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The point-biserial correlation is mathematically equivalent to the Pearson (product moment) correlation coefficient; that is, if we have one continuously measured variable X and a dichotomous variable Y, r XY = r pb. This can be shown by assigning two distinct numerical values to the dichotomous variable.
In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of one parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size ...
In other words, the correlation is the difference between the common language effect size and its complement. For example, if the common language effect size is 60%, then the rank-biserial r equals 60% minus 40%, or r = 0.20. The Kerby formula is directional, with positive values indicating that the results support the hypothesis.
Point-biserial correlation coefficient; Point estimation; Point pattern analysis; Point process; Poisson binomial distribution; Poisson distribution; Poisson hidden Markov model; Poisson limit theorem; Poisson process; Poisson regression; Poisson random numbers – redirects to section of Poisson distribution; Poisson sampling
Examples are Spearman’s correlation coefficient, Kendall’s tau, Biserial correlation, and Chi-square analysis. Pearson correlation coefficient. Three important notes should be highlighted with regard to correlation: The presence of outliers can severely bias the correlation coefficient.
Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and/or Y. Pearson / Spearman correlation coefficients between X and Y are shown when the two variables' ranges are unrestricted, and when the range of X is restricted to the interval (0,1).
[3] [4] Identifying and removing (or revising) poorly-performing items is a critical way that psychometric analysis can improve the quality of a measure. When items are scored dichotomously, as in exams with correct and incorrect answers, the item-total correlation may be calculated as either a point-biserial correlation or a biserial ...
It is worth also mentioning some specific similarities between CTT and IRT which help to understand the correspondence between concepts. First, Lord [27] showed that under the assumption that is normally distributed, discrimination in the 2PL model is approximately a monotonic function of the point-biserial correlation. In particular: