Sit down kid, I'll tell you a story of long ago, before the weebs, furrys and degenerates ruined this game. Back when a man was a man and a toolbox was his most prized possession, back when slipping the floors didn't cause an aneurysm in an admins brain. Robust is what we called those among us that had the recation time, knowlage, and sheer fucking will to kill without fail, these men, these absalute legends were called "robust" and they were feared amongst the servers , antag ir not, they always had guns stashed, chems ready, and bombs implanted in their chests linked to a code word so vulgar you would be banned on the spot for saying it now. Ahh I miss hippie, tg and og goon, ss13 is a shell of its former self. More on reddit.com

why tHE FUCK IS THE CLOWN IN THE ARMORY!?!

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They seem to mean the same thing at first but there are nuances to the words. Just to let you know my only qualification to answer this is being a native English speaker. Robust means strong and healthy and, according to Google, is synonymous with vigorous. The difference between robust and vigorous is that vigorous gives the connotation of being energetic as well. Also in my opinion robust is mostly used for living things while vigorous could describe a living thing or a non-living thing. Sturdy means tough, not likely to fall or be broken. This word could apply to both living things and non-living things. A telephone pole could be sturdy. More on reddit.com

My knowledge comes largely from linear models, but there is a whole field of robust statistics that relates to this and expands upon it.

In many situations, there is a common parametric assumption you can make on the errors in a model (e.g. normal). This gives rise to what you are calling the 'regular standard error.' On the other hand, this assumption is not strictly necessary for inference because we can use the sandwich form standard error to approximate (appealing to the CLT) the true standard error.

Thus, you can see that the robust standard error should work even if your parametric assumption fails.

The 'regular' standard error can be used because the sandwich error may be unstable in small sample sizes, or if you have a strong belief in your parametric assumption. If your assumption fails, but you use your parametric standard errors, you may be in danger of over- or under-estimating the true standard error. [Under-estimating the true standard error is often the more egregious error in practice.]

I won't go into how to calculate it explicitly, but https://en.wikipedia.org/wiki/Heteroscedasticity-consistent_standard_errors gives some more information on the subject. If you have a particular data set and want to use sandwich errors, then I recommend the sandwich package in R.

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