Equivalence tests can enhance environmental science and management

Australian and New Zealand Journal of Statistics

Volumn 41, Issue 1, 1999, Pages 19-29

  Mcbride, Graham B ^a  

^a NATIONAL INSTITUTE OF WATER AND ATMOSPHERIC RESEARCH   (New Zealand)

Author keywords

Bioequivalence; Environmental management; Equivalence test; Interval hypothesis; Precautionary principle

Indexed keywords

EID: 18844448186     PISSN: 13691473     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-842X.00058     Document Type: Article

References (66)

1. ABRAMOWITZ, M. & STEGUN, I.A. (1970). Handbook of Mathematical Functions. New York: Dover.
2. ANDERSON, S. & HAUCK, W.W. (1983). A new procedure for testing equivalence in comparative bioavailability and other clinical trials. Comm. Statist. A12, 2663-2692.
3. _ &_ (1985). Letter to the Editor. Biometrics 41, 561-563.
4. BERGER, J.O. & DELAMPADY, M. (1987). Testing precise hypotheses (with discussion). Statist. Sci. 2, 317-352.
5. BERGER, R.L. & HSU, J.C. (1996). Bioequivalence trials, intersection-union tests and equivalence confidence sets. Statist. Sci. 11, 283-319.
6. CHOW, S-C. & LIU, J-P. (1992). Design and Analysis of Bioavailability and Bioequivalence Studies. New York: Marcel Dekker.
7. DILETTI, E., HAUSCHKE, D. & STEINIJANS, V.W. (1991). Sample size determination for bioequivalence assessment by means of confidence intervals. Internat. J. Clin. Pharmacol., Therapy and Toxicology 29, 1-8 (also 30, Supplement No. 1: S51-58).
8. DILETTI, E., HAUSCHKE, D. & STEINIJANS, V.W. (1991). Sample size determination for bioequivalence assessment by means of confidence intervals. Internat. J. Clin. Pharmacol., Therapy and Toxicology 29, 1-8 (also 30, Supplement No. 1: S51-58).
9. DIXON, P.M. & GARRETT, K.A. (1994). Statistical issues for field experimenters. In Wildlife and Population Modelling: Integrated Studies of Agroecosystems, eds R.J. Kendall & T.E. Lacher Jr, 439-450. Boca Raton, FL: Lewis.
10. _ (1998). Assessing effect and no effect with equivalence tests. In Risk Assessment: Logic and Measurement, eds M. Newman & C. Strojan. Chelsea, MI: Ann Arbor Press.
11. ERICKSON, W.P. & McDONALD, L.L. (1995). Tests for bioequivalence of control media and test media in studies of toxicity. Environ. Toxic. Chem. 14, 1247-1256.
12. FAIRWEATHER, P.G. (1991). Statistical power and design requirements for environmental monitoring. Austral. J. Mar. Freshwater Res. 42, 555-567.
13. FERGUSON, T.S. (1967). Mathematical Statistics: A Decision Theoretic Approach. New York: Academic Press.
14. FLEISS, J.L. (1981). Statistical Methods for Rates and Proportions. 2nd edition. New York: Wiley.
15. GARDNER, M.J. & ALTMAN, D.G. (1986). Confidence intervals rather than P values: estimation rather than hypothesis testing. British Med. J. 292, 746-750.
16. GOLDSTEIN, R. (1989). Power and sample size via MS/PC-DOS computers. Amer. Statist. 43, 253-260.
17. GREEN, R.H. (1979). Sampling Design and Statistical Methods for Environmental Biologists. New York: Wiley.
18. _ 1989. Power analysis and practical strategies for environmental monitoring. Environ. Res. 50, 195-205.
19. HAUCK, W.W. & ANDERSON, S. (1984). A new statistical procedure for testing equivalence in two-group comparative bioavailability trials. J. Pharmacokinetics and Biopharmaceutics 12, 83-91.
20. HAUSCHKE, D., STEINIJANS, V.W. & DILETTI, E. (1990). A distribution-free procedure for the analysis of bioequivalence studies. Internat. J. Clin. Pharmacol., Therapy and Toxicology 28, 72-78.
21. HINTZE, J.L. (1996). PASS 6.0 User's Guide (Power and Sample Size Analysis for Windows). Kaysville, Utah: Number Cruncher Statistical Systems.
22. IDV-Datenanalyse und Versuchsplanung. (1993). N Handbook, Version 2.2. Munich.
23. JOWETT, I.G., HAYES, J.W., DEANS, N. & ELDON, G.A. (1998). Comparison of fish communities and abundance in unmodified streams of Kahurangi National Park with other areas of New Zealand. N.Z. J. Mar. Freshwater Res. 32, 335-350.
24. JOHNSON, N.L. & KOTZ, S. (1970). Distributions in Statistics. Continuous Univariate Distributions - 2. Boston: Houghton-Mifflin.
25. KATZ, R.W. (1992). Role of statistics in the validation of circulation models. Clim. Res. 2, 35-45.
26. LEHMANN, E.L. (1959). Testing Statistical Hypotheses. New York: Wiley.
27. LETTENMAIER, D.P. (1978). Design considerations for ambient stream quality monitoring. Water Res. Bull. 14, 884-902.
28. LIU, J-P. & CHOW, S-C. (1996). Comment on Berger, R.L. & HSU, J.C. Bioequivalence trials, intersection-union tests and equivalence confidence sets. Statist. Sci. 11, 306-312.
29. McBRIDE, G.B. (1995). Difference versus equivalence tests: what's the difference? In Proceedings of the A.C. Aitken Centenary Conference, eds L. Kavalieris, F.C. Lam, L.A. Roberts & J.A. Shanks, 193-199. Dunedin, New Zealand: Otago Conference Series No. 5, University of Otago.
30. _, LOFTIS, J.C. & ADKINS, N.C. (1993). What do significance tests really tell us about the environment? Environ. Manag. 17, 423-432 (erratum, 18, 317).
31. McDONALD, L.L. & ERICKSON, W.P. (1994). Testing for bioequivalence in field studies: has a disturbed site been adequately reclaimed? In Statistics in Ecology and Environmental Monitoring, eds D.J. Fletcher & B.F.J. Manly, 183-197. Dunedin, New Zealand: Otago Conference Series No. 2, University of Otago.
32. MANDALLAZ, D. & MAU, J. (1981). Comparison of different methods for decision-making in bioequivalence assessment. Biometrics 37, 213-222.
33. MAPSTONE, B.D. (1995). Scalable decision rules for environmental impact studies: effect size, Type I, and Type II errors. Ecol. Apps. 5, 401-410.
34. MARTIN ANDRÉS, A. (1990). On testing for bioequivalence. Biometrical J. 32, 125-126.
35. MEREDITH, M.P. & HEISE, M.A. (1996). Comment on Berger, R.L. & Hsu, J.C. Bioequivalence trials, intersection-union tests and equivalence confidence sets. Statist. Sci. 11, 304-306.
36. MILLARD, S.P. (1987). Environmental monitoring, statistics, and the law: room for improvement. Amer. Statist. 41, 249-253.
37. MINNS, C.K. (1990). Patterns of distribution and association of freshwater fish in New Zealand. New Zealand J. Mar. Freshwater Res. 24, 31-44.
38. Ministry for the Environment (1995). Principles and priorities for the development of environmental standards and guidelines: an issues and options paper. Wellington, New Zealand: Ministry for the Environment.
39. MULLER, K.E. & BENIGNUS, V.A. (1992). Increasing scientific power with statistical power. Neurotox. Teratol. 14, 211-219.
40. OSENBERG, C.W., SCHMITT, R.J., HOLBROOK, S.J., ABU-SABA, K.E. & FLEGAL, A.R. (1994). Detection of environmental impacts: natural variability, effect size, and power analysis. Ecol. Apps. 4, 16-30.
41. OWEN, D.B. (1965). A special case of a bivariate non-central t-distribution. Biometrika 52, 437-446.
42. PATEL, H.I. & GUFTA, G.D. (1984). A problem of equivalence in clinical trials. Biometrical J. 26, 471-474.
43. PETERMAN, R.M. (1990). Statistical power analysis can improve fisheries research and management. Canad. J. Fish. Aquat. Sci. 47, 2-15.
44. PHILLIPS, K.F. (1990). Power of two one-sided tests procedure in bioequivalence. J. Pharmacokinetics and Biopharmaceutics 18, 137-144.
45. PRATT, J.W., RAIFFA, H. & SCHLAIFER, R. (1995). Introduction to Statistical Decision Theory. Cambridge, Mass.: The MIT Press.
46. PRESS, W.H., FLANNERY, B.P., TEUKOLSKY, S.A. & VETTERLING, W.A. (1986). Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge, England: Cambridge University Press.
47. QUINN, J.M., DAVIES-COLLEY, R.J., HICKEY, C.W., VICKERS, M.L. & RYAN, P.A. (1992). Effects of clay discharges in streams. 2. Benthic invertebrates. Hydrobiologia 248, 235-247.
48. RECKHOW, K.H. (1990). Bayesian inference in non-replicated ecological studies. Ecol. 71, 2053-2059.
49. ROCKE, D.M. (1984). On testing for bioequivalence. Biometrics 40, 225-230.
50. RODDA, B.E. & DAVIS, R.L. (1980). Determining the probability of an important difference in bioavailability. Clin. Pharmacol Therapy 28, 252-57.
51. SASABUCHI, S. (1980). A test of a multivariate normal mean with composite hypotheses determined by linear inequalities. Biometrika 67, 429-439.
52. _ (1988a). A multivariate one-sided test with composite hypotheses when the covariance matrix is completely unknown. Mem. Fac. Sci., Kyushu Univ. Ser. A 42, 37-46.
53. _ (1988b). A multivariate one-sided test with composite hypotheses when the covariance matrix has an unknown scale factor. Mem. Fac. Sci., Kyushu Univ. Ser. A 42, 9-19.
54. SCHERVISH, M.J. (1996). P values: what they are and what they are not. Amer. Statist. 50, 203-206.
55. SCHUIRMANN, D.J. (1981). On hypothesis testing to determine if the mean of a normal distribution is contained in a known interval. Biometrics 37, 617 (abstract).
56. _ (1987). A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. J. Pharmacokinetics and Biopharmaceutics 15, 657-680.
57. _ (1996). Comment on Berger, R.L. & Hsu, J.C. Bioequivalence trials, intersection-union tests and equivalence confidence sets. Statist. Sci. 11, 312-313.
58. SELWYN, M.R. & HALL, N.R. (1984). On Bayesian methods for bioequivalence. Biometrics 40, 1103-1108.
59. SOKAL, R.R. & ROHLF, F.J. (1981). Biometry. The Principles and Practice of Statistics in Biological Research. 2nd edition. New York: Freeman.
60. STEINIJANS, V.W., HAUCK, W.W., DILETTI, E., HAUSCHKE, D. & ANDERSON, S. (1992). Effect of changing the bioequivalence range from (0.80, 1.20) to (0.80, 1.25) on the power and sample size. Internat. J. Clin. Pharmacol., Therapy and Toxicology 30, 571-575.
61. _ & HAUSCHKE, D. (1993). International harmonization of regulatory bioequivalence requirements. Clin. Res. Reg. Aff. 10, 203-220.
62. STUNKARD, C.L. (1994). Tests of proportional means for mesocosm studies. In Aquatic Mesocosm Studies in Ecological Risk Assessment, eds R.L. Graney, J.H. Kennedy & J.H. Rogers Jr, 71-83. Boca Raton: Lewis.
63. THOMAS, L. & KREBS, C.J. (1997). A review of statistical power analysis software. Bull. Ecol. Soc. Amer. 78, 126-139.
64. TOFT, P.J. & SHEA, P.J. (1983). Detecting community-wide patterns: estimating power strengthens statistical significance. Amer. Naturalist 122, 618-625.
65. WESTLAKE, W.J. (1981). Response to T.B.L. Kirkwood on Bioequivalence testing - a need to rethink. Biometrics 37, 589-594.
66. ZAR, J.H. (1984). Biostatistical Analysis. 2nd edition. Englewood Cliffs, New Jersey: Prentice-Hall.