The base rate fallacy, also called base rate bias, indicates the fact that people usually focus on the special information, and ignore the base rate information which will be happening in a large percentage of samples. For example, there are two groups of people. There are 10 people in the first group and 90% of them can play piano. There are 1000 people in the second group and only 10% of those people can play piano. If you meet a person who can play piano, which group does he probably come from? group 1 or group 2? If we only consider the percentage of people who can play piano, you may feel that this person is very likely coming from group 1 because it has a much higher percentage than group 2. However, if we take the base rate into consideration, the result might be totally different. Group 1 has a total of 9 people who can play piano. In comparison, group 2 has 100 people who can play piano. The probability that the person from group 1 is only 8.2%. So, if we only put our focus on the percentage in a group but neglect the base numbers in this group, we may make false decisions or judgements.
Let's consider another example of the base rate fallacy called false positive paradox. For example, imagine doctors are running a test for a certain kind of disease in a group of 1000 people. Let's assume that 40% of the total people are infected with this disease. So, the total number of people having the positive result will be 400. Also, let's assume that the false positive rate of this method is 5%, which means that in all people who are negative, 5% of those people will still receive positive results, which is 30 people. So, if a person's result is positive, the probability that he does get this disease is 93%. Now, let's move another group of 1000 people in which only 2% of them are getting infected. So, the real positive number will be 20 and the false positive number will be 49 people. In this group, if a person gets a positive result, there is only a 29% probability that he will get infected. If we compare the results in these two groups, we will find that, for the same test method which has an accuracy of 95%, in group one the final result is 93% which is close to the accuracy rate. However, in group two, the real accuracy is only 29%, which is much less than the original one. This is what the base rate fallacy is talking about. Since the base rate is small in the second group, the natural error which will take precedence in the final result.
