R libraries for sample size justification

There are a lot of good commercial and free sources for sample size justification. Note that most people use the term power calculation, but there is more than one way to justify a sample size, so I try to avoid the term “power calculation” as being too restrictive. Anyway, I just noted an email on the MedStats list that suggests two R libraries.

The MBESS R package

• cran.at.r-project.org/src/contrib/Descriptions/MBESS.html

estimates sample size by setting a goal on how precise you want the confidence intervals to be. It has a nice function that looks at the confidence interval for R-squared that would be hard to find in most other places.

The pwr R package:

• cran.at.r-project.org/src/contrib/Descriptions/pwr.html

uses a more traditional approach that follows the effect size notation noted in Cohen’s book on sample size.

• Statistical Power Analysis for the Behavioral Sciences Revised Edition. Jacob Cohen (1977) New York: Academic Press. (Sample Size, General)

Key papers, books and website

• Structural Equation Modeling in Practice: A Review and recommended Two-Step Approach. J.C. Anderson, D.W. Gerbing. Psychological Bulletin 1988: 103(3); 411-423. (Sample Size, SEM)
• Ethics and sample size. Peter Bacchetti, Leslie E Wolf, Mark R Segal, Charles E McCulloch. American Journal of Epidemiology 2005: 161(2); 105-110. (Sample, Ethics)
• Bacchetti et al. Respond to “Ethics and Sample Size - Another View”. Peter Bacchetti, Leslie E Wolf, Mark R Segal, Charles E McCulloch. American Journal Epidemiology 2005: 161(2); 113. (Sample, Ethics)
• How likely is it to go wrong Doctor?. Bandolier. Accessed on 2005-03-10. (Sample Size, Rule of three) Patients rightly pose difficult questions, and we often wonder too. If you have never seen a horrible complication from a particular drug or intervention how likely is it to happen? A short and illuminating paper from Germany may be very helpful [1] - as the authors say “experience and Murphy’s law teach us that catastrophes do happen, and their probability can in fact be calculated by a simple rule of thumb.” www.jr2.ox.ac.uk/bandolier/band23/b23-2.html
• The Observation to Variable Ratio in Factor Analysis. P.T. Barrett, P. Kline. Personality Study and Group Behavior 1981: 1; 23-33. (Sample Size, SEM)
• Pracatical Issues in Structural Modelling. P. M. Bentler, C. Chou. Sociological Methods and Research 1987: 16; 78-117. (Sample Size, SEM)
• Inherent variability among measures of fertility of rats and its implications in the design of mating trials. W. E. Berndtson, J. E. Judd, A. C. Castro. Journal of Andrology 1997: 18(6); 717-24. [Medline] (Sample Size, Example)
• An examination of methods for sample size recalculation during an experiment. R. A. Betensky, C. Tierney. Statistics in Medicine 1997: 16(22); 2587-98. (Sample Size, General)
• Additional power computations for designing comparative Poisson trials. C. C. Brown, S. B. Green. American Journal of Epidemiology 1982: 115(5); 752-8. [Medline] (Sample Size, Poisson Regression)
• Estimating sample sizes for binary, ordered categorical, and continuous outcomes in two group comparisons [Education and Debate]. M. J. Campbell, S. A. Julious, D. G. Altman. British Medical Journal 1995: 311(7013); 1145-8. [Medline] [Full text] (Sample Size, General)
• Sample size calculations for the log rank test: a Gompertz model approach. A. B. Cantor. J Clin Epidemiol 1992: 45(10); 1131-6. (Sample Size, Log Rank test)
• Sample Size Requirements for Precise Estimates of Reliability, Generalizability, and Validity Coefficients. Richard A Charter. Journal of Clinical and Experimental Neuropsychology 1999: 21(4); 559-566. (Sample Size, Reliability/Validity)
• Statistical Power Analysis for the Behavioral Sciences Revised Edition. Jacob Cohen (1977) New York: Academic Press. (Sample Size, General)
• Confidence limits and sample size in quarantine research. HM Couey. Forum: Journal of Economic Entomology 1986: 79(4); 887-90. (Size, Confidence Intervals)
• Sample Size Calculator. Creative Research Systems. Accessed on 2003-02-25. (Sample Size, General) This Sample Size Calculator is presented as a public service of Creative Research Systems. You can use it to determine how many people you need to interview in order to get results that reflect the target population as precisely as needed. You can also find the level of precision you have in an existing sample. www.surveysystem.com/sscalc.htm
• Statistical and design issues in studies of groups. Accounting for within-group correlation. P Cummings, T D Koepsell. Inj Prev 2002: 8(1); 6-7. [Full text] [PDF] (Sample Size, Cluster)
• Power Calculations for Logistic Regression with Exposure Measurement Error. Dartmouth-Hitchcock Medical Center. Accessed on 2003-04-23. (Sample Size, Logistic) This program provides provides power calculations for logistic regression with a continuous exposure variable and an additional continuous covariate or confounding variable. A classical measurement error model is assumed for this implementation. biostat.hitchcock.org/MeasurementError/Analytics/PowerCalculationsforLogisticRegression.asp
• Sample Size Methodology. M.M. Desu, D. Raghavarao (1990) Boston: Academic Press. (Sample Size, General)
• Power for Simple Mixed Models. Pat Dickson, School of Nursing, The University of Texas at Austin. Accessed on 2003-08-28. (Sample Size, Mixed Model) Mok’s often-cited 1995 article ends: ‘To the extent that these data are representative, one might offer as a rule of thumb, in the 2-level random slope balanced case with intraclass correlation of below, say, 0.15, at the x-intercept, that an actual sample size of 3500, and an effective sample size at the x-intercept of 400, to ensure reasonable efficiency and lack of bias.’ www.nur.utexas.edu/Dickson/stats/mxpower.html
• Sample size requirements for reliability studies. A. Donner, M. Eliasziw. Stat Med 1987: 6(4); 441-8. (Sample Size, General)
• Power and Sample Size Calculations for Studies Involving Linear Regression. William D Dupont, W D Jr. Plummer. Controlled Clinical Trials 1998: 19; 589-601. (Sample Size, Linear Regression)
• Sample size requirements for case-control study designs. M. D. Edwardes. BMC Med Res Methodol 2001: 1(1); 11. [Medline] [Abstract] [Full text] [PDF] (Sample size, Case control)
• Why “underpowered” trials are not necessarily unethical. S. J. Edwards, R. J. Lilford, D. Braunholtz, J. Jackson. Lancet 1997: 350(9080); 804-7. [Medline] (Sample Size, Ethics)
• Sample Size Calculation for clinical trials: the impact of clinician beliefs. P M Fayers, A Cuschieri, J Fielding, J Craven, B Uscinska, LS Freedman. British Journal of Cancer 2000: 82(1); 213-219. (Sample Size, Clinical Importance)
• Effects of Sample Size and Non-Normality on the Estimation of Mediated Effects in Latent Variable Models. J.F. Finch, S.G. West, D.P. MacKinnon. Structural Equation Modeling 1997: 4(2); 87-107. (Sample Size, SEM)
• Sample size determination in studies with matched pairs. J. L. Fleiss, B. Levin. J Clin Epidemiol 1988: 41(8); 727-30. (Sample Size, Matched Pairs)
• Post hoc power analysis--another view. J. Fogel. Pharmacotherapy 2001: 21(9); 1150. [Medline] [Full text] (Sample Size, Post Hoc Power)
• Current concepts review: sample size and statistical power in clinical orthopaedic research. Kevin B Freedman, Joseph Bernstein. J Bone Joint Surg Am 1999: 81(10); 1454-60. [Medline] [Full text] [PDF] (Sample Size, Overview)
• Power computations for designing comparative poisson trials. M Gail. Biometrics 1974: 30(?); 231-37. (Sample Size, Poisson Regression)
• Power and sample size calculations in case-control studies of gene-environment interactions: comments on different approaches. M Garcia-Closas, Lubin JH. AJE 1999: 149(8); 689-92. (Sample Size, General)
• Sample Size Requirements for Association Studies of Gene-Gene Interaction. James W. Gauderman. Am. J of Epidemiology 2002: 155(5); 478-484. (Sample Size, General)
• The Determination of the Number of Patients Required in a Preliminary and a Follow-Up Trial of a New Chemotherapeutic Agent. Edmund A. Gehan. Journal of Chronic Diseases 1961: 13(4); 346-353. (Sample Size, General)
• Planning the size and duration of a clinical trial studying the time to some critical event. S. L. George, M. M. Desu. J Chronic Dis 1974: 27(1); 15-24. [Medline] (Sample Size, Survival Curve)
• Handout: Sample Size and the Nuremberg Code. Lane Goldsmith, Paul Simmons, JSM. Accessed on 2001-(Sample Size, Ethics) In 1947 the Nuremberg Code was formulated during the trial of Nazi scientists accused of murder and torture in medical experiments in concentration camps during World War II (Shuster, 1998). Characterized as the most authoritative set of rules for the protection of human subjects in medical research, the Nuremberg Code has had a profound effect on the ethics of human experimentation, particularly in its requirement of informed consent of experimental subjects. The 10 principles of the Nuremberg Code deal with other ethical issues, and there are strong implications for correct sample size estimation. “Ethical Guidelines for Statistical Practice,” approved by the American Statistical Association in 1999, calls for statisticians to “avoid the use of excessive or inadequate numbers of research subjects by making informed recommendations for study size.” A recent article “Why ‘underpowered’ trials are not necessarily unethical” (S. J. L. Edwards, et al, 1997) will be analyzed with regard to subject equipoise, utility functions, meta-analysis, and the “implicit contract” with research subjects (Harrington, 2000). www.amstat.org/meetings/jsm/2001/index.cfm?fuseaction=abstract_details&abstractid=301013
• The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results. Steven Goodman. Annals of Internal Medicine 1994: 121(3); 200-206. [Medline] [Abstract] [Full text] (Sample Size, Post Hoc Power)
• Sample size estimation in occupational mortality studies with use of confidence interval theory. I. Gordon. Am J Epidemiol 1987: 125(1); 158-62. (Sample Size, General)
• Computing sample size for data to be analyzed with nonparametric tests.. GraphPad Software. Accessed on 2005-03-08. (Sample Size, Nonparametric) Nonparametric tests are used when you are not willing to assume that your data come from a Gaussian distribution. Commonly used nonparametric tests are based on ranking values from low to high, and then looking at the distribution of sum-of-ranks between groups. This is the basis of the Wilcoxon rank-sum (test one group against a hypothetical median), Mann-Whitney (compare two unpaired groups), Wilcoxon matched pairs (compare two matched groups), Kruskal-Wallis (three or more unpaired groups) and Friedman (three or more matched groups). www.graphpad.com/library/BiostatsSpecial/article_154.htm
• On sample-size and power calculations for studies using confidence intervals. S Greenland. American Journal of Epidemiology 1988: 128(1); 231-7. (Sample Size, General)
• “Underpowered” trials. M. Griffiths. Lancet 1997: 350(9088);
  1406. [Medline] (Sample Size, Ethics)
• Relation of Sample Size to the Stability of Component Patterns. E. Guadagnoli, W.F. Velicer. Psychological Bulletin 1988: 103(2); 265-275. (Sample Size, SEM)
• Sample size formulas for some binomial type problems. WC Guenther. Technometrics 1974: 16(3); 465-67. (Sample Size, Proportions)
• The Continuing Unethical Conduct of Underpowered Clinical Trials. S. D. Halpern, J. H. Karlawish, J. A. Berlin. JAMA 2002: 288(3); 358-62. [Medline] [PDF] (Sample Size, Ethics)
• If nothing goes wrong, is everything all right? Interpreting zero numerators. J. A. Hanley, A. Lippman-Hand. Jama 1983: 249(13); 1743-5. [Medline] (Sample Size, Rule of Three)
• Multivariable prognostic models: issues in developing models, evaluating assumptions and adequacy, and measuring and reducing errors. F. E. Harrell, Jr., K. L. Lee, D. B. Mark. Stat Med 1996: 15(4); 361-87. (Sample Size, Logistic)
• Regression modelling strategies for improved prognostic prediction. Jr Harrell, Frank E, Kerry L Lee, Robert M Califf, David B Pryor, Robert A Rosati. Statistics in Medicine 1984: 3; 143-152. (Sample Size, Logistic Regression Model)
• Regression models for prognostic prediction: advantages, problems, and suggested solutions. Jr Harrell, Frank E, Kerry L Lee, David B Matchar, Thomas A Reichert. Cancer Treatment Reports 1985: 69(10); 1071-77. (Sample Size, Logistic Regression reference)
• Simple sample size calculation for cluster-randomized trials. R. J. Hayes, S. Bennett. Int J Epidemiol 1999: 28(2); 319-26. [Medline] [Abstract] [PDF] (Sample Size, Cluster)
• Setting the minimal metrically detectable change on disability rating scales. R. Hebert, D. J. Spiegelhalter, C. Brayne. Arch Phys Med Rehabil 1997: 78(12); 1305-8. [Medline] (Sample Size, Clinically Relevant Difference)
• The abuse of power: the pervasive fallacy of power calculations for data analysis. John M Hoenig, Dennis M Heisey. The American Statistician 2001: 55(1); 19-24. (Sample Size, Post Hoc Power)
• Binomial Program to Calculate Power or Sample Size. Brent Hostetler, Southwest Oncology Group Statistical Center. Accessed on 2003-05-08. (Sample Size, Proportion) Two Arm Binomial is a program to calculate either estimates of sample size or power for differences in proportions. The program allows for unequal sample size allocation between the two groups. www.swogstat.org/Stat/Public/binomial/binomial.htm
• Statistical Strategies for Small Sample Research. RH Hoyle (1999) Thousand Oaks: Sage Publications. (Sample Size, General)
• A simple method of sample size calculation for unequal-sample-size designs that use the logrank or t-test. F. Y. Hsieh. Stat Med 1987: 6(5); 577-81. [Medline] (Sample Size, Logrank Test)
• Sample size formulae for intervention studies with the cluster as unit of randomization. F. Y. Hsieh. Stat Med 1988: 7(11); 1195-201. [Medline] (Sample Size, Cluster)
• Sample size tables for logistic regression. F. Y. Hsieh. Stat Med 1989: 8(7); 795-802. [Medline] (Sample Size, Logistic)
• A simple method of sample size calculation for linear and logistic regression. F. Y. Hsieh, D. A. Bloch, M. D. Larsen. Stat Med 1998: 17(14); 1623-34. [Medline] (Sample Size, Logistic)
• Sample-size calculations for the Cox proportional hazards regression model with nonbinary covariates. F. Y. Hsieh, P. W. Lavori. Control Clin Trials 2000: 21(6); 552-60. [Medline] (Sample Size, Cox)
• The ethics of underpowered clinical trials. J. R. Hughes. Jama 2002: 288(17); 2118; author reply 2119. [Medline] (Sample Size, Ethics)
• The ethics of underpowered clinical trials. J. E. Janosky. Jama 2002: 288(17); 2118; author reply 2119. [Medline] (Sample Size, Ethics)
• The Overemphasis On Power Analysis. Thomas Knapp. Nursing Research 1996: 45(6); 379. [Medline] (Sample Size, Post Hoc Power)
• How Many Subjects? Statistical Power Analysis in Research. Helena Chmura Kraemer, Sue Thiemann (1987) Newbury Park, CA: Sage Publications. (Sample Size, General)
• A more powerful test for comparing two Poisson means. K. Krishnamoorthy, Jessica Thomson, University of Louisiana at Lafayette. Accessed on 2003-02-10. (Sample Size, Poisson Regression) The problems of hypothesis testing about two Poisson means is addressed. The usual conditional test (C-test) and a test based on estimated p-values (E-test) are considered. The exact properties of the tests are evaluated numerically. Numerical studies indicate is more powerful than the c-test. Power calculations for both tests are outlined. The test procedures are illustrated using two examples. www.mathpreprints.com/math/Preprint/krishna/20021020/1/?=&coll=Selection
• Introduction to Sample Size Determination and Power Analysis for Clinical Trials. John M. Lachin. Controlled Clinical Trials 1981: 2(2); 93-113. (Sample Size, General)
• Power and Sample Size Evaluation for the McNemar Test With Application to Matched Case-Control Studies. John M. Lachin. Statistics in Medicine 1992: 11(9); 1239-1251. (Sample Size, McNemar)
• Sample Sizes Based on the Log-Rank Statistic in Complex Clinical Trials. Edward Lakatos. Biometrics 1988: 44(1); 229-241. (Sample Size, Logrank Test)
• Sample size calculations for within-patient comparisons with a binary or survival endpoint. M. G. Law. Control Clin Trials 1996: 17(3); 221-5. (Sample Size, Survival)
• A Monte Carlo study of the power of some two-sample tests. ET Lee. Biometrika 1975: 62(2); 425-32. (Sample Size, General)
• Java applets for power and sample size. Russ Lenth, University of Iowa. Accessed on 2003-06-13. (Statistics, Software, Free) Each selection provides a graphical interface for studying the power of one or more tests. They include sliders (convertible to number-entry fields) for varying parameters, and a simple provision for graphing one variable against another. www.stat.uiowa.edu/~rlenth/Power/
• Some Practical Guidelines for Effective Sample Size Determination. R.V. Lenth. The American Statistician 2001: 55(3); 187-193. [PDF] (Sample Size, General Sample Size, Post Hoc Power)
• Post hoc power analysis: an idea whose time has passed? M. Levine, M. H. Ensom. Pharmacotherapy 2001: 21(4); 405-9. [Medline] [Abstract] (Sample Size, Post Hoc Power)
• The ethics of underpowered clinical trials. R. J. Lilford. Jama 2002: 288(17); 2118-9; author reply 2119. [Medline] (Sample Size, Ethics)
• Design and Analysis of Multiarm Clincial Trials with Survival Endpoints. Ping-Yu Lin, Steve Dahlberg. Controlled Clinical Trials 1995: 16(2); 119-130. (Sample Size, Logrank Test)
• Necessary Sample Size for Method Comparison Studies Based on Regression Analysis. Kristian Linnet. Clinical Chemistry 1999: 45(6); 882-894. (Yet To Be Coded)
• Design Sensitivity. Statistical Power for Experimental Research. Mark W. Lipsey (1990) Newbury Park, California: SAGE Publications. (Sample Size, General)
• Sample size determination for studies of gene-environment interaction. J. A. Luan, M. Y. Wong, N. E. Day, N. J. Wareham. Int J Epidemiol 2001: 30(5); 1035-40. (Sample Size, General)
• Sample size determination under an exponential model in the presence of a confounder and type I censoring. K. J. Lui. Control Clin Trials 1992: 13(6); 446-58. (Sample Size, Survival)
• The Research Sample, Part II: Sample Size. Thomas R. Lunsford, Brenda Rae Lunsford. Journal of Prosthetics & Orthotics 1995: 7(4); 137-141. [Full text] (Sample Size, T)
• Why Have Recent Trials of Neuroprotective Agents in Head Injury Failed to Show Convincing Efficacy? A Pragmatic Analysis and Theoretical Considerations. Andrew I.R. Maas, Ewout W. Steyerberg, Gordon D. Murray, Ross Bullock, Alexander Baethmann, Lawrence F. Marshall, Graham M. Teasdale. Neurosurgery 1999: 44(6); 1286-1298. [Medline] (Sample Size, Design Considerations)
• Power analysis and determination of sample size for covariance structure modeling. R MacCallum, M Browne, H Sugawara. Psychological Methods 1996: 1; 130-131. (Sample Size, SEM)
• Sample Size Tables for Clinical Studies. David Machin, Michael Campbell, Peters Fayers, Alain Pinol (1997) Osney Mead, Oxford: Blackwell Science, Ltd. (Sample Size, General)
• The Value of a Post Hoc Power Analysis. Richard Madsen, Heather V. Lochner, Mohit Bhandari, Paul Tornetta. J Bone Joint Surg Am 2002: 84(7); -b1272-. [Full text] (Sample Size, Post Hoc Power)
• Sample size requirements for comparing time-to-failure among k treatment groups. R. W. Makuch, R. M. Simon. J Chronic Dis 1982: 35(11); 861-7. (Sample Size, Logrank Test)
• A framework for power analysis using a structural equation modelling procedure. J. N. Miles. BMC Med Res Methodol 2003: 3(1);
  27. [Medline] [Abstract] [PDF] (Sample Size, SEM)
• Interpreting the results of small trials. F. Molnar, M. Man-Son-Hing, A. Byszewski, N. Azid. Cmaj 2000: 162(10); 1401. [Medline] [Full text] [PDF] (Sample Size, Small Trials)
• Power calculations for general linear multivariate models including repeated measures applications. K. E. Muller, L. M. Lavange. Journal of the American Statistical Association 1992: 87; 1209-16. (Sample Size, Regression)
• Power in comparing Poisson means: I. One-sample test. LS Nelson. Journal of Quality Technology 1991: 23(1); 68-70. (Sample Size, Poisson Regression)
• Power in comparing Poisson means: II. Two-sample test. LS Nelson. Journal of Quality Technology 1991: 23(2); 163-66. (Sample Size, Poisson Regression)
• Within-subject variability and per cent change for significance of spirometry in normal subjects and in patients with cystic fibrosis. B. G. Nickerson, R. J. Lemen, C. B. Gerdes, M. J. Wegmann, G. Robertson. Am Rev Respir Dis 1980: 122(6); 859-66. [Medline] (Sample Size, General)
• Sample size calculations in studies of test accuracy. Nancy Obuchowksi. Statistical Methods in Medical Research 1998: 7; 371-92. (Sample Size, Diagnostic)
• Sample Size Choice: Charts for Experiments with Linear Models. Robert E. Odeh, Martin Fox (1991) New York: Marcel Dekker, Inc. (Statistics, Sample Size)
• Approaches to sample size calculation in comparative studies. RM Pandey. Indian J Pediatr 1999: 66; 533-38. [Medline] (Sample Size, Guidelines)
• Further statistics in dentistry. Part 4: Clinical trials 2. A. Petrie, J. S. Bulman, J. F. Osborn. Br Dent J 2002: 193(10); 557-61. [Medline] [Abstract] (Sample Size, Resources)
• Sample size calculations for population- and family-based case-control association studies on marker genotypes. R. M. Pfeiffer, M. H. Gail. Genet Epidemiol 2003: 25(2); 136-48. [Medline] (Sample Size, Genetics)
• A comparison of the power of two tests for qualitative interactions. S. Piantadosi, M. H. Gail. Stat Med 1993: 12(13); 1239-48. [Medline] (Sample Size, Regression)
• Invited Commentary: Ethics and Sample Size - Another View. Ross L. Prentice. American Journal Epidemiology 2005; (Sample Size, Ethics)
• Cluster randomised trials in maternal and child health: implications for power and sample size. Richard Reading, I Harvey, M Mclean. Arch Dis Child 2000: 82(1); 79-83. [Medline] [Abstract] [Full text] [PDF] (Sample Size, Cluster)
• Statistical methods in epidemioogy. II: a commonsense approach to sample size estimation. Alan Rigby. Disability and Rehabilitation 1998: 20(11); 405-10. (Sample Size, General)
• Sample size calculations for two-group repeated-measures experiments. J Rochon. Biometrics 1991: 47(?); 1383-1398. (Sample Size, Longitudinal)
• Planning group sizes in clinical trials with a continuous outcome and repeated measures. H Schouten. Stats in Medicine 1999: 18(3); 255-64. (Sample Size, Repeated measures)
• Sample size formula with a continuous outcome for unequal group sizes and unequal variances. H Schouten. Statistics in Medicine 1999: 18(1); 87-91. (Sample Size, T)
• Sample Size and Design Effect: Introduction and Review [pdf]. Gene Shackman, Newsletter of the Survey Research Methods Section, January 2003, page 8. Accessed on 2003-05-08. (Sample Size, Cluster) Determining sample size is an important step in administering surveys. For designs other than simple random samples, one crucial part in determining size is the design effect. This is an adjustment for any effects that the sampling design may have on efficiency of the sample. In this article I describe the design effect, and briefly review some typical design effect values. www.amstat.org/sections/srms/January2003Newsletter.pdf
• Sample size and design effect [pdf]. Gene Shackman, Presented at the 2001 conference of the Albany Chapter of the American Statistical Association. Accessed on 2003-05-08. (Sample Size, Cluster) This presentation is a brief introduction to the design effect, which is an adjustment that should be used to determine survey sample size. www.albany.edu/~areilly/albany_asa/confweb01/abstract/Download/shackman.pdf
• Sample size calculation for complex clinical trials with survival endpoints. JH Shih. Control Clin Trials 1995: 16(6); 395-407. (Sample Size, Logrank Test)
• CRC Handbook of Sample Size Guidelines for Clinical Trials. Jonathan J. Shuster (1990) Boca Raton, FL: CRC Press. (Statistics, Sample Size)
• Sample size for Poisson regression. DF Signorini. Biometrika 1991: 78(2); 446-50. (Sample Size, Poisson Regression)
• Likelihood ratios with confidence: sample size estimation for diagnostic test studies. DL Simel, GP Samsa, DB Matchar. J Clin Epidemiol 1991: 44(8); 763-70. [Medline] (Sample Size, Diagnostic)
• Confidence limit analyses should replace power calculations in the interpretation of epidemiologic studies. AH Smith, MN Bates. Epidemiology 1992: 3(5); 449-52. [Medline] (Sample Size, Post Hoc Power)
• One sample binomial. Southwest Oncology Group Statistical Center. Accessed on 2003-08-11. (Sample Size, Proportions) One Arm Binomial program calculates either estimates of sample size or power for one sample binomial problem. The first button calculates approximate power or sample size and critical values (reject if >= critical value). The second button calculates “exact” power and alpha for the given null and alternative proportions and sample size. Note, sample size and null and alternative proportions can be changed before using the second button. www.swogstat.org/Stat/Public/one_binomial.htm
• One Sample Normal. Southwest Oncology Group Statistical Center. Accessed on 2003-08-11. (Sample Size, Normal) One Arm Normal is a program to calculate either estimates of sample size or power for one sample normal problem. www.swogstat.org/Stat/Public/one_normal.htm
• Two Arm Normal Sample Size and Power. Southwest Oncology Group Statistical Center. Accessed on 2003-08-11. (Sample Size, T) Two Arm Normal is a program to calculate either estimates of sample size or power for differences in means. The program allows for unequal sample size allocation between the two groups. www.swogstat.org/Stat/Public/two_normal.htm
• Persistent erroneous interpretation of negative data and assessment of statistical power. Toshiaki Tachibana. Perceptual and Motor Skills 1980: 51; 37-38. (Sample Size, General)
• Statistical design and monitoring of the Carotene and Retinol Efficacy Trial (CARET). Mark D Thornquist, Gilbert S Omenn, Gary E Goodman, James E Grizzle, Linda Rosenstock, Scott Barnhart, Garnet L Anderson, Samuel Hammar, John Balmes, Martin Cherniack, James Cone, Mark R Cullen, Andrew Glass, James P Keogh, Jr Meyskens, Frank, Barbara Valanis, Jr Williams, James H. Controlled Clinical Trials 1993: 14(4); 308-24. [Medline] (Sample Size, Example)
• Economics in sample size determination for clinical trials. David J Torgerson. Q J Med 1995: 88; 517-21. (Sample Size, General)
• Power and sample size calculations for generalized regression models with covariate measurement error. TD Tosteson, JS Buzas, E Demidenko, M Karagas. Stat Med 2003: 22(7); 1069-82. [Medline] [Abstract] (Sample Size, Logistic)
• Power Calculator. UCLA Department of Statistics. Accessed on 2004-01-19. (Sample Size, Calculators) Sorry, the power calculator is provided without support. It is based upon the more extensive program STPLAN by Barry Brown et al. which is available in the file: ftp://odin.mdacc.tmc.edu/pub/source/dstplan-4.2.tar.gz. STPLAN contains documentation for the power calculations and the fortran program allows power calculations for several other distributions in addition to those on our power calculator page. If you encounter any errors (the program crashing, the server not responding, files not found, etc.) then please let me know through the email link below. I hope you find the calculator useful. calculators.stat.ucla.edu/powercalc/
• STRUTS: Statistical Rules of Thumb. Chapter 2. Sample Size. Gerald van Belle, Steve Millard, University of Washington: Departments of Environmental Health and Biostatistics. Accessed on 2003-07-10. (Sample Size, Quick) Welcome to the Statistical Rules of Thumb webpage! Chapter 2 can be downloaded by clicking on Book Contents on the left and then selecting Chapter 2. The Monthly Rule section discusses additional aspects not found in the book, contains comments by readers, or develops a new rule. Check it out; the topic is indicated in the month heading. Send me any rules you may have, or use, in your work. I will consider listing and will always acknowledge. Comments on the webpage are always appreciated. Linked you will find an Adobe PDF file: Chapter 2 of STRUTS: Statistical Rules of Thumb, by Gerald van Belle and Steve Millard. Our intent is to give some simple rules of thumb that are widely applicable, robust, elegant and capture key statistical concepts. A statistical rule of thumb provides a framework for considering statistical questions such as sample size, association design of experiments (topics that are usually interrelated). www.nrcse.washington.edu/research/eo-1.html
• Sample size and power estimation for studies with health related quality of life outcomes: a comparison of four methods using the SF-36. SJ Walters. Health Qual Life Outcomes 2004: 2(1); 26. [Medline] [Abstract] [Full text] [PDF] (Sample Size, Ordinal)
• Power analysis examples. Bruce Weaver. Accessed on 2003-01-20. (Sample Size, General) “The following examples are from a paper by D’Amico, Neilands, and Zambarano in Behavior Research Methods, Instruments, & Computers, 2001, 33(4), 479-484. These examples use the MATRIX DATA command to input the data. For a brief explanation of how this works, go to www.utexas.edu/cc/faqs/stat/spss/spss33.html. Example 1: ANCOVA with 3 groups and 2 covariates. Example 2: MANOVA with 3 groups and 2 dependent variables. Example 3: Mixed design (between-within) ANOVA.” www.angelfire.com/wv/bwhomedir/spss/power_analysis.txt
• Sample size for logistic repression with small response probability. Alice Whittemore. Journal of the American Statistical Association 1981: 76(373); 27-32. (Sample Size, Logistic)
• Sample-size calculation for a log-transformed outcome measure. Rory Wolfe, John B Carlin. Controlled Clinical Trials 1999: 20; 547-554. (Sample Size, Lognormal)
• Sample size nomograms for interpreting negative clinical studies. MJ Young, EA Bresnitz, BL Strom. Annals of Internal Medicine 1983: 99(2); 248-251. [Medline] (Sample Size, General)
• Power analysis. Chong-ho Yu. Accessed on 2003-02-10. (Sample Size, General) Power is determined by the following: Alpha level, Effect size, Sample size. Generally speaking, when the alpha level, the effect size, or the sample size increases, the power level increases. Please view this QuickTime animated demo to learn the above relationships If you want to examine the relationships frame by frame, please look at this Shockwave slide show (Caution: Both modules are large in file size, please view them through a T1 network rather than a modem connection). seamonkey.ed.asu.edu/~alex/teaching/WBI/power_es.html

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