Mathematics and Applied Statistics Lesson of the Day – Contrasts

June 19, 2015

(This article was originally published at The Chemical Statistician » Statistics, and syndicated at StatsBlogs.)

A contrast is a linear combination of a set of variables such that the sum of the coefficients is equal to zero. Notationally, consider a set of variables

$\mu_1, \mu_2, ..., \mu_n$ .

Then the linear combination

$c_1 \mu_1 + c_2 \mu_2 + ... + c_n \mu_n$

is a contrast if

$c_1 + c_2 + ... + c_n = 0$ .

There is a reason for why I chose to use $\mu$ as the symbol for the variables in the above notation – in statistics, contrasts provide a very useful framework for comparing multiple population means in hypothesis testing. In a later Statistics Lesson of the Day, I will illustrate some examples of contrasts, especially in the context of experimental design.