Punched card and calculating machine methods for analyzing lattice experiments including lattice squares and the cubic lattice

Abstract

<p>Punched card and calculating machine methods are given for analyzing data from lattice experiments. Numerical examples are worked out for the triple lattice, simple lattice, balanced lattice, lattice square with (k+1) / 2 replicates, lattice square with (k+1 ) replicates and cubic lattice designs. In addition, brief computational directions are given for the quadruple lattice, quintuple lattice and higher order lattices and for duplications of these designs.</p> <p>The use of the punched card machine method materially decreases the time and the chance for errors in making the computations, particularly when the total number of plots is more than about 150 or when more than one character is to be analyzed.</p> <p>The formulas given are appropriate for any k and for any number of repetitions of the basic plan for the simple lattice, triple lattice, quadruple lattice and higher order lattice designs and for the cubic lattice design and for any k for the lattice square with (k + 1)/2 replicates, lattice square with (k + 1) replicates and the balanced lattice designs.</p>