While the attached paper doesn't directly deal with many of the issues raised here it does speak to some of the underlying issues. Best wishes, David Booth

My first problem is that I don't understand what you need to test normality and homoscedasticity if you know that the distribution is skewed.

If you transform a variable, the tests (Shapiro-Wilk or Levene) are about the distribution of the transformed variable. That does not make them more or less accurate.

Removing outliers is only sensible if these values are "bad values", that is, when they are extremely implausible (or even actually impossible, e.g. as result of a typo or some other mistake) o if there are extrenal reasons that invalidates them (e.g. it is known that the animal from which that outlying value was taken was unintendedly sick, or that a person being interviewed turned out to have misunderstood the question, was drunk or sponsored to give a manipulated answer etc.).

You current studies don't seem to involve experiments (it seems you take observational data / questionaires). I personally don't see much sense in significane testing in these cases. Particularily not, if the task is to explore different factors (their correlation with the outcome measure), and to identify or find those with the "biggest effects" (these could be the statistically non-significant ones!).

When using rank-based methods (supposedly what you call "non-parametric") you loose the quantitative relationship between the variables, something I consider not really helpful (at least in 99% of the cases, to make up a statistic, too :)). Be careful when talking about "non-parametric alternatives (to parametric tests)". These "alternatives" are about different hypotheses. For instance, MWU and t-test do not test the same hypothesis (except in those cases where the distribution is in fact normal - where you would not think about any "alternative" at all). The sad truth is that most people re-iterating these textbook phrases just don't know what hypothesis the MWU-test (or similar non-parametric tests) is (are) actually testing. As an analogy of this absurdity I could ask you if the apple or the pear I have is heavier (testing the null then the weight of both fruits is equal). Now you say: "ah, sorry, man, I don't have a good weighing maschine for these things son I wouldn't trust it. But, hey! I can easily spot the color, and let me tell you: the apple is significantly more reddish than the pear (p < 0.01). You have that nice p-value. That should answer your question!"

Ok, it' not that stupid, but the direction is right, I think.

Take-home message: Don't let tests dictate what you should do. Think thoroughly what you want, what data you need to provide the relevant information, and how you can extract, visualize and communicate that information. Tests may not at all be helpful. Look for plausibility rather than for (statistical) significance.

Hello David and Jochen,

First of all, thank you for your responses!

The outliers in my data are completely plausible. Most of them are caused by reasons that are known (system driven statuses). Of course there most likely are some administrative errors but they cannot be distinguished from the real data. The issue I had with this was that these outliers also caused large variation between the different samples of the different locations. As this is the first time I am facing a problem like this I decided that asking for help would be a good idea. (I am still learning after-all).

As for the skewness, the data is heavily right tailed with skewness of 4.0+ and kurtosis of 20.0+ which I know is a good tell-tale sign that the data is not conforming to normality on its own. After giving it some further thought, I also realized that using log transformation would beat the purpose of what I am going to test for.

As for the task, I must elaborate of what my analysis consist of:

For the first part of my analysis I have put forward the following hypothesis (borrowed the wording from David's paper :) ) "If a service location is doing poorly, it must be doing poorly in comparison to other service locations".

This is where establishing whether or not there is a significant difference in the mean turnaround time between locations come in. (And post-hoc testing).

Furthermore I wish to provide some approximation of what the difference between mean turnaround time is. Additionally, the company has their set target they would like to reach in terms of mean turnaround time from which I can also look at what the difference is between current state and desired state.

There are multiple factors and "issues" surrounding several of the locations, which is where my second part of my analysis will come in:

The current data set has approximately 35%~ of the cases where the desired turnaround target is met, therefor I can use this as a target value for developing a model and using all the associated factors as an input. (status codes, process steps, product, location etc.)

Based on my analysis I can develop improvements and further use simulations to explore the possible outcomes.

As you may see, majority of what I am doing is heavily reliant on applying theory and providing evidence.

Jochen Wilhelm, please let me know if you have any further thoughts on this case. I am open to any suggestions. I will take the take-home message to heart :) Thank you.

Best regards,

Janis Frisfelds

If I were you, I would consider outlier or skewness effect as a normal, or something being more normal than normal distribution:

Article Geospatial Analysis Requires a Different Way of Thinking: Th...

Under the framework, there are two laws: scaling law (of far more smalls than larages) for heterogeneity, and Tobler's law (of more or less similar) for homogeneity.

Article Editorial: Spatial Heterogeneity, Scale, Data Character, and...