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### One-Way BG ANOVA

Andrew Ainsworth

Psy 420

Obtained from

www.csun.edu/~ata20315/psy420/One-Way%20BG%20ANOVA.ppt

Effect Size

- A significant effect depends:
- Size of the mean differences (effect)
- Size of the error variance
- Degrees of freedom

- Practical Significance
- Is the effect useful? Meaningful?
- Does the effect have any real utility?

Effect Size

- Raw Effect size –
- Just looking at the raw difference between the groups
- Can be illustrated as the largest group difference or smallest (depending)
- Can’t be compared across samples or experiments

Effect Size

- Standardized Effect Size
- Expresses raw mean differences in standard deviation units
- Usually referred to as Cohen’s d

Effect Size

- Standardized Effect Size
- Cohen established effect size categories
- .2 = small effect
- .5 = moderate effect
- .8 = large effect

- Cohen established effect size categories

Effect Size

- Percent of Overlap
- There are many effect size measures that indicate the amount of total variance that is accounted for by the effect

Effect Size

- Percent of Overlap
- Eta Squared
- simply a descriptive statistic
- Often overestimates the degree of overlap in the population

- Eta Squared

Effect Size

- Omega Squared
- This is a better estimate of the percent of overlap in the population
- Corrects for the size of error and the number of groups

Our Example EPRS8540

- Eta Squared
- Small .01
- Medium .06
- Large .14
Cohen (1977)

- Omega Squared
- Small < .06
- Medium .06 - .15
- Large > .15
Cohen (1977)

Our Example EPRS8540

- There was no significant price difference among the three store types (F2, 9 = 3.12, P > .05, ).

References

- Cohen, J. (1977). Statistical power analysis for the behavioral sciences. NY: Academic Press. Cited with regard to intepretation of omega-square.
- Cohen, J. (1988). Statistical power analysis for the behavioral sciences . Second ed., Hillsdale, NJ: Erlbaum.
- Olejnik, S., & Algina, J. (2003). Generalized eta and omega statistics: Measured for effect size for some common research designs, Psychological Methods, 8, 434 – 447.

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