[lbo-talk] Better live in Sweden than in the US: Why More Equal Societies Almost Always Do Better

[Wojtek S]

[WS:} I already overposted so this my last one today.  The fundamental
assumption of statistical hypothesis testing is that you have a normally
distributed population (albeit normality is not always necessary) of
interchangeable items, from which you sample some items with known
probability.  It is quite obvious that countries are not interchangeable
items - evrery country is different so the notion of drawing a
representative sample of countries is pretty much nonsensical.  All you can
have is sets of countries.

Whether any such set can be considered a population depends on the set and
what you want to do with it.  If you define your set as "high income OECD
countries" it is pretty much a population because to belong to the set,
these countries have to have to have certain structural properties in
common, not just being grouped by a statistician.  Likewise the set of small
island countries is also a population, as there are no other countries with
similar characteristics outside that set.  OTOH, a set of countries that are
served by British Airways is just a set, as new elements can be added to or
taken from it.

And if you use members of these populations in a regression analysis, the
concpet of statistical significance is meaningless, as  the regression
coefficients (or R squares)  are those of the population, not a sample.

Wojtek

On Thu, Feb 18, 2010 at 1:01 PM, Miles Jackson <cqmv at pdx.edu> wrote:


> Wojtek S wrote:
>
>> RE: A distinguished sociologist I know, who prefers to remain nameless,
>> said
>> that Wilkinson's results are very sensitive to how you specify the
>> equations
>> or set up your country universe
>>
>> [WS:]  I just had a quick look at the charts, but I do not think that the
>> above is valid criticism.  First, the selection includes only high income
>> countries, which controls for variance that is associated with income
>> level.  Second, this is almost the entire *population* of high income
>> countries, not a sample, therefore the concept of statistical significance
>> is meaningless.  Statitical significance denotes the probability that the
>> difference observed in the sample will be null if were to draw other
>> samples
>> of the same size from that population.  If that probablity is relatively
>> high (typically higher than 5%) the null hypothesis cannot be rejected by
>> convention.  However, if the difference is observed in th epopulation, it
>> is
>> THE difference, as repeated samples of the same size would yield the exat
>> same difference.
>>
>>
> This raises an interesting statistical question: what is the population of
> interest in research like this?  All high-income nations at a single point
> in time?  All high-income nations at any point in time?  Within some time
> window?  Whether or not a statistical significance test is relevant depends
> on your assumptions about the population.
>
> Miles
>
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