General methods of analysis for incomplete block designs

Abstract

1. The problem of combinatorial arrangements. 2. Analysis of experimental data. (A) Intrablock estimates of varietal effects and analysis of variance. (B) Adjustment for concomitant variation. (C) Adjustment for missing or mixed-up plots. (D) Recovery of interblock information. 3. Combined intra and interblock estimates. 4. Estimation of intra and interblock variances. 5. The two fundamental designs. (A) Partially balanced incomplete blocks. (B) Intra and intergroup balanced incomplete blocks. 6. An illustrative example: Intra and interblock information. Various types of experimental designs have been introduced since 1936 for testing a large number of varieties. They are designed to suit the requirements of the experimenter and with the object of achieving maximum efficiency for testing a given number of varieties with a limited amount of experimental material. The numerical methods for analysis of experimental data arising from any design fall under four categories, (i) intrablock analysis, (ii) adjustment for concomitant variation, (iii) adjustment for missing plots and (iv) recovery of interblock information. The author has attempted in this paper to present a unified method for the reduction of experimental data to suit all types of designs and methods of analysis. This is achieved in two stages. Firstly, it has been noted that there are two fundamental designs which include all the previously known designs as special cases. Secondly, the formulae relating to intrablock analysis have been designed to yield the formulae for the other types of analysis with certain changes of parameters. The problem of unification is thus reduced to the listing of a few formulae relating to intrablock analysis in the case of the two fundamental designs termed as the partially balanced and intra and intergroup balanced incomplete blocks. An example has been worked out to illustrate the practical application of these formulae.