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I read the following article about statistical independence. In summary, the article argues that "It is time for science to retire the fiction of statistical independence," and goes on to explain different reasons why. Having read the article, I tend to agree. I wanted to know the following:

  1. What do other cross-validated users think?
  2. Are there scholarly resources that you all can point me to that either confirm or reject the notion set forth by the article? More specifically, whether real-life datasets do (or do not) exhibit statistical independence?

Thanks!

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10  
I think we are not as naive and ill-informed as "the overwhelming common practice" to which the author refers. There are many false assumptions, straw men, and downright incorrect claims in that little piece. – whuber Jan 8 at 3:22
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I guess the author of this article has never tried flipping coins before.... – RustyStatistician Jan 8 at 6:49
    
His complaint seems to be that sometimes, people use the wrong model and inappropriately apply the independence assumption. That's certainly plausible... but independence exists as a concept not for the service of science but because it arises mathematically. It's almost like the author claims there's no role for mathematics that may be misused in scientific applications. – General Abrial Jan 8 at 14:36

It seems to me that the author assumes that most scientists don't know about or understand how to deal with correlation and assumes almost that the use of methods to handle correlated data doesn't exist (perhaps outside of Makov Chains). That's not the case. There are many statistical methods that account for correlated data and most statisticians, epidemiologists, ecologists, and other scientists know (or should) when to use the appropriate methods. I don't think scientists need to abandon methods that assume independence as they are quite useful -- if they weren't simulations and real-world experiments which have demonstrated their usefulness would not abound. Instead, if anything, scientists need better training or education to understand when to use methods that account for correlation and when to use methods that require assumptions of independence.

That's just my two cents.

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I don't subscribe to the author's view at all. In particular from my experience it is absolutely not the case that "[..] the overwhelming common practice is simply to assume that sampled events are independent". On the contrary, the issue of correlation is something we have to deal with on a regular basis (during my work in the financial industry). And, mostly important, we are clearly aware of this!

I totally agree, though, with the statements on simplifying the real world. For me the famous words attributed to George Box are the leading guide here:

All models are wrong; some models are useful.

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Thanks for reminding us of those famous words from George Box, I think that is very true and relevant here. – Kiran K. Jan 8 at 14:37

Of course the notion of statistical independence as has been popularly preached till now, is pretty much a myth (most of it). I don't think so anybody should disagree that the universe and everything inside it, works in conjunction with everything else.

In fact as far as statistical independence goes, its only in the datasets or kind of, it exists in very specific terms. But in general, dependency is an integral part of the universe.

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Yes, but much of it is negligible in terms of our tools of measurement. – StatsStudent Jan 8 at 7:29
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Exactly. Perhaps thats why we treat such variables as independent since their dependence is negligible. – Shivendra Sharma Jan 8 at 8:04

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