# Does practical insignificance mean no relationship?

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

• Question 2: could you please elaborate what do you mean by "terrorist attacks", "internet use" and "stability"? – user31264 May 2 '16 at 14:48
• Alright. Also question 1 is more important for me right now (if you know how to answer it) – Hutchins May 2 '16 at 14:49
• 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 – DJohnson May 2 '16 at 15:19
• 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?) – Hutchins May 2 '16 at 15:24
• Your coefficient is expressed in the units of the variable itself. Its magnitude is irrelevant to its "practical" importance. – DJohnson May 2 '16 at 18:11