Estimation of Other Coefficients of Correlation from the Phi Coefficient

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Abstract
Formulas are developed for estimating a point-biserial r or a tetrachoric r from an obtained phi coefficient. The estimate of a tetrachoric r, which is called rϕ, is shown to be equivalent to that obtained from first-order use of the tetrachoric r series. A tabulation is made of corrections needed to make rϕ equivalent numerically to the tetrachoric r. In spite of its greater generality than estimates of tetrachoric r by previous methods, there are limitations, which are pointed out.

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