[From Rick Marken (2006.12.15.1750)]
David Goldstein (2006.12.15.1908)--
Dear Rick and listmates:
I was speaking with Bill Powers and we were talking about the difference between traditional and PCT hypothesis testing.
Traditional:
Null Hypothesis: There is no relationship between the IV and DV variable.
Alternative Hypothesis: There is a relationshp between the IV and the DV variable.
A nonzero correlation coefficient (statistically significant) would lead to the rejection of the null hypothesis.
PCT:
Null Hypothesis: There is no control system operating between the IV (Disturbance) and the DV (Action).
Alternative Hypothesis: There is a control system operating between the IV and the DV.
A nonzero correlation coefficient (statistically significant) in which the IV and DV would be negatively correlated (-1) would lead to the rejection of the null hypothesis.
I think I have this right.
Yes. Though I think it's better to cast PCT hypothesis testing in terms of IV and CV (controlled variable). I like doing it that way better because what PCT methodology is about is the discovery of CVs. The relationships between IV and DV is of interest only to the extent that both IV and DV have an effect on a CV. Looking only at IV - DV relationships will not tell you much about whether there is a CV or what the CV might be if there is one. While a strongly negative correlation between IV and DV suggests that there _is_ a CV, the correlation doesn't tell you what that CV _is_. And a low correlation between IV and DV does not necessarily mean that there is not a CV. The low correlation may result from the fact that other outputs are also used to influence the state of the CV.
I believe PCT hypothesis testing should be formulated in terms of an hypothesized controlled variable (HCV). The null hypothesis would be that there IS an effect of the IV on the HCV, which would only be the case if the HCV is _not_ a CV. The alternative hypotheses is that there IS NOT an effect of the IV on the HCV.
So I would re-write your version of PCT hypothesis testing as follows:
PCT:
Null Hypothesis: There is a relationship between the IV (Disturbance) and the HDV (Hypothetical Controlled Variable).
Alternative Hypothesis: There is a no relationship between the IV and the HDV.
A low correlation coefficient (statistically not significant) in which the IV and HCV would be uncorrelated (r = 0.0) would lead to rejection of the null hypothesis.
Best
Rick
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