Correcting Doubly Truncated Correlations: An Improved Approximation for Correcting the Bivariate Normal Correlation when Truncation has Occurred on Both Variables
Restricted accessResearch articleFirst published online June, 1987
Correcting Doubly Truncated Correlations: An Improved Approximation for Correcting the Bivariate Normal Correlation when Truncation has Occurred on Both Variables
Although the problem of correcting correlation coefficients that have arisen from range-restricted distributions has received a great deal of attention in the psychological testing and measurement literature, very little of that literature has dealt with the problem of restriction on both the independent (X) and dependent (1) variable. Wells and Fruchter (1970) presented an approximate correction in such situations. This article reports and improved approximation. This new approximation is recommended for all situations where restriction of range is suspected on either variable or on both X and Y.
Get full access to this article
View all access options for this article.
References
1.
Alexander, R. A. , Alliger, G. M., and Hanges, P. J. (1984). Correcting for range restriction when the population variance is unknown. Applied Psychological Measurement, 8, 431-437.
2.
Alexander, R. A. , Barrett, G. V., Alliger, G. M., and Carson, K. P. (1986). Toward a general model of nonrandom sampling and the impact on population correlation: Generalizations of Berkson's Fallacy and restriction of range. British Journal of Mathematical and Statistical Psychology, 39, 90-105.
3.
Alexander, R. A. , Carson, K. P., Alliger, G. M., and Barrett, G. V. (1984). Correction for restriction of range when both X and Y are truncated. Applied Psychological Measurement, 8, 231-241.
4.
Alexander, R. A. , Carson, K. P., Alliger, G. M., and Barrett, G. V. (1985). Further consideration of the power to detect non-zero validity coefficients under range restriction. Journal of Applied Psychology, 70, 451-460.
5.
Alexander, R. A. , Hanges, P. J., and Alliger, G. M. (1985). Correcting for restriction of range in both X and Y when the population variances are unknown. Applied Psychological Measurement, 45, 797-801.
6.
Barrett, G. V. , Phillips, J. S., and Alexander, R. A. (1981). Concurrent and predictive validity designs: A critical reanalysis. Journal of Applied Psychology, 66, 1-6.
7.
Greener, J. M. and Osburn, H. G. (1979). An empirical study of the accuracy of corrections for restriction of range due to explicit selection. Applied Psychological Measurement, 3, 31-41.
8.
Gross, A. L. (1982). Relaxing assumptions underlying corrections for restriction of range. Educational and Psychological Measurement, 42, 795-801.
9.
Gross, A. L. and Fleischman, L. (1983). Restriction of range corrections when both distribution and selection assumptions are violated. Applied Psychological Measurement, 7, 227-237.
10.
Linn, R. L. (1968). Range restriction problems in the use of self-selected groups for test validation. Psychological Bulletin, 69, 69-73.
11.
Lord, F. M. , and Novick, M. R. (1968). Statistical theories of marital test scores. Reading, MA: Addison-Wesley Publishing Co.
12.
Pearson, K. (1903). Mathematical contributions to the theory of evolution-XI. On the influence of natural selection on the variability and correlation of organs. Philosophical Transactions of the Royal Society, London, Series A, 200, 1-66.
13.
Pearson, K. (1908). On the influence of double selection on the variation and correlation of two characteristics. Biometrika, 8, 437-443.
14.
Regier, M. H. , and Hamdan, M. A. (1971). Correlation in a bivariate normal distribution with truncation in both variables. Australian Journal of Statistics, 13, 77-82.
15.
Thorndike, R. L. (1947). Research problems and techniques. (Report No. 3). Washington, DC: U.S. Government Printing Office.
16.
Weiler, H. (1959). Means and standard deviations of a truncated normal bivariate distribution. Australian Journal of Statistics, 1, 73-81.
17.
Wells, D. G. and Fruchter, B. (1970). Correcting the correlation coefficient for explicit restricton on both variables. Educational And Psychological Measurement, 30, 925-934.
