# Mathematics and Applied Statistics Lesson of the Day – Contrasts

June 19, 2015 3 Comments

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

.

Then the linear combination

is a contrast if

.

There is a reason for why I chose to use 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.

I remember learning about contrasts in my multivariate statistics class. Unfortunately, I’ve forgotten how to use them exactly… I’ll stay tuned for the experimental design lessons, I look forward to learning more!

Hi Mitchell,

Note that I have already written many Statistics Lessons of the Day on experimental design, though this is my first one about contrasts.

Hope you find the other lessons to be useful.

Eric

Okay I will check them out!