rXY is the observed correlation between X and Y in our sample, rXX is the reliability of variable X, and rYY is the reliability of variable Y. Here is an example from my own research: I obtained the correlation between misanthropy and attitude towards animals for two groups, idealists (for whom I predicted there would be only a weak correlation) and nonidealists (for whom I predicted a stronger correlation). The observed correlation was .02 for the idealists, .36 for the idealists. The reliability (Cronbach alpha) was .91 for the attitude towards animals instrument (which had 28 items) but only .66 for the misanthropy instrument (not surprising, given that it had only 5 items). When we correct the observed correlation for the nonidealists, we obtain , a much more impressive correlation. When we correct the correlation for the idealists, the corrected r is only .03. I should add that Cronbach's alpha underestimates a test's reliability, so this correction is an over-correction. It is preferable to use maximized lamba4 as the estimate of reliability. Using labmda4 estimates of reliability, the corrected r is References and Recommended Readings Lance, C. E., Butts, M. M., & Michels, L. C. (2006). The sources of two commonly reported cutoff criteria. What did they really say? Organizational Research Methods, 9, 202-220. Nunnally, J. C. (1978). Psychometric theory (2nd ed.). New York: McGraw-Hill. Schmidt, F. L., & Hunter, J. E. (1996). Measurement error in psychological research: Lessons from 26 research scenarios. Psychological Methods, 1, 199-223. Wuensch, K. L. -- Is it a big problem when results are significant?
rXY is the observed correlation between X and Y in our sample, rXX is the reliability of variable X, and rYY is the reliability of variable Y. Here is an example from my own research: I obtained the correlation between misanthropy and attitude towards animals for two groups, idealists (for whom I predicted there would be only a weak correlation) and nonidealists (for whom I predicted a stronger correlation). The observed correlation was .02 for the idealists, .36 for the idealists. The reliability (Cronbach alpha) was .91 for the attitude towards animals instrument (which had 28 items) but only .66 for the misanthropy instrument (not surprising, given that it had only 5 items). When we correct the observed correlation for the nonidealists, we obtain , a much more impressive correlation. When we correct the correlation for the idealists, the corrected r is only .03. I should add that Cronbach's alpha underestimates a test's reliability, so this correction is an over-correction. It is preferable to use maximized lamba4 as the estimate of reliability. Using labmda4 estimates of reliability, the corrected r is References and Recommended Readings Lance, C. E., Butts, M. M., & Michels, L. C. (2006). The sources of two commonly reported cutoff criteria. What did they really say? Organizational Research Methods, 9, 202-220. Nunnally, J. C. (1978). Psychometric theory (2nd ed.). New York: McGraw-Hill. Schmidt, F. L., & Hunter, J. E. (1996). Measurement error in psychological research: Lessons from 26 research scenarios. Psychological Methods, 1, 199-223. Wuensch, K. L. -- Is it a big problem when results are significant?
Reliab-Nunnally.docx