Fisher, gosset, and alternative hypothesis significance testing (AHST): using the bootstrap to test scientific hypotheses about the multiple correlation

Current Topics in the Theory and Application of Latent Variable Models

Volumn , Issue , 2012, Pages 217-239

  Rodgers, Joseph Lee ^a   Beasley, William Howard ^b  

^a UNIVERSITY OF OKLAHOMA   (United States)

^b UNIVERSITY OF OKLAHOMA HEALTH SCIENCES CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84920431511     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.4324/9780203813409     Document Type: Chapter

References (44)

1. Abelson, R. P. (1997). A retrospective on the significance test ban of 1999 (if there were no significance tests, they would be invented). In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.) What if there were no significance tests? (pp. 117-141). Mahwah, NJ: Erlbaum.
2. Appelbaum, M.I. & Cramer, E. M. (1974). Some problems in the nonorthogonal analysis of variance. Psychological Bulletin, 81, 335-343.
3. Beasley, W.B. (2010). Univariate sampling bootstrap procedures using prior information (Unpublished doctoral dissertation). University of Oklahoma, Norman.
4. Beasley, W. H., DeShea, L., Toothaker, L. E., Mendoza, J. L., Bard, D. E., & Rodgers, J. L. (2007). Bootstrapping to test for nonzero population correlation coefficients using univariate sampling. Psychological Methods, 12, 414-433.
5. Beasley, W. H., & Rodgers, J. L. (2009). Resampling methods. In R. E. Millsap & A. Maydeu-Olivares (Eds.) Quantitative methods in psychology (pp. 362-403). Thousand Oaks, CA: Sage.
6. Bollen, K. A., & Stine, R. A. (1992). Bootstrapping goodness-of-fit measures in structural equation models. Sociological Methods Research, 21, 205-229.
7. Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37, 62-83.
8. Browne, M. W., & Arminger, G. (1995). Specification and estimation of mean- and covariance-structure models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (pp. 185-249). New York: Plenum Press.
9. Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park, CA: Sage.
10. Carlin, B. P., & Louis, T. A. (2009). Bayesian methods for data analysis. Boca Raton, FL: Chapman & Hall.
11. Cohen, J. (1994). The earth is round (p <.05). American Psychologist, 49, 997-1003.
12. Cohen, J., Cohen, P., West, S.G., & Aiken, L.S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Mahwah, NJ: Erlbaum.
13. Cramer, E. M. (1972). Significance tests and tests of models in multiple regression. The American Statistician, 26, 26-30.
14. Cudeck, R., & Browne, M. W. (1992) Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy function value. Psychometrika, 57, 357-369.
15. Diaconis, P., & Efron, B. (1983). Computer-intensive methods in statistics. Scientific American, 248, 116-130.
16. Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1-26.
17. Efron, B. (1982). The jackknife, thebootstrap, and other resampling plans. Philadelphia: Society for Industrial and Applied Mathematics.
18. Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. Boca Raton: Chapman & Hall/CRC.
19. Fisher, R. A., (1934), Discussion of “Statistics in agricultural research” by J. Wishart, Journal of the Royal Statistical Society, Supplement, 1, 26-61.
20. Fisher, R. A. (1936). “The coefficient of racial likeness” and the future of craniometry. Journal of the Royal Anthropological Institute of Great Britain and Ireland, 66, 57-63.
21. Gigerenzer, G. (1993). The superego, the ego, and the id in statistical reasoning. In G. Keren & C. Lewis (Eds.), A handbook for data analysis in the behavioral sciences: Vol 1. Methodological issues (pp. 311-339). Hillsdale, NJ: Erlbaum.
22. Headrick, T. C. (2010). Statistical simulation: Power method polynomials and other transformations. Chapman & Hall: Boca Raton.
23. Headrick, T. C. (2011). A characterization of power method transformations through l-moments. Journal of Probability and Statistics, Article ID 497463, 1-22. doi:10.1155/2011/497463.
24. Konishi, S. (1981). Normalizing transformations of some statistics in multivariate analysis. Biometrika, 68, 647-651.
25. Lee, W., & Rodgers, J. L. (1998). Bootstrapping correlation coefficients using univariate and bivariate sampling. Psychological Methods, 3, 91-103.
26. MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996). Power analysis and determination of sample size for covariance structure modeling. Psychological Methods, 130-149.
27. Maxwell, S. E., & Delaney, H. D. (2004). Designing experiments and analyzing data: A model comparison perspective (2nd ed.). Mahwah, NJ: Erlbaum.
28. McDonald, R. P. (1997). Goodness of approximation in the linear model. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.) What if there were no significance tests? (pp. 199-219). Mahwah, NJ: Erlbaum.
29. Nickerson, R. S. (2000). Null hypothesis significance testing: A review of an old and continuing controversy. Psychological Methods, 5, 241-301.
30. Pruzek, R. M. (1997). An introduction to Bayesian inference and its applications. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.) What if there were no significance tests? (pp. 287-318). Mahwah, NJ: Erlbaum.
31. Rindskopf, D. M. (1997). Testing “small,” not null, hypotheses: Classical and Bayesian approaches. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.) What if there were no significance tests? (pp. 319-332). Mahwah, NJ: Erlbaum.
32. Rodgers, J. L. (1999). The bootstrap, the jackknife, and the randomization test: A sampling taxonomy. Multivariate Behavioral Research, 34, 441-456.
33. Rodgers, J. L. (2010a). The epistemology of mathematical and statistical modeling: A quiet methodological revolution. American Psychologist, 65, 1-12.
34. Rodgers, J. L. (2010b). Statistical and mathematical modeling versus NHST? There’s no competition! Journal of Modern and Applied Statistical Methods, 9, 340-347.
35. Rozeboom, W. W. (1960). The fallacy of the null hypothesis significance test. Psychological Bulletin, 57, 416-428.
36. Rozeboom, W. W. (1997). Good science isabductive, nothypothetico-deductive. In L. L. Harlow, S. A. Mulaik, & J. H. Steiger (Eds.) What if there were no significance tests? (pp. 335-392). Mahwah, NJ: Lawrence Erlbaum Associates.
37. Ruscio, J., & Kaczetow, W. (2008). Simulating multivariate nonnormal data using an iterative algorithm. Multivariate Behavioral Research, 43, 355-381. doi: 10.1080/00273170 802285693.
38. Schmidt, F. L., & Hunter, J. E. (1997). Eight common but false objections to the discontinuation of significance testing in the analysis of research data. In L. L. Harlow, S. A. Mulaik, & J.H. Steiger (Eds.), What if there were no significance tests? (pp. 37-64). Mahwah, NJ: Erlbaum.
39. Serlin, R. C. (2010). Fisher was right. Journal of Modern Applied Statistical Methods, 9, 2-8.
40. Student (1908). The probable error of a mean. Biometrika, 6, 1-25.
41. Trafimow, D. (2003). Hypothesis testing and theory evaluation at the boundaries: Surprising insights from Bayes’ theorem. Psychological Review, 110, 526-535.
42. Widaman, K. F. & Thompson, J. S. (2003). On specifying the null model for incremental fit indices in structural equation modeling. Psychological Methods, 8, 16-37.
43. Wilkinson, L. and Task Force on Statistical Inference, APA Board of Scientific Affairs (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54, 595-604.
44. Zhang, G., & Browne, M. W. (2010) Bootstrap standard error estimates in dynamic factor analysis. Multivariate Behavioral Research, 45, 453-482.