The problem discussed in this paper is the estimation of a single missing observation, two missing observations and several missing observations in a Group Visible (Singular) for Shirley balanced incomplete blocks design with two associate classes. Subsequently the analysis of variance, of the data augmented by the estimates of the missing observations, is derived. The method, first employed by Yates (1933), was followed to minimize the error sum of squares. Explicit formulae were developed, for the estimates of one missing observation, two missing observations occurring in various configurations and general formulae for z (= n) missing observations for certain particular configurations. Analysis of the data augmented by the estimates of the missing observations lead to positive bias in the case of treatment sum of squares, a method of analysis was discussed to eliminate this bias. A numerical example of illustrating the technique of estimating missing observations in a GDS P.B.I.B. design was given. The approximate and exact tests were performed, for the null hypothesis of no treatment differences, using the intra-block error mean square. / Master of Science