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I had doubts on the above flow chart based on measurement scales which I found in a published article. Can anyone correct m please and clear my doubts as I believe non parametric tests are not restricted to just nominal and ordinal scale measurement. Thank you

  • $\begingroup$ Can you please point to the article this graph came from? (Yes, it goes without saying that we can use non-parametric tests with "ordinary" continuous data.) $\endgroup$ – usεr11852 Jul 22 '19 at 13:30
  • $\begingroup$ The whole territory is hopelessly confused. For example, the most important single fact about nominal data is that they can be counted and then distributions such as Poisson, multinomial, negative binomial with specified parameters are central to the action. This can be hidden in elementary teaching but it's still there as the basis. $\endgroup$ – Nick Cox Jul 22 '19 at 16:28
  • $\begingroup$ This is the source of published article. Kishore K, Kapoor R. Statistics Corner: Measurement Scales Journal of Postgraduate Medicine, Education and Research 2019: 53 (1):46-47. $\endgroup$ – Sc2283 Jul 23 '19 at 15:16

Your doubts on the flowchart are well founded. It is no more than a bunch of boxes connected with arrows.

Put simply: nonparametric, semiparametric, and parametric tests represent a gradient of stronger assumptions and, consequently, stronger inference. They have more to do with the distributions of the data than with the way that the data are measured.

Indeed, a simple example of an efficient fully parametric test for nominal data is the simple Pearson Chi-square test of independence. We use a fully specified binomial likelihood for the response.

Ratio data provide the perfect rationale for a non-parametric test. For instance, the ratio of two normally distributed random variables is Cauchy distributed, and Cauchy random variables have nonfinite mean or variance*. In that case, the log-rank test is a highly powered test for differences in median which is a well defined measure of location for a Cauchy-location family of distributions.

*finite mean and variance are the most critical assumptions behind the T-test, a general test for mean differences which is commonly what is referred to as a parametric test, even though it makes no actual distributional assumptions. In either case, the normal probability model is wrong anyway.

  • $\begingroup$ Thank you for clearing my doubts and providing a more insightful view into it. I did read that even for Likert scale data for more than 100 pts t-tests perform equally well for comparison . However when I went through the article published in leading medical institute - Kishore K, Kapoor R. Statistics Corner: Measurement Scales Journal of Postgraduate Medicine, Education and Research 2019: 53 (1):46-47. gave me doubts so wished to clarify the same. $\endgroup$ – Sc2283 Jul 23 '19 at 15:22
  • $\begingroup$ @Sc2283 that journal and that article are low quality. The impact factor is 0.8. As for the article, it only cites two references, one of which is the New York Times. $\endgroup$ – AdamO Jul 23 '19 at 16:26

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