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Measurement, Mathematics and New Quantification Theory

  • Book
  • © 2023

Overview

Authors:
  1. Shizuhiko Nishisato

    1. Toronto, Canada

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  • Examines thoroughly the most fundamentally important topic of measurement: data for analysis
  • Discusses the mathematics needed to convert non-quantitative data to quantitative data for non-mathematicians
  • Provides a full explanation, with illustrative examples, of the jump from non-quantitative data to quantitative results

Part of the book series: Behaviormetrics: Quantitative Approaches to Human Behavior (BQAHB, volume 16)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Measurement

    1. Front Matter

      Pages 1-1
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    2. Information for Analysis

      • Shizuhiko Nishisato
      Pages 3-17

    3. Data Analysis and Likert Scale

      • Shizuhiko Nishisato
      Pages 19-36

  3. Mathematics

    1. Front Matter

      Pages 37-37
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    2. Preliminaries

      • Shizuhiko Nishisato
      Pages 39-54

    3. Matrix Calculus

      • Shizuhiko Nishisato
      Pages 55-73

    4. Statistics in Matrix Notation

      • Shizuhiko Nishisato
      Pages 75-84

    5. Multidimensional Space

      • Shizuhiko Nishisato
      Pages 85-91

  4. A New Look at Quantification Theory

    1. Front Matter

      Pages 1-1
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    2. General Introduction

      • Shizuhiko Nishisato
      Pages 95-124

    3. Geometry of Space: A New Look

      • Shizuhiko Nishisato
      Pages 125-141

    4. Two-Stage Quantification: A New Look

      • Shizuhiko Nishisato
      Pages 143-169

    5. Joint Graphical Display

      • Shizuhiko Nishisato
      Pages 171-196

    6. Beyond the Current Book

      • Shizuhiko Nishisato
      Pages 197-208
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Keywords

About this book

The purpose of this book is to thoroughly prepare diverse areas of researchers in quantification theory. As is well known, quantification theory has attracted the attention of a countless number of researchers, some mathematically oriented and others not, but all of them are experts in their own disciplines. Quantifying non-quantitative (qualitative) data requires a variety of mathematical and statistical strategies, some of which are quite complicated. Unlike many books on quantification theory, the current book places more emphasis on preliminary requisites of mathematical tools than on details of quantification theory. As such, the book is primarily intended for readers whose specialty is outside mathematical sciences. The book was designed to offer non-mathematicians a variety of mathematical tools used in quantification theory in simple terms. Once all the preliminaries are fully discussed, quantification theory is then introduced in the last section as a simple application of those mathematical procedures fully discussed so far. The book opens up further frontiers of quantification theory as simple applications of basic mathematics.

Authors and Affiliations

  • Toronto, Canada

    Shizuhiko Nishisato

About the author

Shizuhiko Nishisato is Professor Emeritus, University of Toronto.


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