Abstract
We apply Shannon entropy as a measure of information content in survey data, and define information efficiency as the empirical entropy divided by the maximum attainable entropy. In a case study of the Norwegian Function Assessment Scale, entropy calculations show that the 5-point response version has higher information efficiency than the 4-point version.
Highlights
When we invest the time and effort of researchers and participants in a population survey, we naturally want the collected information to be as valuable as possible, and informally we may express the value as a product of information quality and quantity
We apply Shannon entropy as a measure of information content in survey data, and define information efficiency as the empirical entropy divided by the maximum attainable entropy
In a case study of the Norwegian Function Assessment Scale, entropy calculations show that the 5-point response version has higher information efficiency than the 4-point version
Summary
When we invest the time and effort of researchers and participants in a population survey, we naturally want the collected information to be as valuable as possible, and informally we may express the value as a product of information quality and quantity. We define the information efficiency of a question in a questionnaire as the empirical entropy divided by the maximum entropy obtainable for the given question It measures to what extent the responders use the available options–on a scale from 0 to 1–and is likely to be more intuitively appealing than the entropy number itself. Wu and Zhang [3] apply an information-theoretic approach to the use of auxiliary information from survey data, including entropy evaluations. Their purpose is to create statistical estimators with low variance, rather than quantifying information. Cox [6] applies entropy computations to questionnaire design, with focus on signal-to-noise relations, which aim at evaluating information quality, rather than quantity
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