In Exercises 21–24, use these results from the “1-Panel-THC” test for marijuana use, which is provided by the company Drug Test Success: Among 143 subjects with positive test results, there are 24 false positive (incorrect) results; among 157 negative results, there are 3 false negative (incorrect) results. (Hint: Construct a table similar to Table 4-1.)




Testing for Marijuana Use


b. How many of the subjects had a true negative result?

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the number of subjects who had a true negative result. A true negative result occurs when the test correctly identifies a subject as not using marijuana.
2. Step 2: Identify the given information. From the problem, we know: (1) There are 157 negative test results in total, (2) Among these, 3 are false negatives (incorrect results).
3. Step 3: Recall the relationship between total negative results, false negatives, and true negatives. The formula is: Total Negative Results = True Negatives + False Negatives.
4. Step 4: Rearrange the formula to solve for True Negatives. This gives: True Negatives = Total Negative Results - False Negatives.
5. Step 5: Substitute the given values into the formula. Use the total negative results (157) and the false negatives (3) to calculate the true negatives. This will give you the number of subjects with a true negative result.

Key Concepts

True Negative

A true negative result occurs when a test correctly identifies a subject as not having the condition being tested for. In the context of drug testing, it means that the test accurately indicates that a person does not use marijuana when they actually do not. Understanding true negatives is crucial for evaluating the effectiveness of a test and calculating its accuracy.

False Positive and False Negative

False positives and false negatives are critical concepts in diagnostic testing. A false positive occurs when a test incorrectly indicates the presence of a condition (e.g., a positive drug test for someone who does not use drugs), while a false negative indicates the absence of a condition when it is actually present. These concepts help in assessing the reliability of a test and understanding its implications in real-world scenarios.

Contingency Table

A contingency table is a statistical tool used to summarize the relationship between two categorical variables. In this case, it can be used to organize the results of the drug test, showing the counts of true positives, true negatives, false positives, and false negatives. This visual representation aids in calculating various statistics, such as sensitivity and specificity, which are essential for evaluating the test's performance.