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| Suppose we have a three way interaction of three factors called age, sex and type. Age and sex are between subject and have two levels and type is within subject and comprises four levels. | Suppose we have a three way interaction of three factors called age, sex and type. Age and sex are between subject and each have two levels whilst type is a within subject factor and has four levels. |
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| There are two between subjects factors (age, sex) with 2 levels each do $$b_{1}=b_{2}$$ = 2. Their interaction (which comprises the term of interest) has (2-1)*(2-1)=1 df. There is one within subjects factor (type) with 4 levels so $$w_{1}$$ = 4. We can now use these to work out our inputs. | There are two between subjects factors (age, sex) with 2 levels each and, so, both have dfs of (2-1)=1. Their interaction (which comprises the term of interest) has (2-1)*(2-1)=1 df. There is one within subjects factor (type) with 4 levels so type has a df of (4-1)=3. We can now use these to work out our inputs. |
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| (sum of age, sex and age*sex interaction dfs). | (sum of dfs for the between subject factor terms: age, sex and age*sex) |
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| wdf = (4-1) = 3 (for type) | wdf = (4-1) = 3 (for the within subject factor, type) |
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| Putting these together, assuming conservatively no correlation between types, with an alpha=0.05, partial eta-squared of 0.10 and a power of 0.80 gives a total sample size of 39 required. | Putting these together, assuming conservatively no correlation between a pair of types, with an alpha=0.05, partial eta-squared of 0.10 and a power of 0.80 gives a total sample size of 39 required. |
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| If we assume an average correlation of 0.25 amongst the types with a partial eta-squared of 0.10 we only need a total sample size of 30 for a power of 0.80. | If we assume an average correlation of 0.25 amongst pairs of types with a partial eta-squared of 0.10 we only need a total sample size of 30 for a power of 0.80. |
Suppose we have a three way interaction of three factors called age, sex and type. Age and sex are between subject and each have two levels whilst type is a within subject factor and has four levels.
Pilot data has suggested an effect size, partial eta-squared, of 0.10 as worthy of interest. We wish to do a power calculation to see how many people we will need to detect an eta-squared of at least 0.10 with a power of 0.80 and a Type I error of 5%.
There are two between subjects factors (age, sex) with 2 levels each and, so, both have dfs of (2-1)=1. Their interaction (which comprises the term of interest) has (2-1)*(2-1)=1 df. There is one within subjects factor (type) with 4 levels so type has a df of (4-1)=3. We can now use these to work out our inputs.
num = numerator df = (2-1)(2-1)(4-1)=3
bsum = (2-1) + (2-1) + (2-1)*(2-1) = 3 (sum of dfs for the between subject factor terms: age, sex and age*sex)
wdf = (4-1) = 3 (for the within subject factor, type)
Putting these together, assuming conservatively no correlation between a pair of types, with an alpha=0.05, partial eta-squared of 0.10 and a power of 0.80 gives a total sample size of 39 required.
If we assume an average correlation of 0.25 amongst pairs of types with a partial eta-squared of 0.10 we only need a total sample size of 30 for a power of 0.80.
Reference
Faul, F. & Erdfelder, E. (1992) GPOWER: A priori, post-hoc, and compromise power analyses for MS-DOS [Computer program]. Bonn, Germany: Bonn University, Dep. of Psychology.