# Base frequency fallacy: characteristics of this reasoning error

**The base frequency fallacy influences the way we think about probabilities.**

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

This time we will focus on one known as the **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.

## What is the base frequency fallacy?

The base frequency fallacy, also known by other names, such as prime rate bias or even prime rate neglect, is a fallacy of a formal type in which, starting from a specific case, a conclusion is drawn about the general prevalence of a phenomenon, even though contrary information to that effect has been given.

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 prime rate that is put in the background, giving greater relevance to the particular case in question.

Of course, as 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. **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 extension neglect, or extension neglect. This error consists, fundamentally, in not taking into account the sample size of a given analysis. This phenomenon can lead to unsubstantiated conclusions if, for example, we extrapolate data from a sample that is too small to an entire population.

In a sense, this is precisely what would be occurring when we speak of the base frequency fallacy, since **the observer could attribute the results of the particular case to the whole study sample, even if there are data that indicate the opposite** or at least qualify such a result.

### The case of false positives

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

Now **We will now imagine two different assumptions in order to be able to establish a later comparison between them.**. First, let us 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 we should also 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 the disease when in fact he or she does not. This would add another 50 people to the pool of positives (even though they are not), giving a total of 550, **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. To do this we must now pose 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 rate, i.e. false positives, which translates into 50 people.

It is time to compare the two scenarios and see the notable difference that arises between them. In the high-incidence scenario, 550 people would be considered infected, of whom 500 would actually be infected, **taking one of the people considered positive, at random, we would have a 90.9% chance of having selected a truly positive subject**and only 9.1% that it would be a false positive.

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

However, only 10 of those 60 people have the disease, while the rest are erroneous cases that have entered this group due to the measurement defect of our test. What does this mean? If we were to choose one of these people at random, we would only have a 17% chance of finding 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**In the first case, we had a 90.9% probability that a positive test was actually positive, and in the second case this indicator dropped to 17%.

Obviously, in these assumptions we are working with very distant figures, where the base frequency fallacy can be clearly observed, but that is precisely the objective, since this way we can visualize the effect and above all the risk we run when we draw hasty conclusions without having taken into account the overview of the problem at hand.

## Psychological studies about 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 led by this error in reasoning. We will now delve into some psychological studies that have been carried out on the subject, which will provide us with more information on the subject.

One of these jobs consisted of asking volunteers to give the academic grades they considered to a fictitious group of students, according to a certain distribution. But **the researchers observed a change when they gave data about a particular student, even though the data had no influence on his or her 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 they 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. It highlighted a very common situation in some educational institutions, namely student selection interviews. Such processes are used to capture 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 regard than the data that an assessment of the individual can provide.**.

Other authors who have devoted much of their careers to the study of different types of cognitive biases are 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 mainly based on the representativeness rule.

Richard Nisbett, also a psychologist, considers this fallacy to be **of one of the most important attribution biases**This is the fundamental attribution error or correspondence bias, since the subject would be ignoring the prime rate (the external motives, for the fundamental attribution bias), and applying the data of the particular case (the internal motives).

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

All these considerations, taken together, will now allow us to have an overall view of the problem of falling into the base frequency fallacy, although it is sometimes complicated to realize this error.

Bibliographical 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.

(Updated at Mar 28 / 2023)