I’ve read numerous definitions of Type I versus Type II errors. Written by statisticians, these definitions are convoluted and hard to understand. Type I errors are false positives and Type II errors are false negatives. Listen to this gobbly gook from an Applied Statistics text:

Type I error is when we reject a true null hypothesis. Type II error is when we do not reject a false null hypothesis. Although we cannot eliminate the possibility of making an error in hypothesis testing, we can control the criterion for rejecting the null hypothesis . . .

I’ve struggled with what this actually means and how to explain it well until a recent science fair experience.

At the fair, on the first day of judging, the scientific posters are evaluated without the students present. The top 25% are identified and these students are called back for finals. This year, eight of my ten students were called for finals. One of the eight was called just for a category award. That basically left three in the lower 75%. One was not surprising to me. His project “a” was weak, poorly conceived, and poorly presented. The other two, however, were a bit surprising.

As I was traveling home from a graduate stats review I was conducting, I had a student “b” call me very upset about her results in the science fair. She did not make finals. I was surprised, because she was a finalist the previous year and her project this year was far stronger. She had, only the week before, won first place at a different science symposium for her work. The other student, “g,” who had not made finals also placed first in her category at yet a third event. Student g failed to heed my advice about her poster – I informed her that it was convoluted and difficult to follow. Without her present, the judges might have a hard time evaluating it. And so it goes – that project was not selected as a fair finalist. However, that student was named a finalist for a special award category. Unfortunately b’s ride ended at that phone call. However, g ’s trip continued on. She wound up winning many special awards, even though she was not recognized as a finalist:

Xerox Computer Science Awards – Medallist
United Technologies Corporation Award
Quinnipiac University ScholarshipConnecticut Academy for Education DeRocco Award for Excellence
IEEE, Connecticut Section Award
Meyerand Young Woman Scientist Award
The Howard Lessoff Award for Excellence

As g received these awards, I thought to myself. Surely a mistake was made in the preliminary judging. I know why it was made – the judges couldn’t get past the poster and see the great science that was there. And then it hit me . . .

This is a Type II error. B and g were false negatives. They should have been there but they weren’t. This was a pretty bad error, because there was no way to correct it. If a project was selected in the prelims but wasn’t good, it would have made it to finals, but would have been weeded out there – the false positive. Not as bad here, because a correction can take place at a later time.

Summary:
The false positive – the student who was recognized, but should not have been.
The false negative – the student who had the great project, but wasn’t recognized.