The accuracy of four approximations to noncentralF
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From a computational standpoint, there is little advantage to using approximate rather than exact methods.
“Thus, from a computational standpoint, there is little advantage to using approximate rather than exact methods (cf.Bradley, Russell, & Reeve, 1998).”
From G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences (2007) · cites this paper as Bradley, Russell, & Reeve, 1998
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Cites
Statistical Power Analysis for the Behavioral Sciences
Muller, K. E., & Cohen, J. (1989) · Technometrics · doi:10.2307/1270020 · Cited by 99,588 · see citing works
Statistical power analysis for the behavioral sciences
Cohen, J. (1990) · Computers Environment and Urban Systems · doi:10.1016/0198-9715(90)90050-4 · Cited by 65,406 · see citing works
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433 · see citing works
Statistical Power Analysis for the Behavioral Sciences (2nd ed.).
Lachenbruch, P. A., & Cohen, J. (1989) · Journal of the American Statistical Association · doi:10.2307/2290095 · Cited by 37,385 · see citing works
Statistical principles in experimental design.
Winer, B. J. (1962) · McGraw-Hill Book Company · doi:10.1037/11774-000 · Cited by 27,137 · see citing works
Statistical Principles in Experimental Design
Myers, J. L., & Winer, B. J. (1964) · The American Journal of Psychology · doi:10.2307/1419292 · Cited by 8,111 · see citing works
GPOWER: A general power analysis program
Erdfelder, E., Faul, F., & Buchner, A. (1996) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03203630 · Cited by 4,864 · see citing works
American Educational Research Journal, 1964-1968
Vesta, F. J. D., & Grinder, R. E. (1968) · American Educational Research Journal · doi:10.2307/1162008 · Cited by 2,606 · see citing works
Kölbig, K. S., & Schäff, F. (1972) · Mathematics of Computation · doi:10.1090/s0025-5718-1972-0314236-2 · Cited by 2,101 · see citing works
The statistical power of abnormal-social psychological research: A review.
Cohen, J. (1962) · The Journal of Abnormal and Social Psychology · doi:10.1037/h0045186 · Cited by 1,824 · see citing works
Iversen, G. R., & Norpoth, H. (1987) · Springer eBooks · doi:10.1007/978-3-642-04898-2_117 · Cited by 1,515 · see citing works
Biometrika Tables for Statisticians
Savage, I. R., Pearson, E. S., & Hartley, H. O. (1967) · Mathematics of Computation · doi:10.2307/2004190 · Cited by 1,440 · see citing works
Continuous Univariate Distributions.Vol. 1
Kocherlakota, S., Johnson, N. L., Kotz, S., & Balakrishnan, N. (1995) · Biometrics · doi:10.2307/2533292 · Cited by 861 · see citing works
The Annals of Mathematical Statistics
King, W. I. (1930) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177733256 · Cited by 832 · see citing works
Do studies of statistical power have an effect on the power of studies?
Sedlmeier, P., & Gigerenzer, G. (1989) · Psychological Bulletin · doi:10.1037/0033-2909.105.2.309 · Cited by 748 · see citing works
The non-central chi2- and F-distributions and their applications.
PATNAIK, P. B. (1949) · PubMed · Cited by 556 · see citing works
Wilks, S. S., Neyman, J., & Pearson, E. S. (1936) · Journal of the American Statistical Association · doi:10.2307/2278685 · Cited by 549 · see citing works
THE DISTRIBUTION OF THE INDEX IN A NORMAL BIVARIATE POPULATION
Fieller, E. C. (1932) · Biometrika · doi:10.1093/biomet/24.3-4.428 · Cited by 342 · see citing works
Statistical power of psychological research: What have we gained in 20 years?
Rossi, J. S. (1990) · Journal of Consulting and Clinical Psychology · doi:10.1037//0022-006x.58.5.646 · Cited by 323 · see citing works
Statistical power of psychological research: What have we gained in 20 years?
Rossi, J. S. (1990) · Journal of Consulting and Clinical Psychology · doi:10.1037/0022-006x.58.5.646 · Cited by 323 · see citing works
Statistical power analysis : a computer program
Cohen, J., & Borenstein, M. (1988) · Medical Entomology and Zoology · Cited by 270 · see citing works
A Review of Statistical Power Analysis Software
Thomas, L., & Krebs, C. J. (1997) · Bulletin of the Ecological Society of America · doi:10.2307/20168137 · Cited by 238 · see citing works
Biometrika Tables for Statisticians, Vol. 2
Kendall, M. G., Pearson, E. S., & Hartley, H. O. (1973) · International Statistical Review · doi:10.2307/1402802 · Cited by 196 · see citing works
THE BULLETIN OF THE ECOLOGICAL SOCIETY OF AMERICA
Johnson, E. A. (2005) · Bulletin of the Ecological Society of America · doi:10.1890/0012-9623(2005)86[248b:tbotes]2.0.co;2 · Cited by 195 · see citing works
The power function of the analysis of variance tests, with tables and illustrations of their use.
Tang, P. C. (1938) · Cited by 161 · see citing works
A statistical power analysis of applied psychological research.
Chase, L. J., & Chase, R. B. (1976) · Journal of Applied Psychology · doi:10.1037/0021-9010.61.2.234 · Cited by 115 · see citing works
On the Power of Statistical Tests in the American Educational Research Journal
Brewer, J. K. (1972) · American Educational Research Journal · doi:10.3102/00028312009003391 · Cited by 100 · see citing works
Normal approximation to the chi-square and non-central F probability functions
Severo, N. C., & Zelen, M. (1960) · Biometrika · doi:10.1093/biomet/47.3-4.411 · Cited by 97 · see citing works
Tables of the Power of theF-Test
TIKU, M. L. (1967) · Journal of the American Statistical Association · doi:10.1080/01621459.1967.10482926 · Cited by 94 · see citing works
Laguerre series forms of non-central X2 and F distributions
TIKU, M. L. (1965) · Biometrika · doi:10.1093/biomet/52.3-4.415 · Cited by 92 · see citing works
Calculating power in analysis of variance.
Koele, P. (1982) · Psychological Bulletin · doi:10.1037/0033-2909.92.2.513 · Cited by 84 · see citing works
Normalizing the Noncentral $t$ and $F$ Distributions
Laubscher, N. F. (1960) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177705682 · Cited by 81 · see citing works
Power and Sample Size via MS/PC-DOS Computers
Goldstein, R. (1989) · The American Statistician · doi:10.1080/00031305.1989.10475670 · Cited by 71 · see citing works
A Note on Approximating to the Non-Central F Distribution
TIKU, M. L. (1966) · Biometrika · doi:10.1093/biomet/53.3-4.606 · Cited by 67 · see citing works
Tables of the Power of the F-Test
TIKU, M. L. (1967) · Journal of the American Statistical Association · doi:10.2307/2283980 · Cited by 63 · see citing works
A power‐analytic examination of contemporary communication research
Chase, L. J., & Tucker, R. K. (1975) · Speech Monographs · doi:10.1080/03637757509375874 · Cited by 51 · see citing works
An Analysis of the Use of Statistical Testing in Communication Research
Katzer, J., & Sodt, J. (1973) · Journal of Communication · doi:10.1111/j.1460-2466.1973.tb00947.x · Cited by 51 · see citing works
Inverse Tables of Probabilities of Errors of the Second Kind
Lehmer, E. T. (1944) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177731209 · Cited by 50 · see citing works
Power Tables for Analysis of Variance
Rotton, J., & Schönemann, P. H. (1978) · Educational and Psychological Measurement · doi:10.1177/001316447803800202 · Cited by 47 · see citing works
Statistical Power: Derivation, Development, and Data-Analytic Implications
Chase, L. J., & Tucker, R. K. (1976) · The Psychological Record · doi:10.1007/bf03394413 · Cited by 40 · see citing works
Some Notes on the Relationship Between the Distributions of Central and Non-Central F
Pearson, E. S., & TIKU, M. L. (1970) · Biometrika · doi:10.1093/biomet/57.1.175 · Cited by 33 · see citing works
A FOUR‐MOMENT APPROXIMATION BASED ON THE F DISTRIBUTION
TIKU, M. L., & Yip, D. Y. N. (1978) · Australian Journal of Statistics · doi:10.1111/j.1467-842x.1978.tb01108.x · Cited by 17 · see citing works
Computer simulation with DATASIM
Bradley, D. R. (1989) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03205564 · Cited by 17 · see citing works
Self-citationStatistical power in complex experimental designs
Bradley, D. R., Russell, R. L., & Reeve, C. P. (1996) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03204790 · Cited by 16 · see citing works
Self-citationA simulation laboratory for statistics
Bradley, D. R., Hemstreet, R. L., & Ziegenhagen, S. T. (1992) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03203496 · Cited by 15 · see citing works
Self-citationMore Tables of the Power of the F-Test
TIKU, M. L. (1972) · Journal of the American Statistical Association · doi:10.2307/2284473 · Cited by 14 · see citing works
The Use of Noncentral F Approximations for Calculation of Power and Sample Size
Guenther, W. C. (1979) · The American Statistician · doi:10.1080/00031305.1979.10482695 · Cited by 14 · see citing works
More Tables of the Power of theF-Test
TIKU, M. L. (1972) · Journal of the American Statistical Association · doi:10.1080/01621459.1972.10481283 · Cited by 13 · see citing works
Generating multivariate data from nonnormal distributions: Mihal and Barrett revisited
Bradley, D. R., & Fleisher, C. L. (1994) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03204610 · Cited by 13 · see citing works
Self-citationStatistical simulation on microcomputers
Bradley, D. R., Senko, M. W., & Stewart, F. A. (1990) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03203153 · Cited by 11 · see citing works
Self-citationCohen, J., & Nee, J. C. M. (1987) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr2204_6 · Cited by 11 · see citing works
Multivariate simulation with DATASIM: The Mihal and Barrett study
Bradley, D. R. (1993) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03204488 · Cited by 9 · see citing works
Self-citationApproximating Probability Levels for Testing Null Hypotheses with Noncentral F Distributions
Fowler, R. L. (1984) · Educational and Psychological Measurement · doi:10.1177/0013164484442010 · Cited by 8 · see citing works
Probabilities and Critical Values for z, chi square, r, t, and F
O’Grady, K. E. (1981) · Behavior Research Methods · doi:10.3758/bf03201874 · Cited by 7 · see citing works
Anatomy of a DATASIM simulation: The Doob and Gross horn-honking study
Bradley, D. R. (1991) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03203364 · Cited by 6 · see citing works
Self-citationSome properties of the distribution of the logarithm of non-central F
Barton, D. E., David, F. N., & O'Neill, A. F. (1960) · Biometrika · doi:10.1093/biomet/47.3-4.417 · Cited by 5 · see citing works
A Computer Program for Calculating Power of the F-Test
Woodward, J. A., & Overall, J. E. (1976) · Educational and Psychological Measurement · doi:10.1177/001316447603600116 · Cited by 5 · see citing works
The Use of Noncentral F Approximations for Calculation of Power and Sample Size
Guenther, W. C. (1979) · The American Statistician · doi:10.2307/2683736 · Cited by 5 · see citing works
Power & Effect: A statistical utility for Macintosh and Windows systems
Meyer, G. E. (1995) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03204717 · Cited by 4 · see citing works
POWERF: A program that computes the power of F tests in fixed-effects ANOVA designs
Parker, R. M., & Borich, G. D. (1980) · Behavior Research Methods · doi:10.3758/bf03208334 · Cited by 3 · see citing works
Intuitive inventory management: An experimental system
Meyer, J., & Eben‐Chaime, M. (1995) · Behavior Research Methods, Instruments, & Computers · doi:10.3758/bf03200447 · Cited by 2 · see citing works
Flagged first, then by citations
Research works printed but not linked: 8
- ABRAMOWITZ, M., & STEGUN, I. A. (EDS.) (1964). Handbook ofmath- ematical functions (Applied Mathematics Series No. 55). Washing- ton, DC: National Bureau of Standards.
- BRADLEY, D. R. (1988). DATASIM. Lewiston, ME: Desktop Press.
- BRADLEY, D. R. (1989b). A general purpose simulation program for sta- tistics and research methods. In G. Garson & S. Nagel (Eds.), Ad- vances in social science and computers (Vol. I, pp. 145-186). Green- wich, CT: JAI Press.
- BRADLEY, D. R. (199Ib). Datasimfor the Macintosh. Lewiston, ME: Desktop Press.
- COHEN,J. (1977). Statistical power analysis/or the behavioral sciences (rev. ed.). Hillsdale, NJ: Erlbaum.
- JOHNSON, N. L., & KOTZ, S. (1970). Continuous univariate distribu- tions (Vol. 2). New York: Houghton Mifflin.
- PEARSON, E. S., & HARTLEY, H. O. (EDS.) (1976). Biometrika tablesfor statisticians (Vol. II). London: Biometrika Trust.
- SCHEFFE, H. (1959). Analysis ofvariance. New York: Wiley.
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- Authors
- Bradley, D. R., Russell, R. L., & Reeve, C. P.
- Affiliations
- Bates College (US)
- Corresponding author
- Bradley, Drake R.
- Venue
- Behavior Research Methods, Instruments, & Computers
- Published
- 1998-09
- Volume
- 30
- Issue
- 3
- Pages
- 478-500
- ISSN
- 0743-3808 (ISSN-L)
- 1532-5970
- OpenAlex
- W2030791091
- Cited by
- 2
- References
- 61
- Citations by year
- 2025: 1
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Behavior Research Methods, Instruments, & Computers (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- noncentral F distribution, statistical power, power approximation, two-moment approximation, square root approximation, approximation accuracy, critical values
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