Base frequency fallacy: characteristics of this bias

There are many fallacies we can fall into when defending our arguments, whether consciously or not.

This time we will focus on one known as the base frequency fallacy. We will discover what this bias consists of, what consequences it has when we use it and we will try to support it with some examples that allow us to visualize this concept in a simpler way.

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What is the base frequency fallacy?

The base frequency fallacy, also known by other names, such as base rate bias or even base rate negligence, is a formal fallacy in the that, starting from a specific case, a conclusion is established about the general prevalence of a phenomenon, even if contrary information has been given in that sense.

This fallacy takes place because the person tends to overestimate the importance of the particular case, in contrast to the data of the general population. It is called the base frequency fallacy precisely because it is the base rate that is put in the background, giving greater relevance to the particular case in question.

Of course, as with all fallacies, the immediate consequence of falling into this error is that we will reach biased conclusions that will not necessarily correspond to reality which it is a problem that could even become serious if the reasoning in question is part of a relevant study.

The base frequency fallacy is itself part of a type of cognitive bias known as neglect of extension, or neglect of extension. This error consists, fundamentally, in not taking into account the sample size of a certain analysis. This phenomenon can lead to unfounded conclusions if, for example, we extrapolate data from too small a sample to an entire population.

In a sense, this is precisely what would be happening when we talk about the base frequency fallacy, since the observer could attribute the results of the particular case to the entire study sample, even with data indicating otherwise or at least qualify said result.

The case of false positives

There is a special case of the base frequency fallacy in which the problem it represents can be visualized, and it is the so-called false positive paradox. To do this, we must imagine that the population is threatened by a disease, something simple in these times, where we have experienced the coronavirus or COVID-19 pandemic firsthand.

Now we will imagine two different assumptions to be able to establish a later comparison between them. First, suppose that the disease in question has a relatively high incidence in the general population, for example, 50%. This would mean that out of a group of 1000 people, 500 of them would have this pathology.

But also, we must know that the test used to check whether a person has the disease or not, has a 5% probability of giving a false positive, that is, of concluding that an individual has said ailment when in reality It is not like this. This would add another 50 people to the set of positives (although in truth they are not), for a total of 550. Therefore, we would estimate that 450 people do not have the disease.

To understand the effect of the base frequency fallacy we must continue in our reasoning. For this we must now propose a second scenario, this time with a low incidence of the pathology in question. We can estimate this time that there would be 1% infected. That would be 10 people out of 1000. But we had seen that our test has a 5% error, that is, false positives, which translates to 50 people.

It is time to compare both assumptions and see the remarkable difference that emerges between them. In the high incidence scenario, 550 people would be considered infected, of which 500 would actually be. Namely, taking one of the people considered positive, at random, we would have a 90.9% probability of having selected a truly positive subject, and only 9.1% of it was false positive.

But the effect of the base frequency fallacy is found when we review the second case, since that is when the paradox of false positives happens. In this case, we have a rate of 60 people out of every 1000 who are counted as positive in the pathology that affects this population.

However, only 10 of those 60 have the disease, while the rest are erroneous cases that have entered this group due to the measurement defect of our test. What does it mean? That if we chose one of these people randomly, we would only have a 17% chance of having found a real patient, while there would be an 83% chance of selecting a false positive.

By initially considering that the test has a 5% chance of establishing a false positive, implicitly we are saying that therefore its accuracy is 95%, since that is the percentage of cases where it will not fail. However, we see that if the incidence is low, this percentage is distorted to the extreme, because in the first assumption we had a 90.9% probability that a positive was really positive, and in the second that indicator dropped to 17%.

Obviously, in these assumptions we are working with very distant figures, where it is possible to clearly observe the fallacy of the base frequency, but that is precisely the objective, since this way we will be able to visualize the effect and especially the risk that we run when drawing hasty conclusions without having taken into account the panorama of the problem that occupies us.

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Psychological studies on the base frequency fallacy

We have been able to delve into the definition of the base frequency fallacy and we have seen an example that it reveals the kind of bias we fall into if we allow ourselves to be carried away by this error in reasoning. Now we will investigate some psychological studies that have been carried out in this regard, which will provide us with more information about it.

One of these tasks consisted of asking the volunteers to enter the academic grades that they considered a fictitious group of students, according to a certain distribution. But the researchers observed a change when they gave data about a specific student, although this had no influence on their possible rating.

In this case, the participants tended to ignore the distribution that had been previously indicated for the group of these students, and estimated the grade individually, even when, as we have already said, the data provided was irrelevant for this task in particular.

This study had some impact beyond the demonstration of another example of the base frequency fallacy. And it is that it revealed a very common situation in some educational institutions, which are student selection interviews. These processes are used to attract students with the greatest potential for success.

However, following the reasoning of the base frequency fallacy, it should be noted that general statistics will always be a better predictor in this sense than the data that an evaluation of the person can provide.

Other authors who have devoted a long part of their careers to studying different types of cognitive biases have been the Israelis, Amos Tversky and Daniel Kanheman. When these researchers worked on the implications of the base frequency fallacy, they found that its effect was based mainly on the representativeness rule.

The also psychologist, Richard Nisbett, considers that this fallacy is a sample of one of the most important attribution biases, such as the fundamental attribution error or correspondence bias, since the subject would be ignoring the base rate (the external reasons, for the fundamental attribution bias), and applying the data of the particular case (the reasons internal).

In other words, the information of the particular case, even if it is not really representative, is preferred than the general data that, probabilistically, should have more weight when drawing conclusions in a logical way.

All these considerations, together, will allow us now to have a global vision of the problem that supposes falling into the fallacy of the base frequency, although sometimes it is difficult to realize this error.

Bibliographic references:

• Bar-Hillel, M. (1980). The base-rate fallacy in probability judgments. Acta Psychologica.
• Bar-Hillel, M. (1983). The base rate fallacy controversy. Advances in Psychology. Elsevier.
• Christensen-Szalanski, J.J.J., Beach, L.R. (1982). Experience and the base-rate fallacy. Organizational behavior and Human Performance. Elsevier.
• Macchi, L. (1995). Pragmatic aspects of the base-rate fallacy. The Quarterly Journal of Experimental Psychology. Taylor & Francis.
• Tversky, A., Kahneman, D. (1974). Judgment under uncertainty: Heuristics and biases. Science.