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A General Least Squares Solution for Successive Intervals

Diederich, Gertrude W.; Messick, Samuel J.; Tucker, Ledyard R
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Least Squares Statistics, Scaling, Weighted Scores


A general least squares solution for successive intervals is presented, along with iterative procedures for obtaining stimulus scale values, discriminal dispersions, and category boundaries. Because provisions for weighting were incorporated into the derivation, the solution may be applied without loss of rigor to the typical experimental matrix of incomplete data, i.e., to a data matrix with missing entries, as well as to the rarely occurring matrix of complete data. The use of weights also permits adjustments for variations in the reliability of estimates obtained from the data. The computational steps involved in the solution are enumerated, the amount of labor required comparing favorably with other procedures. A quick, yet accurate, graphical approximation suggested by the least squares derivation is also described.

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