Bootstrapping to Test for Nonzero Population Correlation Coefficients Using Univariate Sampling

Psychological Methods

Volumn 12, Issue 4, 2007, Pages 414-433

  Beasley, William Howard ^a   DeShea, Lise ^b   Toothaker, Larry E ^a   Mendoza, Jorge L ^a   Bard, David E ^a   Rodgers, Joseph Lee ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

^b Oklahoma Health Care Authority   (United States)

Author keywords

bootstrap; correlation; Monte Carlo simulation; nonzero and nil hypotheses; univariate sampling

Indexed keywords

ARTICLE; EPIDEMIOLOGY; HUMAN; METHODOLOGY; MONTE CARLO METHOD; PSYCHOLOGICAL MODEL; PSYCHOLOGY;

HUMANS; MODELS, PSYCHOLOGICAL; MONTE CARLO METHOD; PSYCHOLOGY; SAMPLING STUDIES;

EID: 38349112824     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/1082-989X.12.4.414     Document Type: Article

References (46)

1. Ackerman P.L., Beier M.E., and Boyle M.O. Individual differences in working memory within a nomological network of cognitive and perceptual speed abilities. Journal of Experimental Psychology: General 131 (2002) 567-589
2. Beasley W.H. Ribeye statistics: Univariate sampling bootstrap [Computer software] (2007). http://howardliveoak.com Retrieved October 18, 2007, from http://howardliveoak.com
3. Benton D., and Krishnamoorthy K. Computing discrete mixtures of continuous distributions: Noncentral chisquare, noncentral t and the distribution of the square of the sample multiple correlation coefficient. Computational Statistics & Data Analysis 43 (2003) 249-267
4. Bollen K.A., and Stine R.A. Bootstrapping goodness-of-fit measures in structural equation models. Sociological Methods Research 21 (1992) 205-229
5. Bouchard Jr. T.J., and McGue M. Familial studies of intelligence: A review. Science 212 (1981, May 29) 1055-1059
6. Budescu D.V., and Appelbaum M.I. Variance stabilizing transformations and the power of the F test. Journal of Educational Statistics 6 (1981) 55-74
7. Center for Human Resource Research. NLSY79 child and young adult data users guide (2006), Author, Columbus, OH
8. Cohen J. The earth is round (p < .05). American Psychologist 49 (1994) 997-1003
9. Crow E.L., and Siddiqui M.M. Robust estimation of location. Journal of the American Statistical Association 62 (1967) 353-389
10. Davison A.C., and Hinkley D.V. Bootstrap methods and their application (1997), Cambridge University Press, Cambridge, England
11. Diaconis P., and Efron B. Computer-intensive methods in statistics. Scientific American 248 (1983, May) 116-130
12. Duncan G.T., and Layard M.W.J. A Monte Carlo study of asymptotically robust tests for correlation coefficients. Biometrika 60 (1973) 551-558
13. Efron B. Bootstrap methods: Another look at the jackknife. Annals of Statistics 7 (1979) 1-26
14. Efron B. The jackknife, the bootstrap, and other resampling plans (1982), Society for Industrial and Applied Mathematics, Philadelphia
15. Efron B., and Tibshirani R.J. An introduction to the bootstrap (1993), Chapman & Hall/CRC, Boca Raton, FL
16. Fisher R.A. Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 10 (1915) 507-521
17. Fisher R.A. The genesis of twins. Genetics 4 (1919) 489-499
18. Fisher R.A. Design of experiments. 7th ed. (1960), Hafner Publishing, New York
19. Harley B.I. Relation between the distributions of non-central t and of a transformed correlation coefficient. Biometrika 44 (1957) 219-224
20. Harlow L.L. Significance testing introduction and overview. In: Harlow L.L., Mulaik S.A., and Steiger J.H. (Eds). What if there were no significance tests? (1997), Erlbaum, Mahwah, NJ 1-17
21. Harlow L.L., Mulaik S.A., and Steiger J.H. What if there were no significance tests? (1997), Erlbaum, Hillsdale, NJ
22. Harville D. Matrix algebra from a statistician's perspective (1997), Springer-Verlag, New York
23. Headrick T.C. Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions. Computational Statistics & Data Analysis 40 (2002) 685-711
24. Headrick T.C., and Kowalchuck R.K. The power method transformation: Its probability density function, distribution function, and its further use for fitting data. Journal of Statistical Computation and Simulation 77 (2007) 229-249
25. Hogg R.V. Adaptive robust procedures: A partial review and some suggestions for future applications and theory. Journal of the American Statistical Association 69 (1974) 909-923
26. Kaiser H.F., and Dickman K. Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika 27 (1962) 179-182
27. Kowalski C.J. On the effects of non-normality on the distribution of the sample product-moment correlation coefficient. Applied Statistics 21 (1972) 1-12
28. Lee W., and Rodgers J.L. Bootstrapping correlation coefficients using univariate and bivariate sampling. Psychological Methods 3 (1998) 91-103
29. MacCallum R.C. Working with imperfect models. Multivariate Behavioral Research 38 (2003) 113-139
30. Meehl P.E. Theory-testing in psychology and physics: A methodological paradox. Philosophy of Science 34 (1967) 103-115
31. Micceri T. The unicorn, the normal curve, and other improbable creatures. Psychological Bulletin 105 (1989) 156-166
32. Microsoft Corporation. System: Random Class (2007). http://msdn2.microsoft.com/en-us/library/system.random(vs.80).aspx Retrieved August 22, 2007, from http://msdn2.microsoft.com/en-us/library/system.random(vs.80).aspx
33. Miller R.G. A trustworthy jackknife. Annals of Mathematical Statistics 35 (1964) 1594-1605
34. Mulaik S.A., Raju N.S., and Harshman R.A. There is a time and a place for significance testing. In: Harlow L.L., Mulaik S.A., and Steiger J.H. (Eds). What if there were no significance tests? (1997), Erlbaum, Mahwah, NJ 65-115
35. Preacher K.J., Rucker D.D., MacCallum R.C., and Nicewander W.A. Use of the extreme groups approach: A critical reexamination and new recommendations. Psychological Methods 10 (2005) 179-192
36. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical recipes in C++. 2nd ed. (2003), Cambridge University Press, Cambridge, England
37. Rindskopf D.M. Testing 'small', not null, hypotheses: Classical and Bayesian approaches. In: Harlow L.L., Mulaik S.A., and Steiger J.H. (Eds). What if there were no significance tests? (1997), Erlbaum, Mahwah, NJ 319-332
38. Rodgers J.L. The bootstrap, the jackknife and the randomization tests: A sampling taxonomy. Multivariate Behavioral Research 34 (1999) 441-456
39. Rodgers J.L., and Nicewander W.A. Thirteen ways to look at the correlation coefficient. The American Statistician 42 (1988) 59-66
40. Sawilowsky S.S., and Blair R.C. A more realistic look at the robustness and Type II error properties of the t test to departures from population normality. Psychological Bulletin 111 (1992) 352-360
41. Schenker N. Qualms about bootstrap confidence intervals. Journal of the American Statistical Association 80 (1985) 360-361
42. Strube M. Bootstrap Type I error rates for the correlation coefficient: An examination of alternate procedures. Psychological Bulletin 104 (1988) 290-292
43. Terwilliger J.S., and Anderson D.H. An empirical study of the effects of standardizing scores in the formation of linear composites. Journal of Educational Measurement 6 (1969) 145-154
44. Tucker A. Applied combinatorics (1984), Wiley, New York
45. Tukey J.W. Exploratory data analysis (1977), Addison-Wesley, Reading, MA
46. Zimmerman D.W., Zumbo B.D., and Williams R.H. Bias in estimation and hypothesis testing of correlation. Psicológica 24 (2003) 133-158