## Theory and methods of scaling |

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The best write up on the philosophy and methods of Scaling Theory I have ever seen.

This was also the start of multidimensional scaling. This book is fundamental for understanding scaling as a scientific endeavor.

Easy reading as well for anyone with some understanding of calculus and probability theory.

Murray Turoff 1/12/2010

turoff@njit.edu

http://is.njit.edu/turoff

### Contents

The Importance of Measurement in Science | 1 |

The Nature of Measurement | 13 |

Classification of Scaling Methods 1 | 41 |

Copyright | |

15 other sections not shown

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### Common terms and phrases

abscissa absolute zero accounting equations analysis of variance analytical procedures arithmetic mean Army Service Forces Bradley-Terry model Categorical Data category boundaries centroid chi-square test comparative judgment Coombs correlation ratio cross products deterministic dichotomous discriminal dispersions equal-interval equisection errorless Euclidean space experimental control factor analysis frequency distribution geometric mean Guilford Guttman scale hyperplanes interval scale judgment methods kXii large number latent-distance law of categorical law of comparative Lazarsfeld least-squares linear model linear transformation logistic function mathematical method of paired monotone items monotonic function multicategory multidimensional scaling normal curve normal distribution normal-ogive number of stimuli number of subjects numbers assigned ogive operational definitions ordinal scale paired comparisons pairs of stimuli parallelogram partial derivative perfect scale Phi coefficient physical continuum physical units positive semidefinite matrix Princeton University Psychol psychological continuum psychometric function Psychometrika psychophysical magnitude function psychophysical methods quantitative-judgment rank order ratio scale response patterns scalar products scale analysis scale values scaling methods scalogram set of stimuli spatial model standard deviation stimulus k subjective continuum subjective scale subjective-estimate symmetric matrix Thurstone scale Thurstone's trace line triads underlying continuum unidimensional unit of measurement vector Weber's law