One-Way BG ANOVA
Andrew Ainsworth
Psy 420
Obtained from
www.csun.edu/~ata20315/psy420/OneWay%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
d
Yl  Ys
MS S / A
Effect Size
• Standardized Effect Size
• Cohen established effect size categories
• .2 = small effect
• .5 = moderate effect
• .8 = large effect
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
SS A
 R 
SST
2
2
• simply a descriptive statistic
• Often overestimates the degree of overlap in the
population
Effect Size
• Omega Squared
SS A  df A (MSS / A )
 
SST  MSS / A
2
• 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
• Eta Squared
EPRS8540
• Omega Squared
23.21  2(3.72)
 
56.67  3.72
23.21  7.44 15.76


 .26
60.3942.46 60.39
2
23.21
 
 .409
56.67
2
• Small .01
• Medium .06
• Large .14
• Small < .06
• Medium .06 - .15
• Large > .15
Cohen (1977)
Cohen (1977)
Our Example
EPRS8540
• There was no significant price difference
among the three store types (F2, 9 = 3.12,
P > .05,  2  .41 ).
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.