Modified systematic sampling and the PBIB designs

In this paper, we have made an attempt to show how the techniques used in experimental designs and those of sampling strategies are closely related to each other. For this we have defined an association scheme and based on this association scheme, we have proposed a new sampling strategy which we call modified systematic sampling (MSS). We have also shown how the usual systematic samples can be drawn from this association scheme. The MSS strategy also takes care of a major drawback of the systematic sampling. We have also shown how both the sampling strategies help to construct PBIB designs based on the proposed association scheme. At the end of the manuscript, we have prepared a table which enlists some of the PBIB designs constructed in this paper.