I have also used regression of a derived relationship based on the physics of a process for a guide to the accuracy of the model. This gave a reasonable predictive relationship although I was aware that I had made a number of simplifications in developimg the model. My model which was of a filtration process was based on well established relationships and so the regression should have and did show a good correlation between two primary input variables and one output variable.

The development of models in this way is surely legitimate where the number of variables is small and there is reason to posit one model over others on physical grounds. I see that there are complications with climate models because of the extent of climate, the number of variables required to model climate is large and their measurement is problematical and data sets of climate measurements are incomplete and may be inaccurate and are inconsistent in timing and location. Given also, that irrespective of human activities climate is continuously changing, establishment of some stable basis on which to interpolate or extrapolate seems also to be difficult.

Can I add two further distortions arising from classical statistical methods:

Publication bias (perhaps what you meant by ‘file drawer’ in post 33?),

The notion that p refers to the probability of a particular hypothesis rather than the probability of data arising, given a particular model.

D

Amen to your comment on meta-analyses. I mean to write about that later. In my experience, most meta analyses always seek to prove what the individuals studies that compose it could not, while ignoring the insurmountable file-drawer and never-done-experiment problems.

Briggs

Another point is that a “correlation” i.e. mathematical is taken in many medical reports to be synonymous with “CAUSAL”

Meta-analyses seem these days to used for supporting otherwise unsupported data. This is much used drug studies. Unfortunately, by selection and manipulations such meta-analyses of failed studies can often be “proved” to support the intended theory or belief.

Statistics are very useful but unless the original raw data on which they are based are available, the “statistically significant” claim should be treated with the utmost caution

Most introductory statistics course won’t cover Bayesian statistics. Surprisingly, in classical or frequentist statistics it is forbidden to even ask questions like “What is the probability that this hypothesis is true?”

Briggs

i only ever took a first-level statistics class but this seems like the sort of thing i should have learned. is this statement just a case of the simple math i’m visualizing or is there some more advanced theory or analysis required to arrive at this conclusion?

The book Counterexamples in Probability has some interesting examples showing, among other things, how you can put an incredibly small maximum bound on the correlation between two random variables related via Y = e^X