### Some clarifications regarding power and Type I error control for pairwise comparisons of three groups

#### Abstract

#### References

Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B, 57(1):289–300.

Dunnett, C. W. (1955). A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50(272):1096–1121.

Félix, V. B. and Menezes, A. F. B. (2018). Comparisons of ten corrections methods for t-test in multiple comparisons via Monte Carlo study. Electronic Journal of Applied Statistical Analysis, 11(1):74–91.

Finner, H. and Roters, M. (2001). On the false discovery rate and expected Type I errors. Biometrical Journal, 43(8):985–1005.

Fisher, R. A. (1935). The design of experiments. Oliver and Boyd.

Frane, A. V. (2015a). Are per-family Type I error rates relevant in social and behavioral science?. Journal of Modern Applied Statistical Methods, 14(1):12–23.

Frane, A. V. (2015b). Power and type I error control for univariate comparisons in multivariate two-group designs. Multivariate Behavioral Research, 50(2):233–247.

Hancock, G. R., and Klockars, A. J. (1996). The quest for α: Developments in multiple comparison procedures in the quarter century since Games (1971). Review of Educational Research, 66(3):269–306.

Hayter, A. J. (1986). The maximum familywise error rate of Fisher's least significant difference test. Journal of the American Statistical Association, 81(396):1000–1004.

Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika, 75(4):800–802.

Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2):65–70.

Hommel, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika, 75(2):383–386.

Keselman, H. J., Cribbie, R., and Holland, B. (1999). The pairwise multiple comparison multiplicity problem: An alternative approach to familywise/comparisonwise Type I error control. Psychological Methods, 4(1):58–69.

Keuls, M. (1952). The use of Studentized range in connection with an analysis of variance. Euphytica, 1(2):112–122.

Kramer, C. Y. (1956). Extensions of multiple range tests to group means with unequal number of replications. Biometrics, 12(3):307–310.

Li, D. (2008). A two-step rejection procedure for testing multiple hypotheses. Journal of Statistical Planning and Inference, 138(6):1521–1527.

Newman, D. (1939). The distribution of the range in samples from a normal population, expressed in terms of an independent estimate of standard deviation. Biometrika, 31(1/2):20–30.

Phillips, A., Fletcher, C., Atkinson, G., Channon, E., Douiri, A., Jaki, T., Maca, J., Morgan, D., Roger, J. H., and Terrill, P. (2013). Multiplicity: Discussion points from the statisticians in the Pharmaceutical Industry Multiplicity Expert Group. Pharmaceutical Statistics, 12(5):255–259.

Ramsey, P. H. (1978). Power differences between pairwise multiple comparisons. Journal of the American Statistical Association, 73(363):479–485.

Ramsey, P. H., Barrera, K., Hachimine–Semprebom, P., and Li, C.-C. (2011). Pairwise comparisons of means under realistic nonnormality, unequal variances, outliers and equal sample sizes. Journal of Statistical Computation and Simulation, 81(2):125–135.

Ramsey, P. H. and Ramsey, P. P. (2008). Power of pairwise comparisons in the equal variance and unequal sample size case. British Journal of Mathematical and Statistical Psychology, 61(1):115–131.

Ramsey, P. H. and Ramsey, P. P. (2009). Power and Type I errors for pairwise comparisons of means in the unequal variances case. British Journal of Mathematical and Statistical Psychology, 62(2):263–281.

R Core Team. (2017). R: A language and environment for statistical computing. https://www.R-project.org/

Richter, S. J. and McCann, M. H. (2012). Using the Tukey–Kramer omnibus test in the Hayter–Fisher procedure. British Journal of Mathematical and Statistical Psychology, 65(3):499–510.

Seaman, M. A., Levin, J. R., and Serlin, R. C. (1991). New developments in pairwise multiple comparisons: Some powerful and practicable procedures. Psychological Bulletin, 110(3):577–586.

Shaffer, J. P. (1986). Modified sequentially rejective multiple test procedures. Journal of the American Statistical Association, 81(395):826–831.

Tamhane, A. C. (2009). Statistical analysis of designed experiments: Theory and applications. Wiley.

Tukey, J. W. (1953). The problem of multiple comparisons. In H. I. Braun (Ed.), The collected works of John W. Tukey, volume VIII multiple comparisons: 1948–1983. Wiley.

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