Sunday, April 13, 2008

Falsification and likelihood

A couple of years ago, Mike the Mad Biologist compared likelihood statistics to falsification (he mentions the article today).

Let me first say that Mike is absolutely correct that likelihood statistics is a more productive approach for many many scientific problems. But Mike forgets, I think, that philosophy and working science have different goals and evaluate methodologies in different ways.

Regardless of what Karl Popper might have actually intended, he was not a professional scientist. Any scientist would be foolish, I think, to take Popper's writing as a guide to how to conduct an actual practical scientific inquiry on a specific question. Philosophers are usually — when they are doing anything productive at all — interested in creating the weakest possible definition for a term, the minimal definition.

I'm not a professional statistician, and I don't know that it's always possible to prove falsifiability from likelihood statistics (but I suspect that's the case). However, I can say that by Popper's definition every scientific inquiry using likelihood statistics is in principle also falsifiable.

Popper's falsifiability criterion is not necessarily the best way to do science. It is best viewed as the simplest possible way of distinguishing science from non-science. The falsifiability criterion has the advantage of not itself depending on any statistical assumptions. (Statistical assumptions are required, of course, when the hypothesis itself is statistical.) All that is necessary is that you have a way, some way, any way, of determining if the hypothesis were false.

7 comments:

  1. Good post... I go over the concept of falsifyability in an older blog post of mine.
    It truly is what separates science from pseudoscience.
    http://blogs.scienceforums.net/ecoli/2008/02/03/why-creationism-is-not-science/

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  2. BB,

    I agree that Popper's falsification perspective isn't that useful, but, in my experience, there are many scientists who 'formally' or 'officially' embrace Popperianism. While it's declined significantly, there was a time when many NIH and NSF grants were expected to phrase hypotheses as H0 (the null) and Ha (the hypothesis to be tested).

    Interestingly, later in life, Popper did admit that falsification didn't work for biology (particularly evolution).

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  3. I agree that Popper's falsification perspective isn't that useful...

    It's not always useful for actually doing science efficiently. It's always useful for separating science from pseudoscience.

    ... there are many scientists who 'formally' or 'officially' embrace Popperianism.

    Indeed. But scientists misguidedly attempting to employ a philosophical principle as a required, limited technique of working science doesn't change the philosophical value of the principle, and falsification is of considerable philosophical power.

    Popper did admit that falsification didn't work for biology (particularly evolution).

    I suspect you're misunderstanding both Popper's error as well as missing his later retraction.

    IIRC, Popper actually stated that evolution itself was not falsifiable; he later recanted this statement. I suspect he was looking at evolution as a paradigm, not at various evolutionary theories. Evolution is still falsifiable at very abstract levels, but you can raise it to such a level of abstraction that it becomes an unfalsifiable paradigm... and philosophers routinely raise ideas to the highest level of abstraction they can manage.

    Regardless of what Popper did or didn't say, falsification works perfectly well to distinguish science from pseudoscience in actual biological theories. If you make a statement in biology — just like other science — that cannot in some way be proven false by experiment, it is not a scientific theory.

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  4. Correction: If you make a statement in biology — just like other science — that cannot in some way be proven false by experiment, it is not a scientific hypothesis.

    Let me elaborate a bit.

    You don't necessarily have to actually do the experiments that would potentially prove the hypothesis false; it's necessary only that you could do so in principle.

    In many cases, the experiments that would in principle falsify the hypothesis are so trivial that they're simply not worth doing. That's a feature, not a bug, and it doesn't mean that falsification is trivial; it means that scientists have become skilled at thinking scientifically and don't need to take special pains to remain scientific... and good for them!

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  5. Never look to a philosopher for practical advice.

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  6. While it's declined significantly, there was a time when many NIH and NSF grants were expected to phrase hypotheses as H0 (the null) and Ha (the hypothesis to be tested).

    This is how I was taught experimental methodology in grad school. Our goal was to "reject the null."

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  7. The problem is that just rejecting the null is an inefficient technique: In theory, you have to test against the null for every possible alternative explanation in a separate experiment. And, since you're doing a lot of individual experiments, you're guaranteed a number of false positives (1 in 20 at 5% significance).

    Furthermore, almost all null-hypothesis statistical tests assume the parameter is normally distributed in the control population. If this assumption is violated, then null-parameter testing can be misleading.

    For example, if almost all people recover from a disease on their own, but a few get a lot sicker, then the distribution of the "how sick" parameter in the control population is substantially skewed.

    It's fairly easy then to construct a faulty experiment that apparently shows that some treatment improves the outcome to a high degree of statistical significance (because it assumes the control distribution is normal), when under a more rigorous analysis, does not achieve results better than chance.

    These issues are not a problem for falsification in the philosophical sense; as the hypotheses become more sophisticated and complex, what constitutes falsification becomes proportionately more sophisticated and complex.

    However, from a practical perspective, taking a naive view that just showing statistical significance against chance can often reduce out too much detail for effective and efficient practice.

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