Diagnostic tests are widely used in medicine and many other fields. For electric power infrastructure testing is done on many systems including power transformers and underground cable.
However there is a problem - tests rarely provide perfect predictions. Given this fact, central to diagnostic testing is how to interpret test results. A rigorous framework for probabilistic interpretation is provided here. The framework is implemented as a web app.
Note: This app is not a complete decision model. It illustrates Bayesian Updating. Specifically it does not include test costs and the costs of decision outcomes. For discussion of decision models that integrate Bayesian Updating see Equipment Testing Decision Models.
Two Key Concepts:
The pre-test probability of the condition is the likelihood of the condition based on your assessment prior to the test.
- A test creates two groups - those who test positive and those who test negative -- What is the likelihood that each of these groups has the condition?
The Analytic Framework
Formal probabilistic statements about positive and negative test results require application of Bayes' Theorem and the specification of three parameters. The input parameters are:
- Your pre-test assessment of the likelihood that an object or group of objects has a specific condition.
- For the specific test you must specify the probabilities that the test will return a “false positive” and “false negative” result.
With these parameters and Bayes' Theorem you can make formal probabilistic statements about the likelihood that an object has a condition for both positive and negative test outcomes.
Instructions For Running the Diagnostic Testing Web App
NOTE: The Diagnostic Testing app was designed and written by Stephen Chapel, S.Chapel Associates. The app will run in most web browsers and woks on phones and tablets.
- Enter input parameters or leave the default values.
- Click the Update Assessment button to compute updated likelihoods of the condition.
- Click the Explain Results button for an explanation of the updated probabilities.