There are many mistakes we can fall into when it comes to making our arguments, whether consciously or not.

This time we will focus on the one known as **the base frequency error**. We will find out what this bias is, what consequences it has when we use it and we will try to support it in a few examples that allow us to visualize this concept in a simpler way.

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## What is the base frequency error?

The base frequency fallacy, also known by other names, as the base rate bias or the base rate neglect, is a formal fallacy in which, from a specific case, is established a conclusion on the general prevalence of a phenomenon, although information to the contrary has been provided in this regard.

This error occurs because **the person tends to overestimate the importance of the particular case, as opposed to general population data**. This is called the base rate error precisely because it is the base rate that is put in the background, and gives more 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 come to biased conclusions that do not necessarily correspond to the reality that is. **a problem that could even become serious if the reasoning in question is part of a relevant study**.

Base frequency error is part of a type of cognitive bias known as extension neglect, or extension neglect. This error essentially consists of not taking into account the sample size of a given analysis. This phenomenon can lead to unfounded conclusions if, for example, we extrapolate data from a sample that is too small to a whole population.

In a sense, this is precisely what would happen when we talk about the base frequency fallacy, because **the observer could attribute the results of a particular case to the entire study sample, even if they contain data indicating otherwise** or at least qualify this result.

### The case of false positives

There is a special case of base frequency error in which the problem it represents can be visualized, and this is called the false positives paradox. That is why we have to imagine that the population is threatened by disease, something simple in these times, when we have experienced the coronavirus or COVID-19 pandemic firsthand.

Now **we will imagine two different hypotheses to be able to establish a later comparison between them**. First, we assume that the condition 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 would have this pathology.

But in addition, you should know that the test used to verify whether a person has the disease or not has a probability of 5% of giving a false positive, that is to say of concluding that an individual has this disease then that in fact it is not. like that. This would add 50 more people to the overall good (although in truth they are not), making a total of 550. Therefore, **it is estimated that 450 people do not have the disease**.

To understand the effect of the base frequency error, we must continue in our reasoning. This is why we must now consider 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 make 10 out of 1000 people. But we saw that our test has a 5% error, ie false positives, which translates to 50 people.

It’s time to compare the two hypotheses and see the remarkable difference between them. In the high incidence scenario, 550 people would be considered infected, of which 500 would actually be infected. **by taking one of the people judged positive, at random, we would have a 90.9% chance of having selected a really positive subject**, and only 9.1% false positives.

But the effect of the base frequency error is when we look at the second case, as it is when the false positives paradox occurs. In this case, we have a rate of 60 people out of 1000 who are counted as positive in the pathology that affects this population.

However, only 10 of those 60 people have the disease, while the rest are spurious cases that entered this group due to our test’s failure to measure. What does mean ? That 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.

Considering initially that the test has a 5% chance of establishing a false positive, we implicitly say that, therefore, its accuracy is 95%, because 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**, because in the first case we had a probability of 90.9% that a result would be really positive, and in the second, this indicator fell to 17%.

Obviously, in these cases we are working with very distant figures, where it is possible to clearly observe the fallacy of the base frequency, but this is precisely the goal, because in this way we can visualize the effect and above all the risk we run when extracting ‘n hasty conclusions without taking into account the overview of the problem presented to us.

## Psychological Studies on the Base Frequency Fallacy

We were able to delve deeper into the definition of base frequency error and saw an example that highlights the type of bias we fall into if we get carried away by this error in reasoning. We are now going to investigate some psychological studies that have been done on this subject, which will provide us with more information about it.

One of these jobs involved asking volunteers to write down the academic grades that they considered to be a group of fictitious students, according to a certain distribution. Corn **researchers observed a change when they provided data on a specific student, even though this did not influence the possible grade**.

In this case, participants tended to ignore the distribution that had been previously given to them for all of these students and estimate the score individually, even when, as we have already said, the data provided was not relevant for this. particular task.

This study had repercussions beyond demonstrating another example of the base frequency error. And it is that he showed a very common situation in some educational institutions, which are the student selection interviews. These processes are used to capture the students with the greatest potential for success.

However, following the reasoning of the base frequency error, it should be borne in mind that **general statistics will always be a better predictor in that sense than data that can provide an assessment of the person**.

Other authors who have spent much of their careers studying different types of cognitive bias are the Israelis, Amos Tversky, and Daniel Kanheman. When these researchers worked on the implications of the base frequency error, they found that its effect was based primarily on the representativeness rule.

A psychologist, Richard Nisbett, also considers this error to be **a sample of one of the most important attribution biases**, such as fundamental attribution error or correspondence bias, since the subject would ignore the base rate (external reasons, for fundamental attribution bias), and apply the special case data (internal reasons).

In other words, the information of the particular case is preferred, although it is not really representative, than the general data which, probably, should have more weight at the time of. draw conclusions logically.

All these considerations, taken together, will now allow us to have a global vision of the problem posed by the fallacy of the base frequency, although it is sometimes difficult to realize it.

#### Bibliographical references:

- Bar-Hillel, M. (1980). The base rate error in probability judgments. Psychological record.
- Bar-Hillel, M. (1983). The controversy over the base rate error. Advances in psychology. Elsevier.
- Christensen-Szalanski, JJJ, Beach, LR (1982). The experience and error of the base rate. Organizational behavior and human performance. Elsevier.
- Macchi, L. (1995). Pragmatic aspects of the base rate fallacy. The Quarterly Journal of Experimental Psychology. Taylor and François.
- Tversky, A., Kahneman, D. (1974). Judgment under uncertainty: heuristics and bias. Science.