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As far as I know all methods / models making assumptions about data distribution, data scale, etc. but whenever I read a paper (political sciences) the researcher(s) are violating them (some). E.g. treating ordinal data as metric or "pseudo-metric", don't care about normal distrbution. I always askmyself are they doing this for pratical reasons and are there findings valid? Or are violations not that serve in general or does it really depend on the method / model and if so, could you please give me some examples where it doesn't really matter and some where it does.

Here is a sample as suggested: Högström, J. (2013): Classification and Rating of Democracy: A Comparison. Taiwan Journal of Democracy, Volume 9, No. 2: 33-54 https://www.diva-portal.org/smash/record.jsf?pid=diva2%3A683064&dswid=2340

The author compares three measurements of democracy. Two of them (Freedom House and Polity) are ordinal scaled. He rescales all of them to a 0-100 scale for comparison and uses a paired t-test.

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    $\begingroup$ It will make it easier to understand the setting and the procedure if you can edit to provide a complete citation and link to the article you have in mind, as well as a quotation of the relevant passage. $\endgroup$
    – Sycorax ♦
    May 13 at 15:23
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    $\begingroup$ Search for FM Lord's classic paper on football numbers. In practice, all probability assumptions are violated by real processes and data, so the better question to ask is how and to what extent these deviations from the assumptions might affect the conclusions. $\endgroup$
    – whuber ♦
    May 13 at 17:26

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If you're referring to distributions for parameter estimation of a regression, then one of the simplest example is the the case of the Ordinary Least Squares Estimator (OLS) and the Maximum Likelihood Estimator (MLE).

There are many concepts you need to master in this case: Normality, Asymptotic normality, consistency, bias and efficiency.

While normality is not an actual requirement for the existence of the OLS, it's convenient because that makes it consistent with a Maximum Likelihood Estimator.

In the presence of normality the two formulas are the basically the same. That gives OLS more value. In addition, the MLE has greater variance thus is less efficient than the OLS.

However, when the number of observations ($N$) is really big and there are few parameters ($K$), then aforementioned difference tends to disappear given the asymptotic properties and consistency.

So, to answer your questions:

1.- I always ask myself are they doing this for practical reasons and are there findings valid? Sometimes this is done for convenience, practical (computing or results) or theoretical (asymptotic, etc). However, usually is for practical reasons such as results that support the hypothesis (potential malpractice).

2.- are violations not that serve in general or does it really depend on the method / model Yes, some violations can be bypassed when it's justified and or not needed (i.e. there's no statistical difference between the compliance and not compliance of it). And yes, it depends on the model/method. There are many more examples, of course.

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    $\begingroup$ "However, usually is for practical reasons such as results that support the hypothesis." That sounds like bad practice and bad science to me but I am by no means an expert. $\endgroup$
    – mmw
    May 13 at 15:41
  • $\begingroup$ Yes, indeed, that's bad practice. It occurs, though. $\endgroup$
    – Lima_Institute_of_Econometrics
    May 13 at 15:51

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