On balanced minimal repeated measurements designs

Shakeel Ahmad Mir

Abstract


Repeated Measurements designs are concerned with scientific experiments in which each experimental unit is assigned more than once to a treatment either different or identical. This class of designs has the property that the unbiased estimators for elementary contrasts among direct and residual effects are obtainable. Afsarinejad (1983) provided a method of constructing balanced Minimal Repeated Measurements designs p < t , when t is an odd or prime power, one or more than one treatment may occur more than once in some sequences and  designs so constructed no longer remain uniform in periods. In this paper an attempt has been made to provide a new method to overcome this drawback. Specifically, two cases have been considered                RM[t,n=t(t-t)/(p-1),p], λ2=1 for balanced minimal repeated measurements designs and  RM[t,n=2t(t-t)/(p-1),p], λ2=2 for balanced  repeated measurements designs. In addition , a method has been provided for constructing              extra-balanced minimal designs for special case RM[t,n=t2/(p-1),p], λ2=1.

Keywords


Balanced Minimal Repeated Measurements design; Extra-balanced Repeated Measurements design;Uniform Repeated Measurements design; Cross-over designs ; direct effects; residual effects.

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DOI: http://dx.doi.org/10.18187/pjsor.v10i3.668

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Title

On balanced minimal repeated measurements designs

Keywords

Balanced Minimal Repeated Measurements design; Extra-balanced Repeated Measurements design;Uniform Repeated Measurements design; Cross-over designs ; direct effects; residual effects.

Description

Repeated Measurements designs are concerned with scientific experiments in which each experimental unit is assigned more than once to a treatment either different or identical. This class of designs has the property that the unbiased estimators for elementary contrasts among direct and residual effects are obtainable. Afsarinejad (1983) provided a method of constructing balanced Minimal Repeated Measurements designs p < t , when t is an odd or prime power, one or more than one treatment may occur more than once in some sequences and  designs so constructed no longer remain uniform in periods. In this paper an attempt has been made to provide a new method to overcome this drawback. Specifically, two cases have been considered                RM[t,n=t(t-t)/(p-1),p], λ2=1 for balanced minimal repeated measurements designs and  RM[t,n=2t(t-t)/(p-1),p], λ2=2 for balanced  repeated measurements designs. In addition , a method has been provided for constructing              extra-balanced minimal designs for special case RM[t,n=t2/(p-1),p], λ2=1.

Date

2014-10-13

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 10 No. 3, 2014



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810