Sample size / power

OwensQ/PowerTOST functions rewritten from by Detlew Labes, Helmut Schuetz, Benjamin Lang

Calculation based on Chow S, Shao J, Wang H. 2008. Sample Size Calculations in Clinical Research. 2nd Ed. Chapman & Hall/CRC Biostatistics Series.

Connor R. J. 1987. Sample size for testing differences in proportions for the paired-sample design. Biometrics 43(1):207-211. page 209.

Phillips KF.Power of the Two One-Sided Tests Procedure in BioequivalenceJ Pharmacokin Biopharm. 1990;18(2):137–44. doi: 10.1007/BF01063556

Diletti D, Hauschke D, Steinijans VW.Sample Size Determination for Bioequivalence Assessment by Means of Confidence IntervalsInt J Clin Pharmacol Ther Toxicol. 1991;29(1):1–8.

Owen, D B (1965) "A Special Case of a Bivariate Non-central t-Distribution" Biometrika Vol. 52, pp.437-446.

FORTRAN code by J. Burkhardt, license GNU LGPL

D.B. Owen "Tables for computing bivariate normal Probabilities" The Annals of Mathematical Statistics, Vol. 27 (4) Dec. 1956, pp. 1075-1090

matlab code by J. Burkhardt license GNU LGPL

Confidence intervals

Wilson, E.B. (1927) Probable inference, the law of succession, and statistical inference. J. Amer. Stat. Assoc22, 209–212.

Clopper, C. and Pearson, E.S. (1934) The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26, 404–413.

Blaker, H. (2000). Confidence curves and improved exact confidence intervals for discrete distributions. Canadian Journal of Statistics28 (4), 783–798.

T. Tony Cai One-sided confidence intervals in discrete distributions. doi:10.1016/j.jspi.2004.01.00.

Newcombe, R. G. (1998) Two-sided confidence intervals for the single proportion: comparison of seven methods. Statistics in Medicine. 17 (8): 857–872. doi:10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E. PMID 9595616.

Miettinen O. S., Nurminen M. (1985) Comparative analysis of two rates. Statistics in Medicine4,213–226

Lawson, R (2005):Smallsample confidence intervals for the odds ratio. Communication in Statistics Simulation andComputation, 33, 1095-1113.

Woolf, B. (1955). On estimating the relation between blood group and disease. Annals of human genetics, 19(4):251-253.

Gart, JJand Nam, J (1988): Approximate interval estimation of the ratio of binomial parameters: Areview and corrections for skewness. Biometrics 44, 323-338.

Donner, A. and Zou, G. (2012). Closed-form confidence intervals for functions of the normal mean and standard deviation. Statistical Methods in Medical Research, 21(4):347-359.

Newcombe RG (1998): Interval Estimation for the Difference Between Independent Proportions: Comparison of Eleven Methods. Statistics in Medicine 17, 873-890.

Agresti A, Caffo B., “Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures”, American Statistician 54: 280–288 (2000)

Mee RW (1984) Confidence bounds for the difference between two probabilities,Biometrics40:1175-1176

Rothman, K. J., Greenland, S., & Lash, T. L. (2008). Modern epidemiology (3rd ed.). Philadelphia: Lippincott Williams & Wilkins.

R packages

PowerTOST by by Detlew Labes, Helmut Schuetz, Benjamin Lang

PropCIs by Ralph Scherer

pairwiseCI by Frank Schaarschmidt, Daniel Gerhard

binGroup by Boan Zhang, Christopher Bilder, Brad Biggerstaff, Frank Schaarschmidt Brianna Hitt

proportion by M.Subbiah, V.Rajeswaran

binom by Sundar Dorai-Raj


ORCI by Libo Sun

metafor by Wolfgang Viechtbauer