Psychology 230:
Multidimensional Scaling

Data Theory

Data Theory

  • A data theory is an abstract representation of the varying aspects of data which classifies all possible data situations according to a few parsimonious concepts.

  • There are two major aspects of a data theory
    1. Empirical Design Theory
    2. Measurement Theory
  • We discuss these aspects in this lecture.
  • For most empirical design notions, there is a corresponding measurement theory notion.

    Empirical Design Theory

    The important aspects involve: Many of these notions are the usual ones from experimental design. However, ways, modes and categories deserve special attention here and are used in ways idiosyncratic to this course.

    Examples of Ways & Modes

    1. Responses of 200 subjects to a surver questionnaire having 10 questions. This is a {I x J} design where I=subjects, and J=questions. The design is 2-way, 2-mode, 200X10. There are 200 levels of the subject way and 10 levels of the question way.
    2. Similarity judgments from 1 subject about all pairs of 16 stimuli. This is a {I x I} design where I=stimuli. The design is 2-way, 1-mode, 16X16. There are 16 stimulus levels.
    3. Similarity judgmgents from 20 subjects about all pairs of 16 stimuli. This is a {I x I x J} design where I=stimuli, J=subjects. The design is 3-way, 2-mode, 16X16x20. There are 16 stimulus levels and 20 subject levels.
    4. Similarity judgments from 20 subjects about all pairs of 16 stimuli, judgments made on two occasions. This is a {I x I x J x K} design where I=stimuli, J=subjects, K=occasions. The design is 4-way, 3-mode, 16X16x20x2. There are 16 stimulus levels, 20 subject levels and 2 occasion levels.
    5. Ratings by 50 subjects of 20 stimuli on 10 attributes on 2 occasions. This is a {IxJxKxL} design where I=subjects, J=stimuli, K=attributes, L=occasions. The design is a 4-way, 4-mode, 50x20x10x2. There are 50 subject levels, 20 stimulus levels, 10 attribute levels and 2 occasion levels.

    Measurement Theory

    Correspondence between Empirical and Measurement aspects

    The correspondence between the major two aspects of Data Theory is explained in the accompaning tables. (Click here for Adobe Acrobat versions of Table 1 and Table 2, which can be read with Adobe Acrobat Reader.

    Philosophy of Measurement

  • Measurement properties are not properties of the data themselves.
  • Measurment level is not discrete --- it is continuous.

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