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I hope someone can help me - I have taken over some code from a former colleague and I am rather confused by some of it (my former colleague is long gone so I can't just ask).

The complete population is registered in a registry. It is not a sample, the entire population is known.

We have to estimate a regression model and my former colleague has written in the documentation that potential regressors are chosen based on having significant correlation coefficients - without defining "significant".

I am not sure if it refers to the usual test for significance of a sample correlation coefficient or something else, and in that case: What?

Can somebody help me understand what significance of a population correlation coefficient means when the whole population is known?

Thanks!

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  • $\begingroup$ If you truly have a population, then why is there any need to run the code more than once? $\endgroup$
    – whuber
    Aug 10, 2017 at 14:37
  • $\begingroup$ The population - which is of livestock - changes (but is always completely known with at most a 6 hour delay) and forecasts have to be submitted twice a year. $\endgroup$
    – SiKiHe
    Aug 11, 2017 at 8:35
  • $\begingroup$ It is now clear you do not have any population in the generally accepted statistical sense of the word: you are monitoring a process. If you don't clarify that in your question, you will collect useless or even misleading answers. It's almost always better to describe the actual problem you face rather than trying to abstract it: crucial details get lost in the process of abstraction. $\endgroup$
    – whuber
    Aug 11, 2017 at 13:37
  • $\begingroup$ I am most certainly not monitoring a process. I really don't understand how you can see the entire group of the livestock of interest as anything other than a population. If you run the same statistics - say unemployment counts - every month, would you also claim that the population of the country in question is not a population? $\endgroup$
    – SiKiHe
    Aug 22, 2017 at 12:02
  • $\begingroup$ Tell us, then: are the forecasts only about the individual livestock you currently have in the herd and only about their current (or past) characteristics? If that is so, you might make a case that it's a population. If not--and that seems far more likely--then it cannot possibly be a population in any meaningful statistical sense. The point is that any inferences you make (estimates, forecasts, decisions, etc) can apply at most to the population (or process), never to anything not in the population. $\endgroup$
    – whuber
    Aug 22, 2017 at 17:09

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We can't tell what your colleague did. I would guess that he is probably using significance as a screening tool for model building and using the significance that is output from whatever software he is using. This would be based on the notion that he is dealing with a random sample from some population. This method, called "bivariate screening" is a bad way of building models, regardless of the population/sample question.

When dealing with entire populations, there are varying views. Some people think that statistical significance isn't really meaningful. Others posit that the population is really a sample from some sort of "super population". I, personally, think the first position is more reasonable, but there are intelligent people who disagree.

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