Tuesday, October 04, 2016

Statistical Projection vs. Scientific Generalization

When my daughter was quite young, before she was able to walk, she saw a ball bounce and  roll. She laughed heartily. I don’t think she needed to observe a sample of five hundred round, spongy things bounce and roll in order to conclude that round, spongy things bounce and roll.

Similarly, neurologist V. S. Ramachandran, proponent of the value of individual cases to science, has remarked (quoted in Doidge, p. 178):

Imagine I were to present a pig to a skeptical scientist, insisting it could speak English, then waved my hand, and the pig spoke English. Would it really make sense for the skeptic to argue, “But that is just one pig, Ramachandran. Show me another, and I might believe you!”
The skeptical scientist, typical of nearly all scientists today, insists that the only way to establish knowledge is to observe five hundred cases, or a thousand, or two thousand. Anything less is an isolated instance, often denigrated as anecdotal evidence. In the absence of a sound theory of universals—because David Hume failed to find a necessary connection between cause and effect, and logical positivism picked up the banner of science, followed by Karl Popper’s notion of falsificationism—statistical “generalization” is said to be the only valid method of science.

It is this premise that allows modern psychologists to dismiss the entire Freudian psychoanalytic corpus, including the concept of repression, as unscientific, or worse, as pseudoscientific. Why? Because Freud’s evidence is “anecdotal” and the experimental methods of the physical sciences cannot validate his ideas. It is this premise that allows nearly all scientists to dismiss the notions of consciousness, free will, and introspection.

There is, however, a sound theory of universals: Ayn Rand’s theory of concepts, which I have summarized in my two books (In Defense of Advertising, pp. 147-52, and Montessori, Dewey, and Capitalism, pp. 82-86). Conceptualization is a process of universalization. It is based on Aristotle’s formal cause, which says that an entity’s actions are determined by its identity. Identifying universal relationships between entities and their actions give us principles and laws.
Concepts identify the nature of entities. Their essential distinguishing characteristics are universal. It is not that hard.

Thus, my daughter’s laughter at witnessing the round spongy thing bounce and roll was her conceptualization of that entity, by observing its essential distinguishing characteristic. Of course, she did not have words to describe the process at the time, but her mind, nonetheless, was processing her perception. The same can be said about Ramachandran’s English-speaking pig (assuming no tricks of ventriloquism). One does not need a sample of five hundred English-speaking pigs to conclude that something quite unusual has just happened.

Statistical projection—and the correct word is “projection,” not generalization—has its place in our search for knowledge, but it does not replace scientific (inductive) generalization.

Statistical inference, as it is also correctly called, projects a finding from a sample to a population. Thus, if data in a sample of 500 American men show that two percent have red hair, and the research did not commit any flagrant methodological errors, then a projection (or inference) can be made, within a margin of error, that two percent of men in the entire country have red hair.

A projection moves from some to some—from two  percent of the sample to the same two percent in the population.

A scientific generalization, on the other hand, when, for example, forming a concept of round, spongy things as something that bounces and rolls, or of human beings who possess the capacity to reason, moves from all to all.

All of the balls I have observed bounce and roll; all humans that I have observed possess the capacity to reason. Therefore, all balls, past, present, and future, by their very nature,  bounce and roll. The same conclusion is drawn for all humans.

The place of statistical projection? As I wrote in In Defense of Advertising (p. 157), “Statistics is a branch of mathematics and, as such, is a method of measurement. Statistical inference . . . is used only in contexts in which we do not know—or there do not exist—universal laws that could explain the causal relations of the variables.”

Meteorology represents the former, because of the large number of unknowns and difficult-to- measure variables in constructing weather forecasts (all of which, though given many different names, are forms of statistical projection).

Predictions of people’s behavior, because free will precludes the existence of universal laws governing all of our behavior, represents the latter; we make statistical projections, albeit not based on randomized samples, unless we are professional researchers, of what others will do in the future based on our current and past knowledge of them.

Statistical projection assists scientific research. It is not a substitute for it.

And one does not have to accept everything Freud said to acknowledge his accomplishments, not least of which is his presentation of the first comprehensive theory of psychology.

Freud was looking for universals, and he found a few: repression, defense mechanisms, and the significance of the subconscious to influence our present behavior.

They may not be round, spongy things, but I am laughing heartily—at my discovery of these Freudian universals!


Barry Linetsky said...

Excellent observations on the valid and invalid uses of statistics. Many people have never thought about these issues, so thanks for bringing to the forefront that there IS an issue regarding the use of statistics in validating knowledge.

Teju Teju said...

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