Nashimoto, Kane; Wright, F. T. A note on multiple comparison procedures for detecting differences in simply ordered means. (English) Zbl 1071.62062 Stat. Probab. Lett. 73, No. 4, 393-401 (2005). Summary: In one-way ANOVA we consider procedures that determine whether \(\mu_{i}=\mu_{j}\) or \(\mu_{i}<\mu_{j}\) when the means are known a priori to be nondecreasing. It is known that the one-sided Studentized range test (OSRT) controls the familywise error rate, but the one-sided least significant difference test has larger powers. We show that for balanced designs, the familywise error rate of the latter is largest when all of the means are equal but one. This leads to a modification of the one-sided least significant difference procedure that controls familywise error rate and has larger powers than the OSRT. Some recommendations for unbalanced designs are also given. Cited in 5 Documents MSC: 62J15 Paired and multiple comparisons; multiple testing 62J10 Analysis of variance and covariance (ANOVA) 65C05 Monte Carlo methods 62F30 Parametric inference under constraints Keywords:Analysis of variance; Isotonic inferences; Order-restricted inferences; Simultaneous inferences; Familywise error rate; Total order Software:AS 122 PDFBibTeX XMLCite \textit{K. Nashimoto} and \textit{F. T. Wright}, Stat. Probab. Lett. 73, No. 4, 393--401 (2005; Zbl 1071.62062) Full Text: DOI References: [1] Bohrer, R.; Chow, W., Weights for one-sided multivariate inference, Appl. Statist., 27, 100-104 (1978) · Zbl 0436.62004 [2] Fisher, R. A., The Design of Experiments (1935), Oliver & Boyd: Oliver & Boyd Edinburgh · Zbl 0011.03205 [3] Hayter, A. J., A proof of the conjecture that the Tukey-Kramer multiple comparisons procedure is conservative, Ann. Statist., 12, 61-75 (1984) · Zbl 0545.62047 [4] Hayter, A. J., The maximum familywise error rate of Fisher’s least significant difference test, J. Amer. Statist. Assoc., 81, 1000-1004 (1986) · Zbl 0638.62068 [5] Hayter, A. J., A one-sided Studentized range test for testing against a simple ordered alternative, J. Amer. Statist. Assoc., 85, 778-785 (1990) · Zbl 0706.62069 [6] Hayter, A. J.; Liu, W., Exact calculations for the one-sided Studentized range test for testing against a simple ordered alternative, Comput. Statist. Data Anal., 22, 17-25 (1996) [7] Liu, L.; Lee, C. C.; Peng, J., Max-min multiple comparison procedure for isotonic dose-response curves, J. Statist. Plann. Inference, 107, 133-141 (2002) · Zbl 1017.62028 [8] Nashimoto, K., Wright, F.T., 2005. Multiple comparison procedures for detecting differences in simply ordered means. Comput. Statist. Data Anal. 291-306.; Nashimoto, K., Wright, F.T., 2005. Multiple comparison procedures for detecting differences in simply ordered means. Comput. Statist. Data Anal. 291-306. · Zbl 1429.62315 [9] Robertson, T.; Wright, F. T.; Dykstra, R. L., Order Restricted Statistical Inference (1988), Wiley: Wiley Chichester, UK · Zbl 0645.62028 [10] Singh, B.; Wright, F. T., The power functions of the likelihood ratio tests for a simply ordered trend in normal means, Comm. Statist., A18, 2351-2392 (1989) · Zbl 0696.62065 [11] Slepian, D., The one-sided barrier problem for Gaussian noise, Bell System Tech. J., 41, 463-501 (1962) [12] Sun, H. J., A Fortran subroutine for computing normal orthant probability, Comm. Statist., B17, 1097-1111 (1988) · Zbl 0695.62001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.