Marcus, R., Department of Statistics and Operations Research, Agricultural Research Organization, Bet Dagan,50250, Israel

Talpaz, H., Department of Statistics and Operations Research, Agricultural Research Organization, Bet Dagan,50250, Israel

Talpaz, H., Department of Statistics and Operations Research, Agricultural Research Organization, Bet Dagan,50250, Israel

We consider an experimental setup when one is interested in comparing several treatment means pi,„.,Pk with a control mean po, with prior knowledge that the treatments are at least as effective as the control. The problem is to determine if any treatments are significantly better than the control. Several test procedures were proposed for this problem, such as Dunnett’s (1955) multiple comparisons procedure and the likelihood ratio test developed by Bartholomew (1961). Mukerjee etal (1987) developed a class of multiple contrasts tests for this problem and recommended the use of an orthogonal contrast test. XV XV In this paper a test procedure based on the statistic maxi i pi - po is proposed, where po,pi,.,Pk denote the maximum likelihood estimators of po,pi,.,Pk under the simple tree ordering po £ Pi (i = l,.,k). Its null distribution under Ho: Po = Pi =.= Pk is derived and some upper percentage points are tabulated. These percentiles can also be used in forming simultaneous confidence bounds for contrasts between normal means when the contrasts’ coefficients are restricted to simple tree ordering. Some values of power estimates of the test proposed are provided and compared with other relevant test procedures. © 1992, Taylor & Francis Group, LLC. All rights reserved.

Further results on testing homogeneity of normal means against simple tree alternatives

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Marcus, R., Department of Statistics and Operations Research, Agricultural Research Organization, Bet Dagan,50250, Israel

Talpaz, H., Department of Statistics and Operations Research, Agricultural Research Organization, Bet Dagan,50250, Israel

Talpaz, H., Department of Statistics and Operations Research, Agricultural Research Organization, Bet Dagan,50250, Israel

Further results on testing homogeneity of normal means against simple tree alternatives

We consider an experimental setup when one is interested in comparing several treatment means pi,„.,Pk with a control mean po, with prior knowledge that the treatments are at least as effective as the control. The problem is to determine if any treatments are significantly better than the control. Several test procedures were proposed for this problem, such as Dunnett’s (1955) multiple comparisons procedure and the likelihood ratio test developed by Bartholomew (1961). Mukerjee etal (1987) developed a class of multiple contrasts tests for this problem and recommended the use of an orthogonal contrast test. XV XV In this paper a test procedure based on the statistic maxi i pi - po is proposed, where po,pi,.,Pk denote the maximum likelihood estimators of po,pi,.,Pk under the simple tree ordering po £ Pi (i = l,.,k). Its null distribution under Ho: Po = Pi =.= Pk is derived and some upper percentage points are tabulated. These percentiles can also be used in forming simultaneous confidence bounds for contrasts between normal means when the contrasts’ coefficients are restricted to simple tree ordering. Some values of power estimates of the test proposed are provided and compared with other relevant test procedures. © 1992, Taylor & Francis Group, LLC. All rights reserved.

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