My experimental units are 100 classrooms on campus. As I walk into
each room I flip a perfectly fair coin in a perfectly fair way to determine
whether I turn the room lights on (X = 1) or off (X = 0). I then determine
whether or not I can read the fine print on my bottle of smart pills (Y = 0
for no, Y = 1 for yes). From the resulting pairs of scores (one for each
classroom), I compute the phi coefficient (which is a Pearson r computed
with dichotomous data). Phi = .5. I test and reject the null hypothesis
that phi is zero in the population (using chi-square as the test statistic).
Does correlation (phi is not equal to zero) imply causation in this case?
That is, can I conclude that turning the lights on affects my ability to
read fine print?
I modify my experiment such that Y is now the reading on an
instrument that measure the intensity of light in the classroom. I
correlate X with Y (point biserial r, a Pearson r between a dichotomous and
a continuous variable) and obtain r = .5. I test and reject the null that
this r is zero in the population (using t or F as the test statistic). Does
correlation (point biserial r is not zero) imply causation in this case?
That is, can I conclude that one of things I can do to increase the
intensity of light in the room is to turn on the lights?
I modify this second experiment by creating three experimental
groups, with classrooms randomly assigned to groups. In one group I turn
off the lights and close the blinds. In a second group I raise the blinds
but turn off the lights. In a third group I raise the blinds and turn on
the lights. I compute eta, the nonlinear correlation coefficient relating
group membership to brightness of light in the room. Alternatively I dummy
code group membership and conduct a multiple regression predicting
brightness from my dummy variables. R = eta = .5. I test and reject the
null hypothesis that R and eta are zero in the population (using F as my
test statistic). Does correlation (R or eta are not equal to zero) imply
causation in this case?
I could continue on with other correlations appropriate for various
experimental designs, but I would hope that you have gotten the point by
now.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Karl L. Wuensch, Department of Psychology,
East Carolina University, Greenville NC 27858-4353
Voice: 252-328-4102 Fax: 252-328-6283
mailto:[EMAIL PROTECTED] <mailto:[EMAIL PROTECTED]>
http://core.ecu.edu/psyc/wuenschk/klw.htm
<http://core.ecu.edu/psyc/wuenschk/klw.htm>
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