Eta Squared / Partial Eta Squared

Statistics Definitions > Eta Squared / Partial Eta Squared

What is Eta Squared?

Eta squared is the proportion of variance associated with one or more main effects, errors or interactions in ANOVA.


The formula is:

Eta2 = SSeffect / SStotal, where:

SSeffect is the sums of squares for the effect you are studying.
SStotal is the total sums of squares for all effects, errors and interactions in the ANOVA study.
You might also see the formula written, equivalently, as:
Eta2 = SSbetween / SStotal, where:

partial eta squared
ANOVA results with mean square highlighted. Sums of squares are reported to the left.

Eta squared is easy to calculate from ANOVA output.

For example, let’s say you were studying depression with main effects that include general anxiety, sleep disorders and major illness. You perform an ANOVA and get the following results:

  • Total SS: 62.29
  • Anxiety SS: 4.08
  • Sleep disorders SS: 9.2
  • Major illness SS: 19.54.

Dividing each individual SS by the total, we find Eta2 for each main effect as follows:
Eta2Anxiety: SSAnxiety = 4.08/62.29 = 0.066 = 6.6%.
Eta2Sleep disorders: SSSleep disorders = 9.2/62.29 = 0.148 = 14.8%.
Eta2Major illness: SSMajor illness = 19.54/62.29 = 0.314 = 31.4%.
These results show that 6.6% of variance is associated with anxiety, 14.5% of variance is associated with sleep disorders and 31.5% of variance is associated with major illness. This leads to the conclusion that major illness is the most important main effect.

Partial Eta Squared

Partial eta squared is the ratio of variance associated with an effect, plus that effect and its associated error variance. The formula is similar to eta2:

Partial eta2 = SSeffect / SSeffect + SSerror.

In fact, when you only have one independent variable, partial eta2 is the same as eta2
Partial etas are usually used when a person appears in more than one cell (i.e. the cells are not independent). Non independent cells show up in MANOVA studies. The results show the percentage of variance in each effect or interaction, and the error that is accounted for by that effect.

Caution: values labeled eta squared on some printouts from SPSS are actually partial eta2. For more details, see eta squared hcr.

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