The estimation of a missing value in a lattice design using inter- and intra-block information

Abstract

The procedure introduced by Cornish⁴ for estimating a missing value in a lattice design, has been extended here and modified to include not only intra-block information, but also inter-block information as well. The analysis of the lattice design has been presented with some simplification applicable to this type of lattice; thus, allowing a more uniform development than has appeared before.

The implications in the limit were examined for the use of the modification of intra-block estimation formula, and it was shown that the form used was an appropriate practical tool. An actual experiment was analyzed, where certain plots were considered missing, and it was shown that the additional use of the inter-block information, as evidenced by the modified formula, would give a much better estimate of a missing value than had been possible previously in the presence of significant inter-block variation.

The lattice design has thus been made stable in the event of loss of and plot value. This design has been proven useful in industrial analysis, and its utility may now be protected by a more complete recovery of missing information.