Fisher's exact test

Fisher’s exact test is used in the mathematical field of statistics as well as in other sciences. It involves methods of analyzing variables in an experiment and the relationships between them. Scientists usually use this test when creating tables that compare variables (for example, “Time Spent Studying” and “Test Scores”). English statistician and geneticist Ronald Fisher developed Fisher’s exact test in the early 1920s following a debate about how to make tea. Fisher used a tea-based experiment to determine that adding variables, randomizing samples, and making other changes to the experiment could greatly add to the value and accuracy of experiments.

Background

Ronald Fisher was born in London, England, on February 17, 1890. He excelled at school, particularly in mathematics, and won a math competition that earned him a scholarship to Cambridge University. At Cambridge, Fisher pursued math as well as biology, two fields that would greatly impact the course of his future and contributions to science. Despite a fascination with farming, Fisher received job offers in the mathematical field of statistics.

The job Fisher ultimately accepted was at Rothamsted Agricultural Experiment Station, which was running tests on plant nutrition. This job appealed to both his interests: math and biology. Fisher quickly revolutionized studies at Rothamsted by introducing new variables. Most notably, he created a system of variance in which experiments would be broken into sub-experiments, each of which would be slightly different. He designed these slight variations to highlight instances in which certain variables caused major changes to the results of the experiment. By analyzing the alteration and results, Fisher could use statistical principles to gain a greater understanding of the experiments and results. Such measures eventually became common in many fields of study and experimentation.

In the early 1920s, Fisher took his innovations even farther. First, he debuted new statistical concepts and then proposed a redefinition of statistics itself. He also applied statistical principles to various agricultural projects, including the breeding of plants and small animals. He studied dominant traits, genetic variables, and theories such as Charles Darwin’s natural selection. Fisher began a lifetime of statistical and genetic studies, exploring how various factors contribute to and change numbers as well as organisms of all types. One of his most important and lasting contributions to these studies came to be known as Fisher’s exact test.

Overview

Fisher’s exact test, developed in the early 1920s, is a method of planning and carrying out statistical tests. It is meant to analyze two variables and the relationships between them, often in the creation of contingency tables, which are a way of organizing data to most clearly show the relationships between variables. For example, a contingency table using Fisher’s exact test may address the question, “Is there a relationship between obesity and sugar consumption?” In this case, “Obesity” and “Sugar Consumption” would be the two variables placed on opposite sides of the contingency table. Placing experimental data into each category can help to demonstrate whether a statistical relationship exists between people who eat too much sugar and people who are obese.

This sort of reasoning revolutionized mathematics and many other branches of science. Prior to Fisher’s work in the 1920s, most experiments were not nearly as careful or efficient as they are in modern times. Few scientists used standardized means of performing their experiments, which made it difficult to replicate tests or verify results, a key aspect of the scientific method. Control elements, or aspects of an experiment that are left unchanged and can help to gauge the results of the experiment, were seldom employed. Furthermore, many scientists analyzed their findings incompletely and crudely, failing to draw out the data’s full potential.

Fisher’s findings most impacted the field of statistics, the science that deals with methods for gathering, studying, interpreting, and using empirical data (information gathered by experience or observation). Two concepts underlying statistical studies are uncertainty and variation. Uncertainty refers to people’s inability to know the exact reason for an outcome; this outcome may not have been determined yet or may have been determined but people do not know what it will be yet. Meanwhile, the concept of probability refers to how a statistician approaches various questions and studies the variations in factors that may affect outcomes. Using Fisher’s experimental style, statisticians could better determine the effects of uncertainty and probability on their studies.

For its great importance to science, Fisher’s exact test developed in a rather curious and unassuming manner. While working at the Rothamsted Agricultural Experiment Station, Fisher befriended a colleague, biologist Muriel Bristol. One day, Fisher offered to make Bristol a cup of tea with milk, and she agreed. Without further thought, Fisher poured milk into a cup and then poured in hot tea, as was his habit.

He presented the tea to Bristol, who refused to drink it. Fisher and his colleagues were puzzled by her response, but she explained that he had ruined the cup of tea by adding the milk before the tea, instead of doing the steps in the opposite order. Fisher insisted that there was no difference, since the milk and tea were going to blend in the cup either way. Bristol held fast in her belief that there was a difference, so Fisher challenged her to a taste-test of eight cups of tea. Half were milk-first and half were tea-first. To his amazement, Bristol was able to identify each one correctly. Apparently, the order of adding the hot tea to the cold milk changed the consistency and taste of the drink.

This simple experiment seemed like a mere amusement to some of the scientists but was a revelation to Fisher. He realized that testing the question brought out surprising results. Moreover, by changing the variables of the test, he could make the test more accurate and informative. Fisher used math to determine that the experiment would have been better if he had used more cups of tea, or random numbers of milk-first and tea-first cups in a random order. Changing the experiment in seemingly small ways would highlight various results and help to eliminate the possibility that the results were due to random chance. This principle helped to inspire Fisher’s exact test and encourage scientists of all sorts to conduct and analyze their experiments and variables more carefully.

Bibliography

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