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I am a Math Phd student and a Teaching Assistant for Statistics in Psychology Deparment.

The problem I have is to determine the level of measurement. Let me first present the question:

Assume that a researcher measured self-esteem and obtained the scores 49, 53, 67, 20, 27, 36, 49, 27, 61, and 28. Determine the level of measurement...

I believe it should be an ordinal measurement, since there is no guarantee on how people perceive the scale and hence it is questionable to talk about differences. However, we consider it as an interval scale.

My apologies for a simple question. I really appreciate if you can provide some references for me to read and learn more so that I can guide students better.

Thank you very much.

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    $\begingroup$ You must read Stevens' original paper, On the Theory of Scales of Measurement. Then read F. Lord, On the statistical treatment of football numbers. Finally, study Velleman and Wilkinson, Nominal, Ordinal, Interval, and Ratio Typologies are Misleading. (All can be found freely on the Web--start with Google Scholar.) As a math student you will make short work of this; you will appreciate George Birkhoff's contribution, which apparently few psychologists do :-); and you will get a clearer picture of how misunderstood levels of measurement are. $\endgroup$ – whuber Jan 31 '18 at 0:10
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    $\begingroup$ I can't resist quoting Velleman and Wilkinson's conclusions: "A careful data analyst should not assume that the scale type of a variable is what it appears to be even when clear assurances are made about the data. ... [P]rograms based on Stevens’s typology suggest that doing statistics is simply a matter of declaring the scale type of data and picking a model. Worse, they assert that the scale type is evident from the data independent of the questions asked of the data. They thus restrict the questions that may be asked of the data. Such restrictions lead to bad data analysis and bad science." $\endgroup$ – whuber Jan 31 '18 at 0:13
  • $\begingroup$ @whuber Thank you very much, I will start to read references now. $\endgroup$ – Atbey Jan 31 '18 at 1:09
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Although there is no guarantee, but most people interpret 80 two times more than 40 if he/she asked to evaluate anything on a 0-100 scale. (Moreover, I assume most people in the US believe 20 °F is two times as warm as 10 °F and most people believe the same with °C, both obviously false.) And they interpret 0 as the total lack of the given feature. So people tends to interpret it automatically as a ratio scale. It does not matter they can't evaluate that feature consequently, they use it as a ratio scale.

But still, it's a good question, it would be even the subject of a nice little psychology study.

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  • $\begingroup$ Your argument, if correct, is that this is a ratio scale. So what would twice a self-esteem of 80 be measured as? $\endgroup$ – whuber Jan 30 '18 at 23:26
  • $\begingroup$ I am just saying people will interpret it as a ratio scale. I'm not saying it's a rational thing to do. And although height is a ratio scale there is no twice as high person as a two meter high person. $\endgroup$ – oszkar Jan 30 '18 at 23:34

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