When designs are not to complex and non-parametric approaches are easly applicable, I always run both of them even if assumptions of parametrical test are met.
In my experience they both give pretty much the same results, even with assumptions violations.
Have I just been extremely lucky so far or have you had similar experiences?
I usually do the same, and I have observed the same outcome (Most of the time).
It is important to remember that there are profund differences between both kind of procedures.
What intrigues me is that with such deep differences (and a great obsession for assumptions) the results is often the same in the end!
Both parametric and regular non-parametric tests will show the same results if the violations are not extreme.
There is a misunderstanding about the assumptions to traditional parametric tests. The normality assumption, for instance, is more related to the mean distribution than to data distribution. Of course, if you have a Normal data distribution, you are a hundred percent right that your mean will present a Normal distribution. But other distributions will generate a Normal mean distribution as well, depending on the sample size. This is what central limit theorem tell us. In example, samples with five individuals taken from an Uniform distribution will generate a Normal mean distribution. If your data distribution is quite different from a Normal, than you will need a larger sample size.
All of this is not new and has been shown since 1960's through simulations. But teachers seems to prefer to talk the same over and over.
@Sandro, what you say is exactly what I answer anytime I’m asked to run non-parametrics and I surprise them showing same results with both approaches.
The real matter in my opinion is not parametric tests yes/no but instead mean (and variance) yes/no. In same case they are the misleading statistics to rely on, such as when the data distributions are highly not simmetrical
If there is a fully-fleged alternative, with less assumptions and not too much of a power-loss compared to the standard procedure (in case the assumptions are met), then maybe it is better to apply it right from the start. This might be favorable, because controlling the assumptions is defective as well.
As an example I think of t-test vs. Welch-test (ok, I know it is not nonparametric, but it does not assume variance homogeneity)
If your problem is specific (deterministic) and non-complex, I would like to suggest to fit the data to Gamma density function. As per my experience this can accommodate all possible uncertainties specific to the problem which you have considered.
Thanks,
Krishna.
Massimiliano Grassi , Bernhard Piskernik , I agree that Welch's t-test is preferred even if you have equal sample sizes and variances.
If you want to compare the differences in outcomes between Student's t-test and Welch's t-test, please check out my calculator:
Research Welch's t-test for comparing two independent groups: An Exce...
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