Editing Categorical variable (section)

===Effects coding===

In the effects coding system, data are analyzed through comparing one group to all other groups. Unlike dummy coding, there is no control group. Rather, the comparison is being made at the mean of all groups combined (''a'' is now the [[grand mean]]). Therefore, one is not looking for data in relation to another group but rather, one is seeking data in relation to the grand mean.<ref name = Cohen/>

Effects coding can either be weighted or unweighted. Weighted effects coding is simply calculating a weighted grand mean, thus taking into account the sample size in each variable. This is most appropriate in situations where the sample is representative of the population in question. Unweighted effects coding is most appropriate in situations where differences in sample size are the result of incidental factors. The interpretation of ''b'' is different for each: in unweighted effects coding ''b'' is the difference between the mean of the experimental group and the grand mean, whereas in the weighted situation it is the mean of the experimental group minus the weighted grand mean.<ref name = Cohen/>

In effects coding, we code the group of interest with a 1, just as we would for dummy coding. The principal difference is that we code −1 for the group we are least interested in. Since we continue to use a ''g'' - 1 coding scheme, it is in fact the −1 coded group that will not produce data, hence the fact that we are least interested in that group. A code of 0 is assigned to all other groups.

The ''b'' values should be interpreted such that the experimental group is being compared against the mean of all groups combined (or weighted grand mean in the case of weighted effects coding). Therefore, yielding a negative ''b'' value would entail the coded group as having scored less than the mean of all groups on the dependent variable. Using our previous example of optimism scores among nationalities, if the group of interest is Italians, observing a negative ''b'' value suggest they obtain a lower optimism score.

The following table is an example of effects coding with ''Other'' as the group of least interest.

{| class="wikitable"
|-
| '''Nationality''' || '''C1''' || '''C2''' || '''C3'''
|-
| French || 0 || 0 || 1
|-
| Italian || 1 || 0 || 0
|-
| German|| 0 || 1 || 0 
|-
| Other || −1 || −1 || −1 
|}