Analysis of Covariance in Randomized Experiments with Heterogeneity of Regression and a Random Covariate: The Variance of the Estimated Treatment Effect at Selected Covariate Values

References

• Aguinis, H., Beaty, J. C., Boik, R. J., & Pierce, C. A. (2005). Effect size and power in assessing moderating effects of categorical variables using multiple regression: A 30-year review. Journal of Applied Psychology, 90(1), 94–107. doi:10.1037/0021-9010.90.1.94
   PubMed Web of Science ®Google Scholar
• Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Newbury Park, CA: Sage.
   Google Scholar
• Bosco, F. A., Aguinis, H., Singh, K., Field, J. G., & Pierce, C. A. (2015). Correlational effect size benchmarks. Journal of Applied Psychology, 100(2), 431–489. doi:10.1037/a0038047
   PubMed Web of Science ®Google Scholar
• Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31(2), 144–152. doi:10.1111/j.2044-8317.1978.tb00581.x
   Web of Science ®Google Scholar
• Casella, G., & Berger, R. L. (2002). Statistical inference (2nd ed.). Pacific Grove, CA: Thomson Learning.
   Google Scholar
• Chaplin, W. F. (1991). The next generation of moderator research in personality psychology. Journal of Personality, 59(2), 143–178. doi:10.1111/j.1467-6494.1991.tb00772.x
   PubMed Web of Science ®Google Scholar
• Chaplin, W. F. (1997). Personality, interactive relations, and applied psychology. In R. Hogan, J. Johnson, & S. Briggs (Eds.), Handbook of personality psychology (pp. 873–890). San Diego, CA: Academic Press.
   Google Scholar
• Chen, X. (2006). The adjustment of random baseline measurements in treatment effect estimation. Journal of Statistical Planning and Inference, 136(12), 4161–4175. doi:10.1016/j.jspi.2005.08.046
   Web of Science ®Google Scholar
• Cohen, J. (1988). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.
   Google Scholar
• Crager, M. R. (1987). Analysis of covariance in parallel-group clinical trials with pretreatment baselines. Biometrics, 43(4), 895–901. doi:10.2307/2531543
   PubMed Web of Science ®Google Scholar
• Cronbach, L. J. (1975). Beyond the two disciplines of scientific psychology. American Psychologist, 30(2), 116–127. doi:10.1037/h0076829
   Web of Science ®Google Scholar
• Cronbach, L. J., & Snow, R. E. (1977). Aptitudes and instructional methods: A handbook for research on interactions. New York, NY: John Wiley & Sons.
   Google Scholar
• Fisher, R. A. (1932). Statistical methods for research workers (4th ed.). Edinburgh, Scotland: Oliver and Boyd.
   Google Scholar
• Gelman, A. (2004). Treatment effects in before-after data. In A. Gelman & X. L. Meng (Eds.), Applied Bayesian modeling and causal inference from an incomplete data perspective (pp. 195–202). London, UK: Wiley. https://doi.org/10.1002/0470090456.ch18
   Google Scholar
• Gelman, A. (2005). Analysis of variance—Why it is more important than ever. The Annals of Statistics, 33(1), 1–53. doi:10.1214/009053604000001048
   Web of Science ®Google Scholar
• Harwell, M. R., & Serlin, R. C. (1988). An empirical study of a proposed test of nonparametric analysis of covariance. Psychological Bulletin, 104(2), 268–281. doi:10.1037/0033-2909.104.2.268
   Web of Science ®Google Scholar
• Hayes, A. F., & Matthes, J. (2009). Computational procedures for probing interactions in OLS and logistic regression: SPSS and SAS implementations. Behavior Research Methods, 41(3), 924–936. doi:10.3758/BRM.41.3.924
   PubMed Web of Science ®Google Scholar
• Johnson, P. O., & Neyman, J. (1936). Tests of certain linear hypotheses and their application to some educational problems. Statistical Research Memoirs, 1, 57–93.
   Google Scholar
• Liu, Y., West, S. G., Levy, R., & Aiken, L. S. (2017). Tests of simple slopes in multiple regression models with an interaction: Comparison of four approaches. Multivariate Behavioral Research, 52(4), 445–464. doi:10.1080/00273171.2017.1309261
   PubMed Web of Science ®Google Scholar
• Maxwell, S. E., Delaney, H. D., & Kelley, K. (2018). Designing experiments and analyzing data: A model comparison perspective. New York, NY: Routledge.
   Google Scholar
• Maxwell, S. E., Delaney, H. D., & O’Callaghan, M. F. (1993). Analysis of covariance. In L. K. Edwards (Ed.), Applied analysis of variance in behavioral science (pp. 63–104). New York, NY: Marcel Dekker.
   Google Scholar
• McLouth, C. J. (2018). Analysis of Covariance with Heterogeneity of Regression and a Random Covariate (Unpublished doctoral dissertation). University of New Mexico, Albuquerque, NM.
   Google Scholar
• Neter, J., Wasserman, W., & Kutner, M. H. (1985). Applied linear statistical models: Regression, analysis of variance, and experimental designs. Homewood, IL: R. D. Irwin, Inc.
   Google Scholar
• Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). Computational tools for probing interactions in multiple linear regression, multilevel modeling, and latent curve analysis. Journal of Educational and Behavioral Statistics, 31(4), 437–448. doi:10.3102/10769986031004437
   Web of Science ®Google Scholar
• Rencher, A. C., & Schaalje, G. B. (2008). Linear models in statistics. Hoboken, NJ: Wiley.
   Google Scholar
• Rogosa, D. (1980). Comparing nonparallel regression lines. Psychological Bulletin, 88(2), 307–321. doi:10.1037/0033-2909.88.2.307
   Web of Science ®Google Scholar
• Rosenthal, R., & Jacobson, L. (1992). Pygmalion in the classroom: Teacher expectation and pupils’ intellectual development. New York, NY: Irvington Publishers.
   Google Scholar
• Sampson, A. R. (1974). A tale of two regressions. Journal of the American Statistical Association, 69(347), 682–689. doi:10.2307/2286002
   Web of Science ®Google Scholar
• Scheffé, H. (1959). The analysis of variance. New York, NY: John Wiley & Sons.
   Google Scholar