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A Note on Orthogonal Polynomials Applied to Treatment Levels with Unequal Replications a
Author(s) -
EISEN JACOB N.
Publication year - 1964
Publication title -
journal of food science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.772
H-Index - 150
eISSN - 1750-3841
pISSN - 0022-1147
DOI - 10.1111/j.1365-2621.1964.tb01702.x
Subject(s) - mathematics , orthogonal polynomials , regression , regression analysis , statistics , combinatorics , pure mathematics
SUMMARY This paper demonstrates how orthogonal polynomials are constructed and used when the treatment levels have unequal, rather than equal, replications. These polynomials are applied to hypothetical data on shear force of broccoli stems cooked for four cooking times with unequal replications. The variation for between cooking times (treatment levels) is broken down into independent regression components to determine the simplest regression curve appropriately representing the data. Also illustrated is how to calculate a regression equation in terms of orthogonal polynomials for treatment levels with unequal replications.