By David Stockburger
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Additional resources for Introductory Statistics: Concepts, Models, and Applications
The Ruler and Scale Types Suppose a ruler was constructed in a non-industrialized country in the following manner: peasants were given a stick of wood and sat painting interval markings and numbers on the wood. Would anything measured with this ruler be an interval scale? No, because no matter how good the peasant was at this task, the intervals would simply not be equal. 40 Suppose one purchases a ruler at a local department store. This ruler has been mass-produced at a factory in the United States.
It is appropriate to compute the statistics described in the rest of the book when the scale type is interval. Ratio Scales Ratio scales are measurement systems that possess all three properties: magnitude, intervals, and rational zero. e. 32, whereas this is not possible with interval scales. It is at this point that most introductory statistics textbooks end the discussion of measurement systems, and in most cases never discuss the topic again. Taking an opposite tack, some books organize the entire text around what is believed to be the appropriate statistical analysis for a particular scale type.
A measurement system may be "better" than another system because it more closely approximates the properties necessary for algebraic manipulation or costs less in terms of money or time, but no measurement system is perfect. In the view of the author, S. S. Stevens has greatly added to the understanding of measurement with the discussion of properties of measurement, but an unquestioning acceptance of scale types has blurred important concepts related to measurement for decades. A discussion of error in measurement systems is perhaps a more fruitful manner of viewing measurement than scale types.
Introductory Statistics: Concepts, Models, and Applications by David Stockburger