Mathematics and Applied Statistics Lesson of the Day – Contrasts

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.

3 Responses to Mathematics and Applied Statistics Lesson of the Day – Contrasts

  1. msanregret says:

    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!

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