## The Annals of Mathematical Statistics

### On Estimates for Fractions of a Complete Factorial Experiment as Orthogonal Linear Combinations of the Observations

#### Abstract

A procedure for adjusting the treatment design matrix to furnish estimates as orthogonal linear functions of stochastic variates has been given for fractional replicates of factorial experiments composed of $ks^{-m}s^n$ treatments for $m < n$, for $s$ a prime number, and $k$ not a multiple of $s$. These are irregular fractional replicates. Ordinarily irregular fractional replicates do not lead to estimates of effects which are orthogonal linear combinations of the observations. In this paper a new relationship and some generalizations on the theory of irregular fractional replicates of complete factorials have been developed. En route to these developments two theorems in matrix transformations were proved. In addition, the relationship between the method utilized here and ordinary missing plot techniques is pointed out.

#### Article information

Source
Ann. Math. Statist., Volume 34, Number 3 (1963), 1068-1078.

Dates
First available in Project Euclid: 27 April 2007

https://projecteuclid.org/euclid.aoms/1177704031

Digital Object Identifier
doi:10.1214/aoms/1177704031

Mathematical Reviews number (MathSciNet)
MR152073

Zentralblatt MATH identifier
0122.14604

JSTOR