The Predictive Probability of Test Calculator

People use tests all the time, even when they don’t think of them as tests. Same with organizations. The Predictive Probability of Test Calculator is designed to overcome a small problem people have dealing with the probabilities associated with tests.

Consider a test advertised as 90% accurate. If the test says it has found what it is looking for, what is the probability that it actually has found it? Most of us want to say 90%. That’s not correct. The answer is we don’t know, not at least until we factor in the base rate. The base rate is the proportion of the population that has the condition.

Try it yourself. Consider any test. An employee drug testing program. Road side breathalyzer. Cancer screening test. Cracks in a pipeline. Performance appraisal. Road surface inspections.  You only have to answer two questions:

1. What is the Base Rate? This is the rate at which the condition you are looking for occurs in the population. Take a reasonable guess based on your experience or empirical evidence.

2. What is the Test Accuracy? This is the advertised or assumed accuracy rate of the test. Is it 90% accurate? 95%?

The Results are the Proportion of False Positives also called the predictive probability. This is the probability that given a positive test (condition found) that the test subject is truly positive (condition present).

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Here are some ideas to spur any creative juices concerning predictive probabilities.

1. Testing Positive for Cancer. What is the chance you have cancer if you have tested positive for it? The Base Rate is the rate of cancer in the population. Play with the numbers. The rarer the cancer, the higher the proportion of false positives. This is why doctors struggle providing advice to patients even after they test positive for rare conditions. Chances are, you still don’t have the condition.

2. Performance Appraisals. What is the proportion of people classified as superior performers that actually are. The Base Rate is the proportion of superior performers you believe to be in your organization. Test accuracy is how good you believe your performance appraisal process to be.

3. Employee drug testing program. Given that an employee has tested positive for drugs and will be fired because of it, what is the probability that the employee is actually doing drugs? The Base Rate is the estimated level of employees actually doing drugs.

4. Breathalyzer Testing. You just blew over .08, the legal limit. What proportion of people testing positive are actually over the limit? The Base Rate is your estimate of the proportion of people driving with blood alcohol levels above .08. Test accuracy is usually assumed to be 99%. Check it out.

5. Physical condition inspections. What is the probability that something actually needs to be repaired given that an inspection says it needs a repair? Take a pipeline inspected for cracks that could cause the pipeline to break. The Base Rate is the proportion of the pipeline that has cracks in it. If an inspection has found cracks, what is the likelihood the cracks are really there? Similar inspections apply to road conditions, new construction and engineering drawing reviews.






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