fairfolio
Saved Projects

False Positive and False Negative Paradox

CSEF · 2015 Mathematics & Software

Adlae H. D'Orazio · Hall (Henry) Middle School, Larkspur, Marin County

Overview

Objectives/Goals Testing for diseases sometimes gives false positive or false negative results. Even for tests that are 99% accurate, it was hypothesized that, in the testing of a population, there would be more false positives than true positives and more false negatives than true negatives for rare diseases. The objectives of this project were to see if the hypothesis was correct and to determine the conditions causing false test results to be greater than true test results. Methods/Materials Calculations were done using a population of 100,000 with various disease rates and test accuracies. An Excel spreadsheet was programmed to cover a wide range of possibilities. Experiments were run to simulate the calculations and to check if the calculations worked for a population as low as 200. The experiments involved rolling dice, sometimes 2 and sometimes 3, to match disease rates and test accuracies. Results were tallied and analyzed. Results Calculations showed that there is a greater likelihood of getting more false positives than true positives if the disease is rare and more false negatives than true negatives if the disease is common. The experiments verified the calculations and showed that even a population as low as 200 had a similar result. Conclusions/Discussion The detailed hypothesis, which guessed that greater false tests would occur for rare diseases, was found correct for false positives but incorrect for false negatives (because more false negatives occurred for common diseases). The work from this project adds to the knowledge of doctors and health officials who are concerned about scaring people with false positive results or failing to correctly notify people with false negatives.

Summary statement

The conditions causing the paradox of more false positive than true positive disease test results and more false negative than true negative disease test results were investigated.

Help received

My dad checked my math and helped me write the abstract in the proper format.

Competition history

  • CSEF 2015 Mathematics & Software · Entry J1403

Resources

Related projects

Closest projects by meaning, across every fair and year in the corpus.

Browse more like this

Source: California Science & Engineering Fair public projects

Save projects to your library

Sign in with Google to keep track of projects you find interesting, organized into folders. An account also raises your daily allowance for “Has this been done?”, and lets you create a key for the MCP server with a much higher limit than anonymous use. Browsing stays public.

Continue with Google