Some New Construcations of Non-Circular Balanced and Strongly Balanced Repeated Measurements Designs

Abstract

Experiments involving humans or animals as experimental units and each experimental unit participates under all conditions in a research study, are known as repeated measurements designs abbreviated as RMDs. It is not necessary for experimental units to be humans or animals, but mostly. In these designs p treatments are applied on each subject and each treatment is applied for same length of time. RMDs have applications mostly in animal sciences, pharmacology, psychology and medicine where residual/ carry over effects may arise. Effect of a treatment that may persist into the next period of application may persist into the next period of application is called residual effect or carry over effect. As RMDs have application in many branches of scientific inquiry, therefore, choice of RMDs should be such that the treatments can be compared efficiently in the presence of residual effects. Minimal balanced RMDs are designs that balance out these residual effects at low cost. Minimal BRMD is a design in which each treatment is preceded exactly once by every other treatment (excluding itself). Strongly balanced RMD (SBRMD) is a design in which each treatment is preceded by every other treatment including itself. In this study: Some generators are formulated to obtain minimal non-circular BRMDs, SBRMDs and WBRMDs in periods of (i) equal sizes, (ii) two different sizes, (iii) three different sizes, and (iv) generally k different sizes through the method of cyclic shifts using Rule I and Rule III. Some generators are formulated to obtain minimal non-circular WBRMDs in periods of (i) equal sizes, (ii) two different sizes, (iii) three different sizes, and (iv) generally k different sizes in which λ1 = 0, λ2 = 1 and λ1 = 1, λ2 = 2. Minimal non-circular BRMDs, SBRMDs and WBRMDs are also constructed in periods of (i) equal sizes, (ii) two different sizes, (iii) three different sizes and (iv) four different sizes through the method of cyclic shifts Rule I and Rule III. Catalogues are also presented for these designs along with their efficiency of direct, residual effects and separability for v ≤ 70. Minimal non-circular WBRMDs are also constructed in periods of (i) equal sizes, (ii) two different sizes, (iii) three different sizes and four different sizes with λ1 = 0, λ2 = 1 and λ1 = 1, λ2 = 2, through the method of cyclic shifts using Rule I and Rule III. Catalogues are also presented for these designs along with their efficiency of direct, residual effects and separability for v ≤ 70.