Measurement scales on the continuum

Area of Science:

• Measurement theory
• Psychophysics
• Social sciences

Background:

• S. S. Stevens' 1946 work identified three admissible transformation groups for numerical measures: similarity, affine, and monotonic.
• The existence and nature of other possible scale types remained unclear until recently.

Purpose of the Study:

• To explore and define additional measurement scale types beyond those previously established.
• To characterize homogeneous situations on the continuum and their corresponding scale types.
• To integrate these scale types into the framework of physical units.

Main Methods:

• Analysis of admissible transformation groups for numerical measures.
• Characterization of homogeneous situations on the continuum.
• Theoretical integration with the structure of physical units.

Main Results:

• Identified three established scale types (similarity, affine, monotonic) and one additional type.
• This new type lies between the similarity and affine scale types.
• Defined classes of structures corresponding to these scale types.

Conclusions:

• The identified scale types offer a more comprehensive understanding of measurement.
• These findings have potential applications in behavioral and social sciences.
• The results facilitate the incorporation of scale types into physical unit structures.