by RCTs in the Garden of Eden Suppose researchers come to a town and do an RCT on the town population to check whether the injection of a green chemical improves memory and has adverse side effects. Suppose it is found that it has no side effects and improves memory greatly in 95% of cases. If the study is properly done and the random draw is truly random, it is likely to be treated as an important finding and will, in all likelihood, be published in a major scientific journal. Now consider a particular woman called Eve who lives in this town and is keen to enhance her memory. Can she, on the basis of this scientific study, deduce that there is a probability of 0.95 that her memory will improve greatly if she takes this injection? The answer is no, because she is not a random draw of an individual from this town. All we do know from the law of large numbers is that for every randomly drawn person from this population the probability that the injection will enhance memory is 0.95. But this would not be true for a specially chosen person in the same way that this would not be true of someone chosen from another town or another time. To see this more clearly, permit me to alter the scenario in a statistically neutral way.
Topics:
Lars Pålsson Syll considers the following as important: Statistics & Econometrics
This could be interesting, too:
Lars Pålsson Syll writes What statistics teachers get wrong!
Lars Pålsson Syll writes Statistical uncertainty
Lars Pålsson Syll writes The dangers of using pernicious fictions in statistics
Lars Pålsson Syll writes Interpreting confidence intervals
RCTs in the Garden of Eden
Suppose researchers come to a town and do an RCT on the town population to check whether the injection of a green chemical improves memory and has adverse side effects. Suppose it is found that it has no side effects and improves memory greatly in 95% of cases. If the study is properly done and the random draw is truly random, it is likely to be treated as an important finding and will, in all likelihood, be published in a major scientific journal.
Now consider a particular woman called Eve who lives in this town and is keen to enhance her memory. Can she, on the basis of this scientific study, deduce that there is a probability of 0.95 that her memory will improve greatly if she takes this injection? The answer is no, because she is not a random draw of an individual from this town. All we do know from the law of large numbers is that for every randomly drawn person from this population the probability that the injection will enhance memory is 0.95. But this would not be true for a specially chosen person in the same way that this would not be true of someone chosen from another town or another time.
To see this more clearly, permit me to alter the scenario in a statistically neutral way. Suppose that what I called the town in the above example is actually the Garden of Eden, which is inhabited by snakes and other similar creatures, and Eve and Adam are the only human beings in this place. Suppose now the same experiment was carried out in the Garden of Eden. That is, randomisers came, drew a large random sample of creatures, and administered the green injection and got the same result as described above. It works in 95% of cases. Clearly, Eve will have little confidence, on the basis of this, to expect that this treatment will work on her. I am assuming that the random draw of creatures on which the injection was tested did not include Eve and Adam. Eve will in all likelihood flee from anyone trying to administer this injection to her because she would have plainly seen that what the RCT demonstrates is that it works in the case of snakes and other such creatures, and the fact that she is part of the population from which the random sample was drawn is in no way pertinent.
Indeed, and the importance of this will become evident later, suppose in a neighbouring garden, where all living creatures happen to be humans, there was a biased-sample (meaning non-random8) trial of this injection, and it was found that the injection does not enhance memory and, in fact, gives a throbbing headache in a large proportion of cases, it is likely that Eve would be tempted to go along with this biased-sample study done on another population rather than the RCT conducted on her own population in drawing conclusions about what the injection might do to her. There is as little hard reason for Eve to reach this conclusion as it would be for her to conclude that the RCT result in her own Garden of Eden would work on her. I am merely pointing to a propensity of the human mind whereby certain biased trials may appear more relevant to us than certain perfectly controlled ones.
Basu’s reasoning confirms what yours truly has repeatedly argued on this blog and in On the use and misuse of theories and models in mainstream economics — RCTs usually do not provide evidence that the results are exportable to other target systems. The almost religious belief with which its propagators portray it, cannot hide the fact that RCTs cannot be taken for granted to give generalizable results. That something works somewhere is no warranty for it to work for us or even that it works generally.