Standard errors of estimators that are functions of correlation coefficients are shown to be quite different in magnitude than standard errors of the initial correlations. A general large-sample methodology, based upon Taylor series expansions and asymptotic correlational results, is developed for the computation of such standard errors. Three exemplary analyses are conducted on a correction for attenuation, a correction for range restriction, and an indirect effect in path analysis. Derived formulae are consistent with several previously proposed estimators and provide excellent approximations to the standard errors obtained in computer simulations, even for moderate sample size (n = 100). It is shown that functions of correlations can be considerably more variable than product-moment correlations. Additionally, appropriate hypothesis tests are derived for these corrected coefficients and the indirect effect. It is shown that in the range restriction situation, the appropriate hypothesis test based on the corrected coefficient is asymptotically more powerful than the test utilizing the uncorrected coefficient. Bias is also discussed as a by-product of the methodology.Many estimators in the social sciences are functions of Pearson product-moment correlation coefficients. For example, the correction of a validity coefficient for attenuation due to unreliability is a function of both the original correlation and a reliability estimate. Discussion of the corrected coefficient in its use as a parameter estimate usually revolves around its magnitude and/or practical significance. Therefore, some indication of the standard error of these corrected coefficients is crucial to the interpretability of the findings. That corrected coefficients may be greater than unity (cf. Karren, 1978) also supplies impetus to this investigation.The present paper presents a large-sample methodology for deriving estimates of the standard errors of functions of correlation coefficients. For example, it is shown below that correlations corrected for attenuation are considerably more variable than product-moment correlations. The APA Standards for Educational and Psychological Tests (American Psychological Association, 1974) indicates that &dquo;where correlation coefficients are corrected for attenuation or restriction in range, full information relevant to the correction should be presented&dquo; (Section E8.2.1.). Thus, the derivation of standard errors of these corrected coefficients would represent important progress towards &dquo;full information.&dquo;
The effects of different amounts of single- and dual-task practice were evaluated on the fourth, final training trial and with two transfer trials-a dual-task setting with the same tracking task that was used during practice and a dual-task setting with two different component tasks. Results showed that single-task practice contributed little to subsequent dual-task performance, but that the amount of dual-task practice was a major determinant of subsequent dual-task performance. In addition, the amount of dual-task practice resulted in positive transfer to the dual-task setting with the same tracking task in a linear fashion. A post hoc analysis revealed that the effects of practice on the transfer tasks were partially dependent upon the subject ability levels.
The present study was designed to compare single-task and dual-task measures of S-R compatibility. A numeral-motor choice-reaction task was performed alone and with a secondary tracking task. The level of compatibility was varied by manipulating the S-R assignments in the choice-reaction task. Results of the single-task trials indicated that reaction time was significantly slower for the incompatible conditions. Reaction time was slower, more errors were made, and fewer problems were attempted in the incompatible dual-task trials. Despite instructions to maintain choice-reaction performance at single-task levels, incompatible task performance was significantly degraded in the dual-task setting. Results indicated that resistance to task-induced stress may be a major indicant of the level of compatibility.
The effects of continuous and time-varied 85 dBA broadband noise on the performance of a Stroop-type color-word test and a related word-reading task were investigated. 10 subjects served in one of three groups receiving either continuous, periodic, or aperiodic noise. All subjects performed in both low noise (65 dBA) and high noise (85 dBA) conditions on 80 trials of both word reading and color naming. Median reaction times in the word-reading task were unaffected by either noise intensity or the time-varied aspects of the noise. However, median reaction times in the color-naming task were significantly elevated in the 85-dBA noise condition. Also, reaction times in the high aperiodic noise condition were significantly elevated relative to the continuous and periodic noise conditions. Results are discussed within the framework of arousal, filter, and information theories.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.