On Tue, 20 Apr 2010 14:03:08 -0700, Karl L Wuensch wrote: >See: The Theory of Correlation Between Two Continuous Variables >when One is Dichotomized >Author(s): Robert F. Tate >Source: Biometrika, Vol. 42, No. 1/2 (Jun., 1955), pp. 205-216
For those without access to Biometrika or www.jstor.org, but do have access to Gene Glass & Ken Hopkins "Statistical Methods in Education and Psychology" (3rd Ed), see their coverage of the biserial correlation in section 7.24 and 7.25, p134-136 (cautions about the size of the biserial are on page 136). The use of the biserial assumes that the dichotmized variable has an underlying normal distribution (Glass & Hopkins eq. 7.17 explicitly uses the the ordinate or the probability density for the standard normal distribution at the "threshold" between dichotomies). If memory serves, the historical reason for the computation of the biserial and the tetrachoric coefficient (i.e., correlation between two dichotmized variables with underlying normal distributions) was because the computation of these coefficients was easier than using the raw values in the days when an "calculator" referred to a human being (usually a young woman). Today, this shortcut is not needed because of ready access to statistical software on computers. However, the biserial and tetrachoric coefficient have not disappeared and have enven been extended to multiple categories or polychotomies. The biserial now becomes the polyserial and the tetrachoric becomes the polychoric. In the context of structural equation modeling (SEM) the issue is not one of easing computation but dealing with crudeness of measurement, such as when an ordinal scale response is obtained but the underlying variable is continuous. Bollen's "Structural Equations with Latent Variables" covers this in part on pages 442-446. I am unaware of biserial/polyserial coefficients being greater then 1.00 when estimated by SEM and would like references to such a case. -Mike Palij New York University [email protected] --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=2118 or send a blank email to leave-2118-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
