If there are more levels, there are more comparisons, which increases likelihood of:
Type 1/alpha error (finding significant results when there isn't one)
Type 2/beta error (failing to reject the null)
Type 1/alpha error (failing to reject the null)
Type 2/beta error (finding significant results when there isn't one)
If there are more levels, there are more comparisons, which increases likelihood of type 1/alpha error. This is known as:
Familywise error
Order effects
Cohen's d
Pearson's r
How can you reduce Familywise error:
Stricter probability
Ignoring it
Having more levels
Using a t-test
An ANOVA is an omnibus test, meaning:
It discovers overall difference, not where it lies, reducing Familywise error by conducting 1 test rather than many t-tests
Discovers where the difference lies by using Tukey
Compares only 2 groups
It has nothing to do with main or interaction effects
Two-way ANOVA means there are:
Two IV's
Only 2 groups
One IV
Three IV's
An example Two-way ANOVA is: impact of gender AND type of exercise ON depression
In this last example two-way ANOVA, identify which are predictor variables and which are outcome variables: (3)
Gender: predictor
Exercise: predictor
Depression: outcome
Depression: predictor
If gender (predictor 1) has 2 levels (male or female) AND exercise (predictor 2) has 3 levels (cardio, strength, control), this can be described as a:
3 x 2 design
2 x 2 design
T-test
One-way ANOVA
If both IV's/predictors are between groups = ❌ design
If 1 predictor is within, and the other is between, it is known as a mixed design
If 1 predictor is within, and the other is between, it is known as a fully between design
Identify one-way and two-way ANOVA: (2)
One-way = 1 effect with more than 2 levels (IV or DV)
Two-way = 3 effects (2 main and 1 interaction)
One-way = 3 effects (2 main and 1 interaction)
Three-way = 1 effect with more than 2 levels (IV or DV)
A three-way ANOVA has 7 effects (3 main, 4 interaction)
On SPSS, you'd conduct a two-way ANOVA by:
Analyse - General linear model - Univariate
Analyse - Compare means - one-way ANOVA
Analyse - Compare means - Independent t-test
Analyse - Plots
The lower the SD, the..
More accurate model
More inaccurate model
'3 x 2 x 3' indicates what? (2)
Number of factors by looking at how many numbers (in this example, 3)
Number of levels within each factors by looking at the value of each number (e.g. factor 1 has 3 levels)
Effect size using Cohen's d
The result of a Tukey post-hoc
What is a factorial design?
When we have manipulated more than 1 IV/factor
When we have manipulated only 1 IV/factor
When there is more than 1 DV/outcome
Systematic error
How many effects in this design?
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