Page's statistic in balanced incomplete block designs

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Title: Page's statistic in balanced incomplete block designs
Author: Duran, Benjamin S.
Abstract: A block is a collection of experimental units that are as nearly alike as possible relative to the extraneous variable . Each treatment is then randomly assigned to one experimental unit within each block . If the experimental units within blocks are relatively alike and units in different blocks are relatively different , then the randomized complete block design is usually more sensitive to differences in treatment means than the one -way classification design , a design which assumes all experimental units are relatively homogeneous . Often , one may not be able to run all of the treatments in each block . Possible reasons may be due to shortages of experimental units , the physical size of the blocks , or that the cost is too great to use a complete block design . Assuming a complete block design cannot be used , the designer must turn to alternative methods . One popular choice is the randomized incomplete block design , a design which allows for analyzing treatment effects without running every treatment within each block . By assigning treatments in a balanced manner among the experimental units in a block , accurate analysis of treatment effects can be accomplished while reducing the number of treatment runs needed in each block . When performing a normal -theory F test to analyze the treatment effects , the experimenter must assume that the error variables are normally distributed . However , a design could occur in which the normality assumption is invalid , and the designer may wish to use a distribution -free procedure . Nonparametric methods for determinig differences in treatment effects have been proposed for complete randomized block designs by Friedman [3] and for balanced incomplete block designs by Durbin [2] . An analyst may be interested in detecting some specific relationship among the treatment effects . In particular , one may be interested in the simple order alternative , which is useful for testing treatment effects versus a control . For the complete block design , a statistic for the simple order alternative was proposed by Page [5] . We intend to use Page's statistic with incomplete block designs while creating exact distributions for small designs and simulated distributions for larger designs . In the absence of exact or simulated tables , the normal approximation can be used to make a decision with respect to the rejection of the null hypothesis .
URI: http : / /hdl .handle .net /2346 /22456
Date: 1995-08

Citation

Page's statistic in balanced incomplete block designs. Master's thesis, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /22456 .

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