Level of Measurement 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.
 A: 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.
A: I would like to answer this question as both a statistician AND a psychologist.  I am assuming this question came from a introductory statistics textbook FOR psychology majors (or some other social science focus).
In this context, the question is not just asking if the variable has been measured on some measurement level, but also the nature of that which is being measured.
Self-esteem is not a concrete quantity that can be measured.  And, it is not the case that you have no self-esteem (at least that is not how most psychologists would state it).  A person may have low or weak self-esteem, but they never have NO self-esteem.  So, from this context, we have to rule out a ratio level measurement.
Clearly, this data would not be nominal.  So, it remains to decide if it would be ordinal or interval.  Because the data here has been quantified to a rather precise degree, the textbook authors are directing the students toward the interval option for the answer.  The differences should be comparable, 10 to 20 should be interpreted as as much of a gain as from 70 to 80...but there is no "fixed" zero indicating nothing of the quantity.
While there always will be some questions about the validity of the measurement instrument being used, the idea of psychometrics is that we can measure along a unidimensional scale, and the observed scores from such instruments as these are reliable proxy scores for those latent (directly unobservable) scores.
My hope is that my answer sheds light into the different epistemological approaches to questions such as this across the two disciplines.
