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In considering (for example) homicide rates reported annually for each country, it occurs to me that the U.S., being larger in population, might thereby be expected to have a rate closer to the worldwide mean.

However, I don't know how to evaluate that idea quantitatively. What kind of additional data (if any) and calculations would be required to support that idea (not sure I should call it a hypothesis, because it relates to the model rather than to the world).

Another way of thinking about this: with respect to statistics reported per country, does the U.S. look like a group of smaller countries combined?

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    $\begingroup$ Could you please describe the objective of the regression you are trying to create? $\endgroup$
    – Jack Ryan
    Jan 28, 2014 at 15:58
  • $\begingroup$ There may be a case for using weighted least squares regression to address heteroscedasticity in respect of the variances of homicide rates in different countries, but it is difficult to advise without more detail on what you are trying to do. 'Evaluate that idea quantitatively' is rather vague. $\endgroup$ Jan 29, 2014 at 8:05
  • $\begingroup$ To Jack Ryan: re your inquiry, let me explain. I am considering the implications of mediocre U.S. scores in measures of well-being -- including, (to name a few examples) high school math achievement, life expectancy, number of murders, low birth weight infants and so forth. $\endgroup$ Jan 30, 2014 at 10:30

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Even small countries are generally large enough that nationwide parameters (such as the underlying homicide rate) can be estimated pretty accurately on a year-by-year basis. Any observed differences between countries are therefore likely due to genuine differences between the countries rather than statistical noise. True, the CI for the US homicide rate will be narrower than the corresponding CI for Sweden, but both are likely to be very small.

It's true that the world-wide mean will be more greatly influenced by the rates in the large countries (China and India much more than the US), but I'm not sure what you would do with this. I guess it might be interesting if, for instance, you found that fluctuations in the global homicide rate were more closely correlated with fluctuations in the US rate than the Chinese rate. Is that the sort of thing you had in mind?

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  • $\begingroup$ Your first paragraph gives me exactly what I wanted to know. $\endgroup$ Jan 29, 2014 at 0:59

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