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I have two problems:

1) I have a regression coefficient that is very significant (large dataset), but has low practical significance. Can I say there is no relationship? And I mean really tiny, like .000005.

2) I have a specific question about my project. So I am regressing "terrorist attacks" to "internet use" to see if being in a "high internet access area" relates to local terrorism. However, I feel like I should control for "stability," since that presents a fairly likely confounder. But when I control for it, the sign of the internet coefficient switches due to multicollinearity. I'm not sure about the relative trade-offs of including it or not. Whats your advice?

Definitions: attacks - attack count per country per year

internet access - proportion of population with internet access per country per year

stability - an index from the Failed States Index

Thanks

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  • $\begingroup$ Question 2: could you please elaborate what do you mean by "terrorist attacks", "internet use" and "stability"? $\endgroup$ – user31264 May 2 '16 at 14:48
  • $\begingroup$ Alright. Also question 1 is more important for me right now (if you know how to answer it) $\endgroup$ – Hutchins May 2 '16 at 14:49
  • $\begingroup$ You are correct to query the distinction between statistical significance vs practical, particularly with large n. However, using a coefficient for evaluating this would be incorrect - unless that coefficient is standardized. A useful heuristic is the F- or t-value associated with that parameter. It's magnitude is a much more reliable index $\endgroup$ – DJohnson May 2 '16 at 15:19
  • $\begingroup$ I'm not sure what you mean. If my coefficient makes no sense practically (e.g. 1% increase in water increases productivity 0.000000000000000000000000000000001%) I still can't say there is no relationship?) $\endgroup$ – Hutchins May 2 '16 at 15:24
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    $\begingroup$ Your coefficient is expressed in the units of the variable itself. Its magnitude is irrelevant to its "practical" importance. $\endgroup$ – DJohnson May 2 '16 at 18:11
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  1. The absolute value of the coefficient is not that important. What is important is what fraction of the variance it explains. Anywhere, if there is a statistically significant coefficient, you cannot say there is no relationship. There is a relationship, albeit maybe practically insiginificant.

  2. If by "relating" you mean a correlation, you have it. If by "relating" you mean causation (internet access causes terrorism), it is very hard to infer such a complicated causation. At the very least, you should control many variables which could influence both internet access and terrorism. The more variables you control, the more accurate result you receive.

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  • $\begingroup$ Add 1) As general rule, that is just plain wrong. Add 2) True, but perhaps it is much better, and easier, to find an instrument variable and do IV-regression. $\endgroup$ – Repmat May 5 '16 at 18:03
  • $\begingroup$ (1) what is plain wrong? there are 4 statements $\endgroup$ – user31264 May 5 '16 at 19:39
  • $\begingroup$ All of it, the value is important (keeping the scale in mind), many people don't care about fit from a policy perspective it is entirely irrelevant, significance does not guarantee a relationship $\endgroup$ – Repmat May 5 '16 at 19:46
  • $\begingroup$ (1) "the value keeping the scale in mind" is the same as "what fraction of the variance it explains". (2) "significance does not guarantee a relationship" - it does, albeit not necessarily directly causal (3) many people don't care about fit from a policy perspective it is entirely irrelevant - it doesn't matter whether people care or not, the relationship is still here. $\endgroup$ – user31264 May 5 '16 at 19:54
  • $\begingroup$ This is counter productive, so I'll will just end by saying no and I don't agree with you. $\endgroup$ – Repmat May 5 '16 at 19:58
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The largest issue with this is that I would assume that internet access generally increases as time goes along. Unfortunately so do many other factors(population, electricity use, number of kitten videos on youtube, etc.). It may be beneficial to compare values within the same year, to prevent essentially regressing terrorist attacks against time.

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