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In this question there was an interesting discussion concerning the Pearson goodness-of-fit test going on which was far from conclusive: Is there any statistical test that is parametric and non-parametric?

Also, when you surf around you find arguments for and against its being of either sort - obviously because the line between parametric and non-parametric statistics seems to be rather blurred?!?

But I ask this question because many people still differentiate in this way: Is the Pearson goodness-of-fit test parametric or non-parametric (or even some kind of combination)?

(NB: There is a similar but more general question - which was not answered here: https://stats.stackexchange.com/questions/60181/are-goodness-of-fit-tests-parametric-or-nonparametric)

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vonjd
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    What hinges on what you call it? – Nick Cox Mar 31 '14 at 08:37
  • @NickCox: This is a good question. I think it serves as a litmus test whether the concept of "parametric" makes sense at all. – vonjd Mar 31 '14 at 09:09
  • I don't know which question you are regarding as good (your own?), but you didn't answer my question that I can see, or if you did you have it the wrong way round. It's whether the idea of a non-parametric test is coherent that troubles many people. – Nick Cox Mar 31 '14 at 09:13
  • I don't know what you are getting at but parametric is just the opposite of non-parametric, isn't it. – vonjd Mar 31 '14 at 09:15
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    Supposedly, but that doesn't help us one little bit. I can define non-unicorns as the opposite of unicorns, but a definition doesn't bring entities into existence. The idea of a parameter is that of a constant defining a population or process. Even chi-square tests make use of such parameters, as when probabilities are estimated or postulated tacitly; so, what is meant by non-parametric tests? In practice, the term seems most used when there is no strong expository emphasis on using a particular named distribution, but why is that is interesting or useful or important? – Nick Cox Mar 31 '14 at 09:23
  • So you are basically saying that you can define non-parametric however you like and therefore the question is not interesting nor important? If this were so why do so many people seem obsessed by it? – vonjd Mar 31 '14 at 09:35
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    Not quite: I am very prepared to learn that the term might be useful, but that is not my experience. Your last question is a good one; my own answer would be phrased in terms in the sociology of knowledge, i.e. that most people just copy out of texts and some people try to understand them. – Nick Cox Mar 31 '14 at 09:46

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