Dogs Detecting Malaria The following table lists results from ...

Question

Dogs Detecting Malaria The following table lists results from an experiment designed to test the ability of dogs to use their extraordinary sense of smell to detect malaria in samples of children’s socks (based on data presented at an annual meeting of the American Society of Tropical Medicine, by principal investigator Steve Lindsay). Assuming that the dog being correct is independent of whether malaria is present, find the expected value for the observed frequency of 123.

Table showing results of a study on dogs detecting malaria, with counts of correct and incorrect detections.

Accepted Answer

Hello. In this video, we are told that a study was conducted to evaluate the ability of a machine learning model to detect a bacterial infection in patients using blood samples. The experiment recorded whether the model correctly identified the presence or absence of the infection. The results are summarized in the table below. Assuming that the model's accuracy is independent of whether the infection is present, calculate the expected frequency for the observed frequency of 90. So, let's go ahead and just evaluate what the problem is asking us to find. So, we want to find the expected frequency for the observed frequency of 90, and that observed frequency is given in this cell here, where the model was correct while the infection was present. Now, in order to find the expected frequency, The expected frequency is going to be the total from the row involving the cell of 90, multiplied by the total of the column, and this will be divided by the grand total, which is the amount of times that the model was correct and wrong when the infection was present and not present. So, for the expected frequency, let's go ahead and calculate the amount of times that the model was correct when the infection was present and the infection was not present. That is going to be 90 plus 110, which is going to give us a total of 200. Now we need to calculate the amount of times that the model was correct and wrong when the infection was present. That's going to be 90 + 30, which is going to give us 120. Now, for the grand total, we need to take the sum of the amount of times that the model was correct and wrong when the infection was present and not present. So, first, let's sum up the amount of times that the model was correct and wrong when the infection was not present. That is 110 + 70, which is going to give us 180. So for a grand total, That is going to be 120. Plus 180 and this is going to simplify to give us 300. Now, for the expected frequency, we're going to take the sum of the row where the model was correct, while the infection was present and not present, and that is going to be 200. Then we will multiply this by the column where the model is correct and wrong while the infection was present, and that is going to be 120, and we will divide this product by a grand total, which is 300. This is going to simplify to give us 80, and this represents the number of times the model is correct and the infection is present. And with that being said, the solution to this problem is going to be D. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

Key Concepts

Expected Value

Independence

Contingency Table

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