# Eta-squared and partial eta-squared

## About eta-squared

- A measure of relationship; like a correlation coefficient it tells you on
a scale 0 to 1 how much of variance in DV can be account for by each IV.
- Analogous to r
^{2} and can be thought of as a % on a scale 0-100.
- It is a useful addition to just being told if a relationship or difference
is significant.
- Eta-squared reflects the percentage of DV variance explained by the IVs in
the sample data. As an estimate of variance explained in the population
it is upwardly biased (i.e., an overestimate). Thus, omega-squared is a
recommended alternative.

## How to calculate eta-squared

## Eta-squared

- h
^{2 }= SS_{between} / SS_{total}
- There will be one h
^{2 }per effect
(i.e. per IV plus for an interaction).
- The h
^{2}s will sum to 1.
- Not supplied by SPSS.
- Preferred to h
_{p}^{2}
- % of variance explained by each IV.

## Partial eta-squared

- h
_{p}^{2
}= SS_{between} / SS_{total + }
SS_{error}
- Supplied by SPSS.
- Do not sum 1, and therefore can be difficult to interpret.
- Generally not recommended.

## Designs

- In 1-way ANOVA, eta-squared and partial eta-squared are the same.
- For more complex designs, the partial eta-squared will generally be larger
than eta-squared.
- For a mixed ANOVA, eta-squareds needs to be calculated separately within
the context of the within-subject effects ANOVA table and the between-subject
effects ANOVA table. In this situation, the eta-squareds will sum to 1
for within-subjects, and the eta-squared will to 1 for the between-subject
effects. But they cannot all be combined to equal 1.