Wednesday, September 21, 2011

Are You in Need of Some Psychic Help?

Occasionally I bid for items on ebaY. Sometimes I'm successful.  A few years ago I bought an item in this way, and it turned out that the seller lived here in my home town. I arranged to collect my purchase from his house, and in the course of the transaction he passed me his business card.

Apart from his first name, and telephone number, the only other word on the front of the very colourful card was "PSYCHIC". I kid you not!

Needless to say, I've kept his card. In my line of business, you never know when you might need some extra help.

Listed on the reverse side are several offerings, including "Spiritual Interior Design" and "Pet/Animal Communicator". I can't see myself needing the first of these, but our dog get's a bit out of control at times, so the second item may be useful. And yes, private consultations and parties are apparently available!

For the longest time, I kept this business card in full view on my office desk. In fact, I placed it at the front of the small stash of my own cards that sits in a little holder, facing visitors. After all, it's a lot more interesting than my card, and definitely much more colourful.

It stayed there for nearly five years before I eventually put it in a drawer. It wasn't that I was afraid that someone would steal it. It was because in all of that time, not one student ever commented on it! I admit, a few of them glanced at it, but they seemed to be lost for words!

I started my econometric life working with the research group at New Zealand's central bank - the Reserve Bank of New Zealand. My first spell there was in the summer of 1969 or 1970, and a small group of us worked on the construction of the Bank's first macroeconometric model. I returned later and spent quite a bit of time building larger models and using them for policy analysis and forecasting.

These were quarterly macroeconometric models, and at that time New Zealand did not have quarterly national accounts (just annual ones), so I could certainly have used that business card back then!

Now, I'm pleased to relay to you that I'm not the only econometrician or statistician who's been tempted to dabble in the occult. You may not be aware of the fact that the great Sir Ronald Fisher published two important papers in the Proceedings of the Society for Psychical Research - one in 1928 (here), and one in 1929 (here). Read the title of the journal carefully - it's not a typo!

The second of these papers is particularly interesting. It's also very short, and contains no mathematical symbols. On p.191 we find the following passage:



(The first word on the last line is "suspense".)

In case you hadn't guessed, Fisher is talking about the notion of a p-value. He'd previously devoted a large part of the 1925 masterpiece, Statistical Methods for Research Workers, to this topic. You'll also see that he talks of "...once in twenty trials", which he then describes as being "...an arbitrary, but convenient, level of significance..." And so it remains.

Notice, too, the emphasis on "experimentation". It's clear that Fisher saw experimentation as a crucial element in hypothesis testing. From all accounts, his practice was to declare that an effect had been shown if p < 0.01, in which case the hypothesis would be rejected. If the p-value was greater than 0.20, Fisher tended to conclude that if there was an effect, then it was so tiny that it could not be detected from the experiment that he'd undertaken. And finally, for p-values in between, Fisher advocated that the next experiment should be designed carefully to get further insights into the effect.

You'll see that nowhere is there any suggestion of reaching the conclusion of "no effect" - that is, of "accepting the hypothesis". In this last respect, Fisher was consistent with the later Neyman-Pearson theory of hypothesis testing, and the notions of the null and alternative hypotheses.

Remarkably, and despite the emphasis placed on this topic in Statistical Methods for Research Workers, the passage quoted above is apparently the only place where Fisher write explicitly about how a researcher should interpret (as opposed calculate) a p-value.

If you ever have the urge to delve into Fisher's writings, you can get free access to his papers relating to statistics and mathematics through the University of Adelaide's Library, here. Why Adelaide, Australia? Because that's where Fisher spent the last years of his life, and his papers are held by the U. of A.

And if you need a little help with your forecasting, and you're not getting the inspiration you need from Econometrica, then you'll be pleased to know that the Proceedings of the Society for Psychical Research is still published. If it's early volumes that you're after, try the Vail Collection in the MIT Libraries; or the Harry Houdini Collection in the New York Public Library.

Given the topic, I'm sure you don't need me to provide links!



Note: The links to the following references will be helpful only if your computer's IP address gives you access to the electronic versions of the publications in question. That's why a written References section is provided.

References

Fisher, R. A. (1928). The effect of psychological card preferences. Proceedings of the Society for Psychical Research, 38, 269-271. 

Fisher, R. A. (1929). The statistical method in psychical research. Proceedings of the Society for Psychical Research, 39, 189-192. 

© 2011, David E. Giles

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