This paper is concerned with the application of the Properties A and B associated with the incidence matrix to the analysis of Partially Balanced Designs having Binary Number Association Scheme (BNAS) or Balanced Factorial Experiments (BFE). We present a practical method of intra-and inter-block analysis of Partially Balanced Block Designs (PBBD) having BNAS. All group divisible association scheme designs, rectangular association scheme designs, hierarchical group divisible block designs, and direct product designs are BNAS PBB designs. The method presented in this paper will unify and simplify the calculations for the above various designs when compared with presently available procedures. Also, we extend the method to the PAB type rectangular designs. The various computational steps in the statistical analysis are presented with numerical examples.