A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions

Educational and Psychological Measurement

Volumn 61, Issue 4, 2001, Pages 532-574

  Cumming, Geoff ^a   Finch, Sue ^b  

^a LA TROBE UNIVERSITY   (Australia)

^b UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035535636     PISSN: 00131644     EISSN: None     Source Type: Journal    
DOI: 10.1177/00131640121971374     Document Type: Article

References (53)

1. Altman, D. (2000). Clinical trials and meta-analyses. In D. Altman, D. Machin, T. Bryant, & M. Gardner (Eds.), Statistics with confidence (2nd ed., pp. 120-138). London: BMJ.
2. American Psychological Association. (1994). Publication manual of the American Psychological Association (4th ed.). Washington, DC: Author.
3. Bakan, D. (1966). The test of significance in psychological research. Psychological Bulletin, 66, 423-437.
4. Chambers, T., & Lau, J. (1993). Meta-analytic stimulus for changes in clinical trials. Statistical Methods in Medical Research, 2, 161-172.
5. Chandler, R. (1957). The statistical concepts of confidence and significance. Psychological Bulletin, 54(5), 429-430.
6. Cohen, J. (1969). Statistical power analysis for the behavioral sciences. New York: Academic Press.
7. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.
8. Cohen, J. (1990). Things I have learned (so far). American Psychologist, 45, 1304-1312.
9. Cohen, J. (1994). The earth is round (p <.05). American Psychologist, 49, 997-1003.
10. Cook, T., Cooper, H., Cordray, D., Hartmann, H., Hedges, L., Light, R., Louis, T., & Mosteller, F. (1992). Meta-analysis for explanation: A casebook. New York: Russell Sage.
11. Cowles, M. (1989). Statistics in psychology: An historical perspective. Hillsdale, NJ: Lawrence Erlbaum.
12. Cox, D., & Hinkley, D. (1974). Theoretical statistics. London: Chapman & Hall.
13. Duval, S., & Tweedie, R. (2000). Trim and fill: A simple funnel plot based method of testing and adjusting for publication bias in meta-analysis. Biometrics, 56, 276-284.
14. Fidler, F., & Thompson, B. (2001). Computing correct confidence intervals for ANOVA fixed- and random-effects effect sizes. Educational and Psychological Measurement, 61, 575-604.
15. Finch, S., Cumming, G., & Thomason, N. (2001). Reporting of statistical inference in the Journal of Applied Psychology: Little evidence of reform. Educational and Psychological Measurement, 61, 181-210.
16. Finch, S., Cumming, G., Williams, J., Palmer, L., Griffith, E., Alders, C., Anderson, J., & Goodman, O. (2001). Reform of statistical inference in psychology: The case of Memory and Cognition. Manuscript in preparation.
17. Finch, S., Thomason, N., & Cumming, G. (2001). Past and future APA guidelines for statistical practice. Manuscript submitted for publication.
18. Gigerenzer, G., & Murray, D. (1987). Cognition as intuitive statistics. Hillsdale, NJ: Lawrence Erlbaum.
19. Glass, G. (1976). Primary, secondary, and meta-analysis of research. Educational Researcher, 5, 3-8.
20. Glass, G., McGaw, B., & Smith, M. (1981). Meta-analysis in social research. Beverly Hills, CA: Sage.
21. Grant, D. (1962). Testing the null hypothesis and the strategy and tactics of investigating theoretical models. Psychological Review, 60, 54-61.
22. Greenland, S. (1987). Quantitative methods in the review of epidemiologic literature. Epidemiologic Reviews, 9, 1-30.
23. Greenland, S. (1988). On sample-size and power calculations for studies using confidence intervals. American Journal of Epidemiology, 128, 231-237.
24. Hays, W. (1988). Statistics (4th ed.). New York: Holt, Rinehart & Winston.
25. Hogben, D., Pinkham, R., & Wilk, M. (1961). The moments of the non-central t-distribution. Biometrika, 48, 465-468.
26. Howell, D. (1997). Statistical methods for psychology (4th ed.). Belmont, CA: Duxbury.
27. Hunter, J. E. (1997). Needed: A ban on the significance test. Psychological Science, 8, 3-7.
28. Hunter, J., & Schmidt, F. (1990). Methods of meta-analysis: Correcting error and bias in research findings. Newbury Park, CA: Sage.
29. Hyde, J. S. (2001). Reporting effect sizes: The roles of editors, textbook authors, and publication manuals. Educational and Psychological Measurement, 61, 225-228.
30. Kendall, M., & Stuart, A. (1961). The advanced theory of statistics (Vol. 2) London: Charles Griffin.
31. Kirk, R. E. (2001). Promoting good statistical practices: Some suggestions. Educational and Psychological Measurement, 61, 213-218.
32. LaForge, R. (1967). Confidence intervals or tests of significance in scientific research. Psychological Bulletin, 64, 446-447.
33. Light, R., Singer, J., & Willett, J. (1994). The visual presentation and interpretation of meta-analysis. In H. Cooper & L. Hedges (Eds.), The handbook of research synthesis (pp. 439-453). New York: Russell Sage.
34. Lockhart, R. (1998). Introduction to statistics and data analysis for the behavioral sciences. New York: Freeman.
35. Loftus, G. (1993). A picture is worth a thousand p values: On the irrelevance of hypothesis testing in the microcomputer age. Behavior Research Methods, Instruments & Computers, 25, 250-256.
36. Meehl, P. (1978). Theoretical risks and tabular asterisks: Sir Karl, Sir Ronald, and the slow progress of soft psychology. Journal of Consulting & Clinical Psychology, 4, 806-843.
37. Moore, D., & McCabe, G. (1993). Introduction to the practice of statistics (2nd ed.). New York: Freeman.
38. Nickerson, R. (2000). Null hypothesis significance testing: A review of an old and continuing controversy. Psychological Methods, 5, 241-301.
39. Owen, D. (1968). A survey of properties and applications of the noncentral t-distribution. Technometrics, 10, 445-478.
40. Pearson, E., & Hartley, H. (1972). Biometrika tables for statisticians (Vol. 2). Cambridge, UK: Cambridge University Press.
41. Rosenberg, M., Adams, D., & Gurevitch, J. (2000). MetaWin: Statistical software for Meta-Analysis. Sunderland, MA: Sinauer.
42. Rosenthal, R. (1991). Meta-analytic procedures for social research (Rev. ed.). Newbury Park, CA: Sage.
43. Rubin, D. (1990). A new perspective. In K. Wachter & M. Straf (Eds.), The future of meta-analysis (pp. 155-165). New York: Russell Sage.
44. Schmidt, F. (1992). What do data really mean? Research finding, meta-analysis, and cumulative knowledge in psychology. American Psychologist, 47, 1173-1181.
45. Schmidt, F. (1996). Statistical significance testing and cumulative knowledge in psychology: Implications for training of researchers. Psychological Methods, 1, 115-129.
46. Schmidt, F., & Hunter, J. (1997). Eight common but false objections to the discontinuation of significance testing in the analysis of research data. In L. Harlow, S. Muliak, & J. Steiger (Eds.), What if there were no significance tests? (pp. 37-64). Mahwah, NJ: Lawrence Erlbaum.
47. Smithson, M. (2000). Statistics with confidence. London: Sage.
48. Smithson, M. (2001). Correct confidence intervals for various regression effect sizes and parameters: The importance of noncentral distributions in computing intervals. Educational and Psychological Measurement, 61, 605-632.
49. Steiger, J., & Fouladi, T. (1997). Noncentrality interval estimation and the evaluation of statistical models. In L. Harlow, S. Muliak, & J. Steiger (Eds.), What if there were no significance tests? (pp. 221-257). Mahwah, NJ: Lawrence Erlbaum.
50. Thomason, N., Cumming, G., & Zangari, M. (1994). Understanding central concepts of statistics and experimental design in the social sciences. In K. Beattie, C. McNaught, & S. Wills (Eds.), Interactive multimedia in university education: Designing for change in teaching & learning (pp. 59-81). Amsterdam, the Netherlands: Elsevier.
51. Thompson, B. (1998). In praise of brilliance: Where that praise really belongs. American Psychologist, 53, 799-800.
52. Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76, 105-110.
53. Wilkinson, L., & Task Force on Statistical Inference, APA Board of Scientific Affairs. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54, 594-604.