Statistics question
 

Quick Question.
True of False: An r of -1.0 proves a strong cause and effect relationship between x and y.
Thanks.

I think it's false, simply because it's a correlation thing not a cause and effect thing. Just because things correlate does not mean one causes the other.

Shred's got it - r values only show the the correlations or relationships between two variables, and never, at ANY time, do they say that X actually causes Y.

Oh I see, there could be a lurking variable or something to that effect, thanks for clearing that up. :thumbsup:

Definately false,
Correlations are measures of association and do not indicate cause and effect. I think this sort of question is on most early stat quizes/tests.
A correct answer would be that it indicates a perfect inverse correlation between x and y.

ok, since we have that question answered...

then how DO you prove a causational effect between two variables?

You cannot say whether it is true or false.

If r-squared equals 1 than obviously you have perfect correlation. -1 or 1 could both give an r-squared value of 1.

Not enough information.

False. "Correlation is not causation."

High correlation (even perfect correlation) proves nothing about causation. Both X and Y could be caused by an uncontrolled variable, yet have no direct connection between them.

Even so, I think Bayesian statistics would give that statement a "mostly true".

You can't. But you can make a very very educated guess by doing an experiment with a control group. In other words, you try to get two nearly identical groups and administer the independent variable (which will mean the IV will be the only difference between the two groups) and see if the variable makes an effect. Quasi Experiments will work too, but we won't go into that...

My guess us that in the kind of research you would be doing where you are measuring simple correlations you can't prove a causal relationship.

But, if you've got a theory: F=ma.

Take a mass, apply a bunch of different F's to it. Measure the a's. Plot the results. Find that yes, indeed, 'F' is proportional to 'a' by a constant 'm' which turns out to be a property of the mass which we can also measure with a scale.

The data supports the theory, and insofar as the theory is correct, F caused a.

Strictly speaking, you can never prove a theory to be true beyond a shadow of a doubt, but you can demonstrate its validity to such a high degree that it would be silly to doubt the accuracy of the theory.

Statistical tests are not set up to prove that anything is true, rather they are set up to test the null hypothesis that some phenomena or event happened by chance, or that there are no differences in groups of subjects/events. They intend to disprove the null hypothesis.
A statistically significant result indicates evidence that the phenomena could not have happened by chance thus, we fail to reject the null hypothesis.
A statistically significant pearson product moment correlation is merely saying that it is highly unlikely that the obtained correlation happened by chance. However, as many people have commented, correlational results do not imply causation because of the potential for spurious variables.
For example, if one were to look at the correlation for per pupil expenditure money for each state in the US, and the academic achievement (SAT scores) of the students within each state, there is a inverse correlation between the amount per pupil expenditure and academic achievement (SAT scores) (More money = Less achievement). However, this correlation fails to take into account the percentage of students taking the SAT for each state. The states that spend the least per pupil have the fewest percentages of their students taking the exam and the states that spend the most per pupil have the highest percentages of students taking the SAT.
Maybe in some states they only want the smart kids to take the SAT, maybe they don't have the expectation for all kids to go to college, so they don't push the SAT on students with lower academic achievement. All of which are valid questions.
Therefore, after you statistically control for the percentage of students taking the SAT in each state, there is a positive correlation (as expected) between per pupil expenditure and SAT achievement.

There's a very strong correlation between being born and dying. Therefore, birth causes death.
;)

ah, r values.

That brings back some memories.

Little did I know when I took sadistics that I would actually use them.

I teach university stats. It's possible to teach it in a stimulating, fun, interesting way. But "sadistics" is a good descriptor for what uninspired teaching does to the subject.

I also teach a university stat course as a GA. We have a good time with it, and I think the students enjoy it. I try to keep my classes relatively small, as it makes things easier for me and the students.