Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Applied Statistics Unit (ASU-Kolkata)


Roy, Bimal Kumar (ASU-Kolkata; ISI)

Abstract (Summary of the Work)

Chis dissertation considers construction of two kinds of combi natorial sesigns as used by statisticians: repeated measurements designs (RMDS) and symmetric balanced squares (SBSS). 1.1. REPEATED MEASUREMENTS DESIGNS The researchers need to perform experiments where each experimental unit receives some or all of the treatments in an appropriate sequence over a number of successive periods. These designs are known by several names in the statistical 1iterature: repeated measurements designs, crossover or changeover designs, (multiple) time series designs, and before-after designs. If there are n experimental units 1,2, ... n, t treatments and p periods 0,1, .. .p-1, applied, then an RMD( t, n, p) is an nxp array, say D = over which these treatments are to b ((d,,)) element of which is one of the t treatments. The ith row of D gives the ea ir sequence of treatments applled to the ith unit over different periods. Generally in statistical 1iterature transpose of the matrix D, DT defined as RMD(t, n, p). however, we will use D and not DT in subsequent sections. The applications of these designs are not limited to any single field of study but are gaining importance over such diverse fields as agriculture, medicine, pharmacology, industry, social sciences, animal husbandry, psychology and education. The designs have proved to be attractive because of their economic use of experimental units and because of the more sensitive treatment comparisons that result from elimination of inter-unit variation. The practical necessity of the experimental setup may also force us to RMDS. These the only options to use are an experimenter in studies to evaluate the effect of different sequences of drugs or nutrients or learning experiences. For details of models, practical applicability and examples, to Hedayat one may refer Af sarine jad (1975), Hedayat (1981), Afsarine jad (1990), Patterson (19551, 52), Patterson and Lucas (1962), Davis and Hall (1969) and Atkinson (1966). The application of a sequence of treat. ments to the same unit in RMDS, however, has the potential of producing residual or carryover treatment effects in the periods following the application of the treatment. A residual effect which persists in the ith period after its application is called a residual effect of the ith order. In most of the work done, till date, it has been assumed that second- and higher-order residual effects are negligible. Consequently, most of the designs developed so far, permit only the estimation of first order residual effects along with the treat ment effects. In this discourse, we also restrict our attention mostly to the first order residual effects except in section 3.3 where have constructed designs considering second-order residual effects. Residual effects are Inherent to RMDS. some cases, effects are undestrable but cannot be avoided due to inherent nature of the experimental requirement, they act as nuisance parameters and may need to be eliminated or measured by a preper design.


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