Pocket Stats: Quick Significance Tests You Can Remember, Part 2

Part 2—Fisher One-Sample Sign Test

This two-part article of this column presents two well-established statistical tools that are easy to remember. Part 1 discussed Tukey’s end count test, which identifies significant differences in the distribution of two samples. In Part 2, you will see how Fisher’s one-sample sign test can be used to determine if the median of a population is different from any given value.

Here is an example one-sample problem:

Example 1: The mortgage department at a local bank has started a project to improve loan processing time. The objective is for 50 percent of loans to be processed from application to closing in 10 days or less. In other words, the median time should be 10 days or less. Baseline measurements of processing time on 20 loan applications are listed below:

13 20 9 12 15 9 12 11 10 14
20 19 12 19 9 28 16 11 27 9

In this sample, five loans took 10 days or less, and 15 did not. Does this data indicate that the median loan processing time is longer than 10 days, or is this just a string of bad luck?

Fisher’s One-Sample Sign Test

Suppose you took a coin out of your pocket and flipped it. You see "heads" and make a note of it. You flip it again and see "heads" again. Then you see three "heads" in a row, and then four, and then five. How many "heads" in a row does it take before you become convinced that the coin is not fair? How confident are you in that conclusion?

Or, suppose you flip the coin 20 times. You observe five "heads" and 15 "tails." Is this series of outcomes unusual enough to convince you that the coin is not fair? How confident are you? This question is identical to Example 1. Example 1 is about loan processing times, not coins. We measured those times in days, but we want to see whether half the times are 10 days or less. To do this, we look at each loan as a trial with two outcomes, either "10 or less" or "more than 10." In the example, we have five "10 or less" outcomes and 15 "more than 10" outcomes, just like the coin experiment.

All these questions can be answered by Fisher’s one-sample sign test. This tool is a well-established method available in MINITAB and other software. This article presents an approximate Pocket Stats version of the same test that is simple enough to remember. Often it is simple enough to calculate in your head. Read more