Statistics Dictionary

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Comparisons

A comparison (aka, a contrast) is a weighted sum of factor level means. Researchers use comparisons to address additional questions that are not answered by a standard, omnibus analysis of variance.

Mathematically, a comparison can be expressed as:

k L = Σ cj Xj j=1

In addition, all comparisons are subject to the following constraint:

k Σ j=1
  nj cj = 0  

In the equations above, L is the value of the comparison, cj is a coefficient (weight) for treatment j, Xj is the mean score for treatment j, nj is the number of subjects assigned to treatment j , and k is the number of treatment groups.

See also:  Comparison of Treatment Means | Orthogonal Comparisons | Multiple Comparisons