Editing Categorical variable (section)

===Contrast coding===

The contrast coding system allows a researcher to directly ask specific questions. Rather than having the coding system dictate the comparison being made (i.e., against a control group as in dummy coding, or against all groups as in effects coding) one can design a unique comparison catering to one's specific research question. This tailored hypothesis is generally based on previous theory and/or research. The hypotheses proposed are generally as follows: first, there is the central hypothesis which postulates a large difference between two sets of groups; the second hypothesis suggests that within each set, the differences among the groups are small. Through its [[A priori (epistemology)|a priori]] focused hypotheses, contrast coding may yield an increase in [[Power (statistics)|power]] of the [[statistical test]] when compared with the less directed previous coding systems.<ref name = Cohen/>

Certain differences emerge when we compare our a priori coefficients between [[ANOVA]] and regression. Unlike when used in ANOVA, where it is at the researcher's discretion whether they choose coefficient values that are either [[Orthogonality|orthogonal]] or non-orthogonal, in regression, it is essential that the coefficient values assigned in contrast coding be orthogonal. Furthermore, in regression, coefficient values must be either in fractional or decimal form. They cannot take on interval values.

The construction of contrast codes is restricted by three rules:

# The sum of the contrast coefficients per each code variable must equal zero.
# The difference between the sum of the positive coefficients and the sum of the negative coefficients should equal 1.
# Coded variables should be orthogonal.<ref name = Cohen/>

Violating rule 2 produces accurate ''R''<sup>2</sup> and ''F'' values, indicating that we would reach the same conclusions about whether or not there is a significant difference; however, we can no longer interpret the ''b'' values as a mean difference.

To illustrate the construction of contrast codes consider the following table. Coefficients were chosen to illustrate our a priori hypotheses: Hypothesis 1: French and Italian persons will score higher on optimism than Germans (French = +0.33, Italian = +0.33, German = −0.66). This is illustrated through assigning the same coefficient to the French and Italian categories and a different one to the Germans. The signs assigned indicate the direction of the relationship (hence giving Germans a negative sign is indicative of their lower hypothesized optimism scores). Hypothesis 2: French and Italians are expected to differ on their optimism scores (French = +0.50, Italian = −0.50, German = 0). Here, assigning a zero value to Germans demonstrates their non-inclusion in the analysis of this hypothesis. Again, the signs assigned are indicative of the proposed relationship.

{| class="wikitable"
|-
| '''Nationality''' || '''C1''' || '''C2'''
|-
| French || +0.33 || +0.50
|-
| Italian || +0.33 || −0.50
|-
| German || −0.66 || 0
|}