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What I want to know

Are there any near-exhaustive (... and preferably free) informational resources that summarize statistical tests/procedures? Please take 'near-exhaustive' to approximately mean "has most of the statistical methods you've heard of". An example of the sort of summary information I would hope for would include usable data types of the variables (ex. ordinal, continuous), assumptions (ex. dependence, normality, or homoscedasticity), and number of dependent variables.

Why do I want to know

I want to be able to have a large resource to consult for deciding what type of analysis I should use for a dataset and experimental design. The idea being that I could then go learn the details of any procedure in this summary that appeared most promising for my current data analysis needs.

What I've been doing

As if I couldn't believe statistics was a huge topic, although I do believe it, I've been reading from a variety of websites (most-frequently wikipedia and university pages) on different methods of statistical analysis out there. I've been building a spreadsheet with each entry being a distinct analysis, and the fields being the properties or assumptions I can find on that analysis. This is proving to be a very difficult task, and resultantly my table is not as complete as I would like. I feel like such a summary would be a useful tool for both noob and veteran alike.

The closest I have found is the NIST/SEMATECH e-Handbook for Engineering Statistics, but there are plenty of methods that even a noob like me has heard of that are not in this document (http://www.itl.nist.gov/div898/handbook/index.htm). Although it is not as complete as I would like, I will caveat I do find its scope impressive.

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    $\begingroup$ "most you've heard of" and "near exhaustive" are not in any way near to the same thing -- unless you're lucky enough to happen across someone with near-encyclopedic knowledge $\endgroup$
    – Glen_b
    Commented Feb 20, 2016 at 8:49
  • $\begingroup$ Realizing that 'near-exhaustive' is not likely, 'most you've heard of' is an acceptable compromise to me. I don't expect anyone to have near-encyclopedic knowledge, but I have seen statisticians show a breadth of understanding that I wish was more accessible. $\endgroup$
    – Galen
    Commented Feb 20, 2016 at 16:24
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    $\begingroup$ In terms of specific test statistics, you may not find, say, this test which was made in response to the specific details in the question; it's an exact small sample test of means for a pair of exponentially distributed variates. I don't think I've seen it presented in any particular place but a decent statistics graduate should be able to come up with it. I wouldn't expect a laundry list will capture most of those sorts of cases. $\endgroup$
    – Glen_b
    Commented Feb 21, 2016 at 0:36
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    $\begingroup$ It's called Google, it has everything $\endgroup$
    – Aksakal
    Commented Feb 21, 2016 at 1:03

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Seems like a mundane answer, but Wikipedia is an outstanding source without a finnish line. I have created for myself several "Wikipedia books" that consist of aggregated Wikipedia articles on specific quantitative subjects. The results are self-customized world class textbooks-equivalent on any statistical or quantitative domain of your choosing. And, whenever you are intested in a new methodology you can add it to your Wikipedia book and it essentially creates a new chapter for it, including the article. Just learn how to create those Wikipedia pdf files that you turn into a book and you are set.

The above, I think, is a highly underutilized capability of Wikipedia. Although it is really easy to do, I don't know of anyone else that has used this method to boost their learning by creating easily worldclass reference material.

Additionally, depending on what software you use those may have really interesting documentation. Software like SAS, SPSS, Matlab, STATA, XLStat have documentation that represents rich references on the subject. If you are an R user, it also has a ton of reference material on an evergrowing number of quantitative methods. And, it is free (a marked advantage vs. the commercial proprietary software mentioned earlier).

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    $\begingroup$ I'd suggest exercising a degree of caution with quite a few of the statistics articles on wikipedia. The material on probability distributions is generally pretty good, but the stats articles are a bit of a mixed bag quality-wise. Some certainly contain errors (some have been pretty serious). Others are not so much incorrect but present a very idiosyncratic view of particular topics. Others still are cover the right things but explain quite poorly. Some of the material is excellent. Wikipedia's stats articles can be very useful in combination with other sources of information. $\endgroup$
    – Glen_b
    Commented Feb 20, 2016 at 8:52
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    $\begingroup$ A friend of mine who is a professor at Stanford stated Wikipedia occasionally can have a mediocre article on a subject, but typically not for long. This reflects Wikipedia live community of constant editors. Along the same line, if you do create a book as I suggest; you will notice that the book does get updated fairly often reflecting more current knowledge on various methods. It is like having a textbook that is being edited on an ongoing basis. That's the beauty of the Open Source movement. Those benefits do not apply to software only (such as R, Python, Linux, etc.). $\endgroup$
    – Sympa
    Commented Feb 21, 2016 at 0:32
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    $\begingroup$ Having actually spent some time trying to fix problems with stats-related articles on Wikipedia (I've edited a good few over many years and posted in Talk about problems with many, many more) it surprises me quite how long some bad things last. If you know your professor's Wikipedia username I could send him or her links to a few articles to fix. I'd then like to see selfies every six months right after they see what happened to their nicely fixed article over that interval. I don't have the time to squat on the stats articles (I do fix most of the worst bits, but my fixes often don't last). $\endgroup$
    – Glen_b
    Commented Feb 21, 2016 at 1:52
  • $\begingroup$ As an example of longevity of nonsense, the serious error discussed here was in the Wikipedia article "Histogram" (hardly an obscure article) for over a year before I fixed it. In the interim, the article was edited eighty-two times without anyone even raising a query in "talk". Fortunately that fix survives (so far). $\endgroup$
    – Glen_b
    Commented Feb 21, 2016 at 2:14
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    $\begingroup$ +1 to the post as well as @Glen_b's comment. I think that for starters Wikipedia is great and given the broadness of the question the only other I could think of would something like Springer's International Encyclopedia of Statistical Science but really... who buys these things anyway? (The Amazon reviews are interesting, they seem written exclusively by co-authors of the series) $\endgroup$
    – usεr11852
    Commented Feb 21, 2016 at 3:53

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