Breaking the F-barrier: How the use of a visual representation of Fisher’s F-ratio can aid student comprehension of orthodox statistics

Abstract

Universal laws are notoriously hard to discover in the social sciences, but there is one which can be stated with a fair degree of confidence: “all students hate statistics”. Students in the social sciences often need to learn basic statistics as part of a research methods module, and anyone who has ever been responsible for teaching statistics to these students will soon discover that they find it to be the hardest and least popular part of any social science syllabus. A typical problem for students is the use of Fisher’s F-test as a significance test, which even in the simple case of a one-factor analysis of variance (ANOVA) presents difficulties. These are two in number. Firstly, the test is presented as a test of the null hypothesis, that is, that there is no effect of one variable (the independent variable, IV) on the other, dependent variable (DV). This highlights the opposite of what one generally wants to prove, the experimental hypothesis, which is usually that there is an effect of the IV on the DV. Students, if they think about the question at all, may be tempted to ask “why not try to prove the experimental hypothesis directly rather than using this back-to-front approach?” Secondly, the F-ratio itself is presented in the form of an algebraic manipulation, involving the ratio of two mean sums of squares, and these means are themselves moderately complicated to understand. Even students specializing in mathematics often find algebra difficult, and to non-mathematicians this formula is simply baffling. Instructors do not usually make a serious attempt to remedy this confusion by attempting to explain what the F-ratio is attempting to measure, and when they do, the explanation is not usually very enlightening. Students may struggle with the statement that the F-ratio is the ratio of “two different estimates of the variance of the population being sampled from, under the null hypothesis”. So what? The result is that students frequently end up applying statistical analysis programs such as SPSS and R, without having the faintest understanding of how the mathematics works. They use the results in a mechanical way, according to a procedure learned by rote memory, and may overlook different tests which might be more appropriate for their data. This might be called the cookbook approach to data analysis, and it is the opposite of the ultimate aim of high quality teaching, which is to provide a deep understanding of principles, which will allow the student to use these principles flexibly in real life challenges, without violating the assumptions of the statistical tests being employed