Base Frequency Fallacy: Characteristics Of This Reasoning Error
There are many fallacies that we can fall into when defending our arguments, whether consciously or not.
On this occasion 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.
The base frequency fallacy, also known by other names, such as base rate bias or even base rate negligence, is a formal fallacy in which, 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 occurs because the person tends to overestimate the importance of the particular case, as opposed 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 happens with any fallacy, the immediate consequence of falling into this error is that we will reach biased conclusions that will not necessarily correspond to reality, which is a problem that could even become serious if the reasoning in question is part of a relevant study
The base frequency fallacy is in turn part of a type of cognitive bias known as extension neglect, or extension neglect. 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 a sample that is too small to an entire population.
In a certain 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 if there is data that indicates otherwise or at least qualify said result.
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 in order to establish a subsequent comparison between them First of all, let’s assume that the pathology 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 in addition, 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 illness when in reality this is not the case. This would add another 50 people to the set of positives (even though they are not really positive), giving 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 our reasoning. To do 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 every 1000. But we had seen that our test has a 5% error, that is, false positives, which translates into 50 people.
It is time to compare both assumptions and see the notable difference that arises between them. In the high incidence scenario, 550 people would be considered infected, of which 500 would actually be infected. That is, 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 false positive paradox occurs. In this case, we have a rate of 60 people out of every 1000 who are counted as positive for the pathology that affects said population.
However, only 10 of those 60 people have the disease, while the rest are erroneous cases that have entered said group due to the measurement defect of our test. What does it mean? If we chose one of these people at random, 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, we are implicitly saying that, therefore, its accuracy is 95%, since that is the percentage of cases in which it will not fail. However, we see that If the incidence is low, this percentage is distorted to the extreme since in the first case we had a 90.9% probability that a positive would really be positive, and in the second this 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 in this way we will be able to visualize the effect and above all the risk that we run by drawing hasty conclusions without have taken into account the overview of the problem at hand.
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 shows the type 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 jobs consisted of asking volunteers to enter the academic grades they considered for a fictitious group of students, according to a certain distribution. But The researchers observed a change when they gave data about a specific student, even though this had no influence on their possible grade
In that case, the participants tended to ignore the distribution that had been previously indicated to them for the group of those students, and estimated the grade individually, even when, as we have already said, the data provided was irrelevant for this particular task. .
This study had some impact beyond demonstrating another example of the base frequency fallacy. And it revealed a very common situation in some educational institutions, which are student selection interviews. These processes are used to recruit students with the greatest potential for success.
However, following the base frequency fallacy reasoning, 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 dedicated a long part of their career 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 rule of representativeness.
The 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 internal reasons).
In other words, information from the particular case is preferred, even if it is not truly representative, than general data that, probabilistically, should have more weight when drawing conclusions in a logical manner.
All of these considerations, taken together, will now allow us to have a global vision of the problem of falling into the base frequency fallacy, although sometimes it is difficult to realize this error.
