Naked Statistics

Charles Wheelan's Naked Statistics is an introduction to interpreting statistical ideas. It is a useful choice if formulas feel disconnected from the claims you see in reports. The calculation below is an original Nuxflo example of why describing a sample matters as much as calculating a percentage.

Who answered the survey?

A library emails a survey to 500 members. One hundred respond, and 80 respondents support longer evening hours. “Eighty percent of respondents support longer hours” accurately describes the returns. “Eighty percent of members support longer hours” adds an assumption: that the people who replied represent all members.

We know the views of 100 members and do not know the views of 400. If every nonrespondent opposed the change, support among all 500 would be 16%. If every nonrespondent supported it, support would be 96%. These are extreme possibilities, not a confidence interval. They show how much information is missing without assumptions about nonrespondents.

More replies are not the only issue

Imagine putting the same survey on a poster beside the evening entrance. You might collect many answers while disproportionately reaching people who already visit late. Increasing the number of responses does not automatically repair the way the sample was selected.

A better report would show the question, number invited, number responding, collection method, and groups that may be underrepresented. A follow-up sample designed to reach daytime visitors and less frequent members could reveal a different pattern. It might also confirm the first result; uncertainty is not evidence that the result is false.

Use the denominator as a reading habit

Whenever you encounter a percentage, finish the sentence “out of which people or events?” Then ask which eligible cases are missing. In this example, also separate preference from likely use: someone can support longer hours without planning to attend.

Choose this book for accessible statistical interpretation. If you want to turn an uncertain quantity into a specific measurement plan, continue with How to Measure Anything.