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Category Archives: Non-parametric Statistics

Article by Jamieson, Susan (2004) in Medical Education, 38.


Many of my colleagues trapped in the middle of a debate whether or not Likert scale (ordinal[1]) data can be analyzed parametrically[2]. Some of them (who stick to the theory that ordinal can not be treated as interval on whatever reason and basis) even ‘aggressively’ criticized my other colleagues who did so in their research.


I did explain to them few times that there are two school-of-thoughts pertaining to this issue. The purist (merely my term) argued that ordinal is ordinal, nothing in this world can make it interval. For this school-of-thought, ordinal must always be analyzed non-parametrically. The other school-of-thought argued that to a certain extent, ordinal and interval can not be distinguished as the ‘border line’ between them is very vague[3] (Abelson (1995) called it ‘fuzzy’[4]). Based on this premise, the second school-of-thought argued that ordinal data can be analyzed parametrically if (and only if) that the data is ‘sufficiently close’ to normal distribution[5].


Participating in such old and endless debate is, for me, a waste effort. As a matter of fact, both have proven contributed significantly to the body of knowledge and theory development. As long as we realize the existence of the school-of-thought, and as long as we know which school-of-thought we are in, I believe it is sufficient for amateur researchers like me to continuously active in research. Time and resources should be focused on conducting research where our contribution is possible, rather than busy looking for pitfalls in the other camp’s research.


[Note: the first three paragraphs is my personal view, it was not taken from this paper.]


This paper discussed the same issue as I described above. The author presented the two school-of-thought by referring to two different views, one by Knapp (1990) and the other one by Kuzon (1996). No conclusion has been made at the end of this paper on whether or not the second school-of-thought is applicable. The author leave the core issue of the debate as it is before, makes it remained as a ‘never-ending story’.

[1] There are 4 different types of measurement levels – ratio, interval, ordinal and nominal. For thorough definition, please refer to Steven, Stanley Smith. (1946) “On the Theory of Scales of Measurement”, Science, 103, pp 677-680. For quick reference, please refer to wikipedia.

[2] There are two types of statistical analysis available, i.e. parametric and non-parametric. Which one to choose is very much dependent to the data properties. For quick and reliable reference on what is parametric and non-parametric tests, go to Wikipedia or just click here and here respectively.

[3] Interesting argument about this issue can be found in Miles, J. and Shevlin, M. (2001), Applying Regression & Correlation: A Guide for Students and Researchers. London: Sage Publication, p. 61.

[4] Abelson, R.P. (10051995). Statistics as Principled Argument. Hillsdale, NJ: Erlbaum.

[5] How ‘close’ is ‘sufficiently close’ to normal? Is there any possibility that we can ‘rest’ from the normality assumption? Please read Sirkin, R. Mark. (2005). Statistics for the Social Sciences. Sage Publication particularly on p. 245. I plan to include my note (here in this weblog) on part of chapter 8 of this book (pp. 244-246), I’m now looking for free time to revise my note before I can post it here.