A Simple Method for Constructing Orthogonal Polynomials When the Independent Variable is Unequally Spaced

Orthogonal polynomials are commonly used in the analysis of variance for the construction of orthogonal contrasts among equally spaced levels of a treatment factor. The existence of tables [1; 2] giving the compounding coefficients for these particular contrasts often influences the experimenter to choose an equal spacing. A simple procedure for constructing orthogonal polynomials when the levels are unequally spaced frees the experimenter from this sometimes undesirable restriction.