# relationship between correlation and average

#### statdummy66

##### New Member
Hi! This is my first post here and, being quite poor at statistics, I have a question.
Let's assume that, if you look at the combined populations of, say, Switzerland and Austria, there is a very modest (r=.3) positive correlation between personal wealth and happiness.
And let's also assume that the people in Switzerland are, on average, wealthier than the people in Austria.
Does that mean that the average Swiss person is happier than the average Austrian?
This is not a trick question; I ask this sincerely.
Thank you.

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#### hlsmith

##### Less is more. Stay pure. Stay poor.
There are other sources of happiness that may need to be controlled for in order to extrapolate results across populations, correct?

PS, welcome to the forum and try not to use "help" as the title of the post. Provide at least an attempt to describe.

#### statdummy66

##### New Member
There are other sources of happiness that may need to be controlled for in order to extrapolate results across populations, correct? I don't know if that's true in this example. Are you saying you're not sure either?

PS, welcome to the Thanks! and try not to use "help" as the title of the post. Provide at least an attempt to describe. Fixed!

#### Karabiner

##### TS Contributor
Does that mean that the average Swiss person is happier than the average Austrian?
Not necessarily, if there's an interaction effect between nationality and income on happiness,
i.e. if the associateion between income and happiness is moderated by nationality.

For example, the correlation could be large and positive (r=0,7) in Austria and small and negative
in Switzerland (r= -0,1).

With kind regards

Karabiner

#### statdummy66

##### New Member
Not necessarily, if there's an interaction effect between nationality and income on happiness,
i.e. if the associateion between income and happiness is moderated by nationality.

For example, the correlation could be large and positive (r=0,7) in Austria and small and negative
in Switzerland (r= -0,1).

With kind regards

Karabiner
Very helpful, thank you so much!

#### statdummy66

##### New Member
P.S. If the correlation between wealth and happiness was positive in both countries, would the answer then be "Yes"?

#### statdummy66

##### New Member
Bumping this up ... anyone know the answer to my follow-up question?
Thank you.

#### spunky

##### Doesn't actually exist
P.S. If the correlation between wealth and happiness was positive in both countries, would the answer then be "Yes"?
No.

#### joeb33050

##### Member
Hi! This is my first post here and, being quite poor at statistics, I have a question.
Let's assume that, if you look at the combined populations of, say, Switzerland and Austria, there is a very modest (r=.3) positive correlation between personal wealth and happiness.
And let's also assume that the people in Switzerland are, on average, wealthier than the people in Austria.
Does that mean that the average Swiss person is happier than the average Austrian?
This is not a trick question; I ask this sincerely.
Thank you.
If what is known is what is written above; then YES. We could list lotsa assumptions; enough to make the samples independent, and the mandatory weasel words, it's still YES. This is what stats is about. (the .09 r sqrd is bothersome)

#### Dason

Joe is just flat out wrong. Without additional assumptions it possible for the average happiness of the Swiss to be below the average Austrian happiness.

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#### joeb33050

##### Member
Joe is just flat out wrong. Without additional assumptions it possible for the average happiness of the Swiss to be below the average Austrian happiness.
Didn't I mention assumptions? Of course I did! Could Dason be flat out wrong?

#### Dason

Didn't I mention assumptions? Of course I did! Could Dason be flat out wrong?
Of course I could be wrong. But read what you wrote again. To me it says regardless of the situation the answer is yes.

Especially your first line implied that even if all we know is what is written then your answer is yes. If that's not what you intended I don't think you did a great job communicating but that's ok as long as we get past it eventually.
If what is known is what is written above; then YES. We could list lotsa assumptions; enough to make the samples independent, and the mandatory weasel words, it's still YES. This is what stats is about. (the .09 r sqrd is bothersome)
You don't say anywhere that the answer is no without additional assumptions

#### fed2

##### Member
I wonder what if any additional constraints could be placed on the data such that the conclusion that 'the average Swiss person is happier than the average Austrian' would hold. You have to feel that it would not take too much?

#### joeb33050

##### Member
I wonder what if any additional constraints could be placed on the data such that the conclusion that 'the average Swiss person is happier than the average Austrian' would hold. You have to feel that it would not take too much?
One assumption that works is: nothing but wealth affects happiness. Any? all? Ho has the Christian Doctrine sorta imported from Fed contract Law. Ho less assumptions and given independence is affected by only a, b, c... It's in there, or assumed to be in there, whether explicit or not.
A NO is if swiss happiness is not connected to wealth. I think.

#### Dason

@joeb33050 I'm literally having trouble trying to imagine what you're trying to get at with that last post.

Obviously we could make insanely restrictive assumptions to place on the data that would make it possible to say what OP was asking about. But if that's the case why not just *assume* that "that the average Swiss person is happier than the average Austrian" and make our lives easier?

There probably are some less restrictive assumptions that one could make that would make it possible to assume what OP wants to. As a matter of fact under most reasonable situations we probably could assume that it would be the case with a reasonable probability. But can we guarantee it? Almost certainly not. Not without knowing more.

#### fed2

##### Member
*assume* that "that the average Swiss person is happier than the average Austrian"
You know what, I didn't say the trivial solution wasn't allowed, and I think its important to explore these avenues, so it counts. Thats +1 for Joeb33050, so you were both right. Like kissing your sister.

Christian Doctrine
Im not really sure how it plays a role here, but lets keep it on the table, you never know.

with a reasonable probability
Is it a matter of probability or data? Couldn't the question just be seen as a theoretical one, in the sense that the E(Swiss happiness) < E(Austrian Happiness).

under most reasonable situations
That's sort of what im getting at, shouldn't there be reasonable mathematical assumptions to represent reasonable situations?

#### joeb33050

##### Member
"There are other sources of happiness that may need to be controlled for in order to extrapolate results across populations, correct?"
No. The act of writing Ho defines the independence, randomness and assumptions associated with Ho.
The fed contracting "Christian Doctrine" states that if a clause is required by law in a contract, it's in there. Somebody maybe forgot, its still in there.
The stats Christian Doctrine states at writing Ho, all the random, independence and assumptions are in there-all required to test Ho.
The answer is then YES, yes means that given the survey and conclusion, wealthier folks are happier than poor folk, France vs Switzerland.
Nobody's proven anything, stats never proves anything.
Priests, rabbis, imams, nuns, teachers police, social workers doctors, nurses, and Mother Teresa are not made happier by more bucks;;;;they were all taken care of in independence or assumptions. Note that true independence means that random sampling is not required.
Finally, we owe questioners answers; yet we're scared to death of one word answers. We have nothing to fear but short answers. Yes. No. 12.7. Paragraphs of weasel words confuse the asker, and don't make us feel much better.
C.D. It's in there!

#### fed2

##### Member
"Christian Doctrine" states that
ok, i see what you mean. well i guess most statisticians aren't big on contract law so you have to let me catch up. In the original question discussing the combined population, there is the country itself which could be considered a "sources of happiness", so there's at least one. When talking about the two populations separately, this probably applies. Namely that we are talking about correlation in the marginal distribution already taken over any 'other factors'.

I was thinking one assumption that is implicit here is most likely that those with 0 wealth have 0 expected happiness. Well its not that insane is it? If you throw some multi-variate normality assumptions, or maybe something weaker, on the fire, and your basically there id think. Normality assumptions can't be insane, because then all statisticians are insane. Or maybe....