Planned Comparisons

Planned Comparisons

• Also called: a-priori comparisons or planned contrasts.
• Used to test specific group differences to evaluate specific hypotheses (stated prior to data collection).
• Two general types of planned comparisons.
  • Simple Comparisons (we'll stick to these here).
    • Each comparison is used to compare two groups.
    • With only two groups always, because
  • Complex Comparisons.
    • Each comparison is used to compare two or more groups.
    • e.g., Orthogonal contrasts.

Simple Comparisons

• Suppose, we hypothesized (prior to data collection) that the Red group would recall more words than the Blue group and the Green group would recall less words than the Blue group.
• To do any simple comparison, we need to calculate for that comparison.
• We need a new (always = 1) and a new grand mean ( ) for each comparison.
• But, we use the same and which leads to the same
• Then, for each comparison the usual steps are involved:
• You may wish to control for family-wise error rate inflation by dividing the significance level by the number of comparisons.

Simple Comparisons Example

• Recall, we hypothesized (prior to data collection) the Red group would recall more words than the Blue group and the Green group would recall less words than the Blue group.
• This necessitates two planned comparisons.
  • One to evaluate and
  • One to evaluate and
• Using and and with a significance level of 0.05, we get for each comparison.

http://faculty.vassar.edu/lowry/apx_d.html

Planned Comparison 1: Red ( ) versus Blue ( )

and are the same as was used for the omnibus , so is the same as well: 2.083

So; we reject the null hypothesis and conclude that the Red group recalled significantly more words than the Blue group.

Planned Comparison 2: Green ( ) versus Blue ( )

and are the same as was used for the omnibus , so is the same as well: 2.083

So; we reject the null hypothesis and conclude that the Green group recalled significantly fewer words than the Blue group.

Family-wise and Pair-wise Error Rates

• Sometimes called the Bonferroni Procedure (after it's founder), it is used to control family-wise error inflation when multiple tests are done in one study.
• FW = desired significance level (or alpha level) divided by the number of comparisons.
• For example, if doing 3 comparisons and wanting a total significance level of 0.05, then:
  • is used for each comparison.
  • Often necessary to find an distribution table with exact values, this can be difficult because; most tables are abbreviated for common cutoff points.
• Should be considered when doing planned comparisons.
• Some Post-hoc tests have embedded controls for error rates.