Effect Size > Omega Squared

*You may want to read this article first: What is Effect Size?*

## What is Omega Squared?

Omega squared (ω^{2}) is a measure of effect size, or the degree of association for a population. It is an estimate of how much variance in the response variables are accounted for by the explanatory variables. Omega squared is widely viewed as a lesser biased alternative to eta-squared, especially when sample sizes are small.

## Formula

For between-subjects, fixed effects designs, the formula is:

ω

^{2}= (SS_{effect}– (df_{effect})(MS_{error})) / MS_{error}+ SS_{total}

These values are obtained from ANOVA output. **This formula cannot be used for repeated measures designs.**

For multi-factor, completely randomized design, Keppel (1991) **recommends the partial omega squared** (or alternatively, the partial eta-squared). The partial ω^{2} formula is:

## Interpreting Results

- ω
^{2}can have values between ± 1. - Zero indicates no effect.
- If the observed F is less than one, ω
^{2}will be negative.

## Issues

Caution should be used when interpreting results if your design includes a **blocking factor**. Omega squared can be misleading, as it tends to over-inflate the design effect (Cohen). This means that you shouldn’t use ω^{2} to compare designs that have blocking with those that do not. As the main purpose of effect sizes is to enable you to compare a series of studies, this can be a major problem.

If you manipulate all of the factors in your experimental design *and *your design includes two or more explanatory variables, partial ω^{2} is a good choice for measuring effect size. However, if your design includes any measured factors, you should not use partial ω^{2} as the results are often untrustworthy (Olejnik & Algina).

**References**:

Cohen, J. (1973). Eta-squared and partial eta-squared in fixed factor ANOVA designs. Educational and Psychological Measurement, 33, 107–112.

Keppel, G. (1991). Design and analysis: A researcher’s handbook. Englewood Cliffs, NJ: Prentice Hall.

Olejnik S and Algina J (2003). Generalized Eta and Omega Squared Statistics: Measures of effect size for some common research designs. Psychological Methods 8(4) 434-447. Retrieved October 11, 2016 from: here.

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