Violation of application requierements / assumptions

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.

• 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.
– Sycorax
May 13 at 15:23
• 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.
– whuber
May 13 at 17:26

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.