOGUE OF BISERIAL CORRELATION: IMPLICATIONS FOR SHORT‐CUT ITEM ANALYSIS

- Psychology
- 1965

The writer's purpose is to propose a new, easily calculable index of item discrimination for use in the validation of dichotomously scored items. The derivation of the index is discussed only briefly…

Bayesian Latent-Normal Inference for the Rank Sum Test, the Signed Rank Test, and Spearman's $\rho$

- Computer Science
- 2017

This work applies a generic data-augmentation method to obtain Bayesian counterparts of three popular rank-based tests: the rank sum test, the signed rank test, and Spearman's $\rho$.

## References

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Inversions and Rank Correlation Coefficients

- Mathematics
- 1951

A relation is developed between Spearman's coefficient of rank correlation rs and the inversions in the two rankings. This leads to an expression for the mean value of rs in samples from a finite…

Rank Correlation Methods

- Mathematics
- 1948

The measurement of rank correlation introduction to the general theory of rank correlation tied ranks tests of significance proof of the results of chapter 4 the problem of m ranking proof of the…