# False Positive Paradox

A disease that can be asymptomatic affects one percent of the population.

There’s a test for it that never produces false negatives but it has a five percent false positive rate.

You take the test before travelling, and it comes back positive.

What are the chances you have the disease?

## Answer

A common answer is 95%, but it’s actually only 16.8%.

This is surprising to many people, but remember that only 1% of the population has the disease.

In a group of 10,000 people, we can expect that 100 people will have the disease and 9,900 will not.

Imagine we test everyone in the group.

All 100 people who have the disease will test positive since there are no false negatives.

Of the 9,900 people who don’t have the disease, 9,405 will test negative, and 495 will show false positives.

This means there are 595 positives: 100 of them are true positives and 495 are false positives.

100 true positives ÷ 595 total positives = 16.8% of the people who test positive are true positives

Note: If you took the test because you had symptoms of the disease, your probability judgment should account for this information.

The False Positive Paradox teaches us that when the prevalence of a disease is low, widespread testing of asymptomatic people leads to a high number of false positives.

## Courses

## Fallacy Detectors Part 1

Develop the skills to tackle logical fallacies through a series of 10 science-fiction videos with activities. **Recommended for ages 8 and up.**

## A Statistical Odyssey

Learn about common mistakes in data analysis with an interactive space adventure. **Recommended for ages 12 and up.**

## Symbolic Logic for Teens Part 1

Learn how to make sense of complicated arguments with 14 video lessons and activities. **Recommended for ages 13 and up.**

## Emotional Intelligence

Learn to recognize, understand, and manage your emotions. Designed by child psychologist Ronald Crouch, Ph.D. **Recommended for ages 5 and up.**

## Worksheets

### Symbolic Logic Worksheets

Worksheets covering the basics of symbolic logic for children ages 12 and up.

### Elementary School Worksheets and Lesson Plans

These lesson plans and worksheets teach students in grades 2-5 about superstitions, different perspectives, facts and opinions, the false dilemma fallacy, and probability.

### Middle School Worksheets and Lesson Plans

These lesson plans and worksheets teach students in grades 5-8 about false memories, confirmation bias, Occam's razor, the strawman fallacy, and pareidolia.

### High School Worksheets and Lesson Plans

These lesson plans and worksheets teach students in grades 8-12 about critical thinking, the appeal to nature fallacy, correlation versus causation, the placebo effect, and weasel words.

### Statistical Shenanigans Worksheets and Lesson Plans

These lesson plans and worksheets teach students in grades 9 and up the statistical principles they need to analyze data rationally.