Evaluating independent proportions for statistical difference, equivalence, indeterminacy, and trivial difference using inferential confidence intervals

Journal of Educational and Behavioral Statistics

Volumn 34, Issue 2, 2009, Pages 171-189

  Tryon, Warren W ^a   Lewis, Charles ^a  

^a FORDHAM UNIVERSITY   (United States)

Author keywords

Confidence intervals; Equivalence; Indeterminacy; Null hypothesis statistical testing; Proportions; Replication; Statistical difference

Indexed keywords

EID: 68049147042     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/1076998609332753     Document Type: Article

References (27)

1. Agresti, A. (2002). Categorical data analysis (2nd ed.). Hoboken, NJ: Wiley-Interscience.
2. Agresti, A., & Coull, B. A. (1998). Approximate is better than "exact" for interval estimation of binomial proportions. American Statistician, 52, 119-126.
3. Agresti, A., & Min, Y. (2001). On small-sample confidence intervals for parameters in discrete distributions. Biometrics, 57, 963-971.
4. Belia, S., Fidler, F., Williams, J., & Cumming, G. (2005). Researchers misunderstand confidence intervals and standard error bars. Psychological Methods, 10, 389-396.
5. Clopper, C. J., & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26, 404-413.
6. Cumming, G., & Finch, S. (2005). Inference by eye: Confidence intervals and how to read pictures of data. American Psychologist, 60, 170-180.
7. Fidler, F., Thomason, N., Cumming, G., Finch, S., & Leeman, J. (2005). Confidence intervals, still much to learn: Reply to Rouder & Morey. Psychological Science, 16, 494-495.
8. Ghosh, B. K. (1979). A comparison of some approximate confidence intervals for the binomial parameter. Journal of the American Statistical Association, 74, 894-900.
9. Glass, G. V., & Hopkins, K. D. (1996). Statistical methods in education and psychology (3rd ed.). Boston: Allyn & Bacon.
10. Goldstein, H., & Healy, M. J. R. (1995). The graphical presentation of a collection of means. Journal of the Royal Statistical Society, 158A (Pt. 1), 175-177.
11. Hunter, J. E., & Schmidt, F. L. (2004). Methods of meta-analysis: Correcting error and bias in research findings (pp. 8-11). Thousand Oaks, CA: Sage.
12. Julious, S. A. (2005). Two-sided confidence intervals for the single proportion: Comparison of seven methods. Statistics in Medicine, 24, 3383-3384.
13. Krantz, D. H. (1999). The null hypothesis testing controversy in psychology. Journal of the American Statistical Association, 44, 1372-1381.
14. Loftus, G. R. (1991). On the tyranny of hypothesis testing in the social sciences. Contemporary Psychology, 36, 102-105.
15. Loftus, G. R. (1996). Psychology will be a much better science when we change the way we analyze data. Current Directions in Psychological Science, 5, 161-171.
16. Masson, M. E. J., & Loftus, G. R. (2003). Using confidence intervals for graphically based data interpretation. Canadian Journal of Experimental Psychology, 57, 203-220.
17. Miettinen, O., & Nurminen, M. (1985). Comparative analysis of two rates. Statistics in Medicine, 4, 213-226.
18. Newcombe, R. G. (1998a). Interval estimation for the difference between independent proportions: Comparison of eleven methods. Statistics in Medicine, 17, 873-890.
19. Newcombe, R. G. (1998b). Two-sided confidence intervals for the single proportion: Comparison of seven methods. Statistics in Medicine, 17, 857-872.
20. Rogers, J. L., Howard, K. I., & Vessey, J. T. (1993). Using significance tests to evaluate equivalence between two experimental groups. Psychological Bulletin, 113, 553-565.
21. Rouder, J. N., & Morey, R. D. (2005). Relational and arelational confidence intervals: A comment on Fidler, Thomason, Cumming, Finch, and Leeman (2004). Psychological Science, 16, 77-79.
22. Schenker, N., & Gentleman, J. F. (2001). On judging the significance of differences by examining the overlap between confidence intervals. The American Statistician, 55, 182-186.
23. Schuirmann, D. J. (1987). A comparison of the two one-sided tests procedure and the power approach for assessing equivalence of average bioavailability. Journal of Pharmacokinetics and Biopharmaceutics, 15, 657-680.
24. StatXact 7 with Cytel Studio. (2005). Statistical software for exact nonparametric inference. Cambridge, MA: Cytel Inc. Retrieved November 3, 2007, from www.cytel.com
25. Tryon, W. W. (2001). Evaluating statistical difference, equivalence, and indeterminacy using inferential confidence intervals: An integrated alternative method of conducting null hypothesis statistical tests. Psychological Methods, 6, 371-386.
26. Tryon, W. W., & Lewis, C. (2008). An inferential confidence interval method of establishing statistical equivalence that corrects Tryon's (2001) reduction factor. Psychological Methods, 13, 272-278.
27. Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22, 209-212.