ERIC Number: ED330706
Record Type: RIE
Publication Date: 1991-Apr
Reference Count: N/A
Robust Approximations to the Non-Null Distribution of the Product Moment Correlation Coefficient I: The Phi Coefficient.
Edwards, Lynne K.; Meyers, Sarah A.
Correlation coefficients are frequently reported in educational and psychological research. The robustness properties and optimality among practical approximations when phi does not equal 0 with moderate sample sizes are not well documented. Three major approximations and their variations are examined: (1) a normal approximation of Fisher's Z, N(sub 1) (R. A. Fisher, 1915); (2) a student's t based approximation, t(sub 1) (H. C. Kraemer, 1973; M. Samiuddin, 1970), which replaces for each sample size the population phi with phi*, the median of the distribution of r (the product moment correlation); (3) a normal approximation, N(sub6) (H. C. Kraemer, 1980) that incorporates the kurtosis of the X distribution; and (4) five variations--t(sub2), t(sub 1)', N(sub 3), N(sub4), and N(sub4)'--on the aforementioned approximations. N(sub 1) was found to be most appropriate, although N(sub 6) always produced the shortest confidence intervals for a non-null hypothesis. All eight approximations resulted in positively biased rejection rates for large absolute values of phi; however, for some conditions with low values of phi with heteroscedasticity and non-zero kurtosis, they resulted in the negatively biased empirical rejection rates. Four tables contain information about the approximations. (Author/SLD)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Sponsor: Minnesota Supercomputer Inst.
Authoring Institution: N/A
Identifiers: Approximation (Statistics); Nonnull Hypothesis; Phi Coefficient; Product Moment Correlation Coefficient
Note: Paper presented at the Annual Meeting of the American Educational Research Association (Chicago, IL, April 3-7, 1991).