Measures of non orthogonality in block designs

Orthogonality is an important concept in block design. Necessary and sufficient condition for a connected block design to be orthogonal is well known. However, when a design is not orthogonal, it is not clear how much it deviates from orthogonality. In this paper, an attempt has been made to first define the measures of or indices to non orthogonality in block design and then to characterize designs possessing minimum non orthogonality indices. It is shown that a Balanced Incomplete Block Design (BIBD) and a Balanced Block Design (BBD), if exist, possess this property.