A Priori Versus Post-Hoc: Comparing Statistical Power among ANOVA, Block Designs, and ANCOVA.
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| Title: | A Priori Versus Post-Hoc: Comparing Statistical Power among ANOVA, Block Designs, and ANCOVA. |
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| Language: | English |
| Authors: | Wu, Yi-Cheng, McLean, James E. |
| Peer Reviewed: | N |
| Page Count: | 28 |
| Publication Date: | 1994 |
| Document Type: | Reports - Evaluative Speeches/Meeting Papers |
| Descriptors: | Analysis of Covariance, Analysis of Variance, Comparative Analysis, Power (Statistics), Research Design, Research Methodology |
| Assessment and Survey Identifiers: | Block Design Test |
| Abstract: | By employing a concomitant variable, block designs and analysis of covariance (ANCOVA) can be used to improve the power of traditional analysis of variance (ANOVA) by reducing error. If subjects are randomly assigned to treatments without considering the concomitant variable, an experiment uses a post-hoc approach. Otherwise, an a priori approach is used if the concomitant variable is utilized for assigning subjects to treatments. Traditionally, a priori has been considered the more powerful approach. This study compared ANOVA, block designs, and ANCOVA under various experimental conditions. The experimental conditions were 48 combinations of 4 levels of the number of treatments (T at 2, 3, 4, and 5), 3 levels of the number of subjects per treatment (n at 8, 40, and 72), and 4 levels of the correlation coefficient between the concomitant and dependent variables (p at 0.00, 0.28, 0.56, and 0.84). The optimal number of blocks to achieve maximum power was also investigated. Results indicated that a priori was not generally more powerful than post-hoc. For ANOVA, a priori became less powerful as T and p increased. For block designs, the preference depended on the experimental conditions. For ANCOVA, a priori was more powerful when T and n were small. Appendix A explores apparent imprecision, Appendix B presents two Statistical Analysis System computer programs, and Appendix C contains a power table. (Contains 9 tables and 3 references.) (Author/SLD) |
| Entry Date: | 1996 |
| Accession Number: | ED387531 |
| Database: | ERIC |
| Abstract: | By employing a concomitant variable, block designs and analysis of covariance (ANCOVA) can be used to improve the power of traditional analysis of variance (ANOVA) by reducing error. If subjects are randomly assigned to treatments without considering the concomitant variable, an experiment uses a post-hoc approach. Otherwise, an a priori approach is used if the concomitant variable is utilized for assigning subjects to treatments. Traditionally, a priori has been considered the more powerful approach. This study compared ANOVA, block designs, and ANCOVA under various experimental conditions. The experimental conditions were 48 combinations of 4 levels of the number of treatments (T at 2, 3, 4, and 5), 3 levels of the number of subjects per treatment (n at 8, 40, and 72), and 4 levels of the correlation coefficient between the concomitant and dependent variables (p at 0.00, 0.28, 0.56, and 0.84). The optimal number of blocks to achieve maximum power was also investigated. Results indicated that a priori was not generally more powerful than post-hoc. For ANOVA, a priori became less powerful as T and p increased. For block designs, the preference depended on the experimental conditions. For ANCOVA, a priori was more powerful when T and n were small. Appendix A explores apparent imprecision, Appendix B presents two Statistical Analysis System computer programs, and Appendix C contains a power table. (Contains 9 tables and 3 references.) (Author/SLD) |
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