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Confidence Intervals

A Bedtime Story

Twa, Michael D.

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Optometry and Vision Science: May 2020 - Volume 97 - Issue 5 - p 315
doi: 10.1097/OPX.0000000000001527
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Given the current disruption of normal life, I have decided to offer a very different format for the next few editorials. Something that is whimsical and hopefully entertaining and maybe a little thought provoking. This first piece is a children's story about P values and confidence intervals.

Once upon a time, there was a small village where all the people lived in complete comfort and certainty. The village was painted in only black or white; there was no color anywhere. The zoo was filled with pandas, ravens, zebras, and other creatures that felt right at home.

Everything was very clear, which made things quite simple and pleasant for everyone. Answers to questions were either yes or no. Explanations were never required. Few people ever bothered themselves with questions like why or how, because that created a lot of unnecessary discussion and confusion and was believed to contribute to wrinkles on the forehead and gray hairs (which were not allowed).

If ever a difficult question was asked that could not be answered with a simple yes or no, the villagers took their question to a special person, Ronald Fisher. Ronald would listen to difficult questions and reduce them to a yes or no response, which was pleasing for everyone. He would then consult his magical tables of probability to divide things into two groups: those that were significant (YES) and those that were not (NO). Although the people were happy and comfortable with the answers that Ronald gave, he was not always correct. It turns out that, 5% of the time, Ronald's answers were wrong.

Then, one day, a traveler from another village came to visit. She was dressed very differently from the villagers. She wore bright colorful clothing with an interesting hat and a lovely bag. It was impossible to describe her in simple terms. This made some people very uncomfortable, and they did not make her feel welcome. Others who saw her were curious to know more and could not look away; they were kind to her. They saw something different and were not afraid. Her name was Jerzy Neyman. She was confident and she embraced uncertainty and possibilities. In fact, variety was so important to her that she introduced the idea to others wherever she traveled. Nothing about her was easily described. Her hair was a shade of brown with hints of red chestnut. Her shoes were not pink or red but somewhere in between. Depending on the light, her ring flashed a spectrum of colors that demanded a more complex description.

When the villagers asked Jerzy to compare two things, her answer was usually: “It depends…not just on the difference, but also on the variety of other possibilities.” Her stories were interesting and brought color to the village. The villagers learned to accept that the answers to questions are more informative when you consider the full range of possibilities and probabilities. The villagers began to understand the reasons behind the answers they were given by Ronald, including why the answers were sometimes wrong. Then, people began asking more interesting questions.

© 2020 American Academy of Optometry