On Variance Balanced Designs

Abstract

Balanced incomplete block designs are not always possible to construct because of their parametric relations. In such a situation another balanced design, the variance balanced design, is required. This construction of binary, equal replicated variance balanced designs are discussed using the half fraction of the 2n factorial designs with smaller block sizes. This method was also extended to construct another variance balanced design by deleting the last block of the resulting variance balanced designs. Its efficiency factor compared with randomized block designs was compared and found to be highly efficient. Keywords:Binary, efficiency factor, balanced incomplete block designs, information matrix and incidence matrix

Variance Balanced Design

“…Kageyama [10] recommended the use of non-binary VB design, when binary VB designs are not available for given values of parameters. Ghosh and Ahuja [34] carried out VB design using fractional factorial designs. Agarwal and Kumar [35,36] developed some methods of constructing ternary VB designs with v þ s ðÞ treatments s ≥ 1 ðÞ , having blocks of unequal sizes, through block designs with v treatment.…”