Module 6 Practice Questions Flashcards
What is the design of a study that is analyzed using a 3x4x2 ANOVA? How many conditions are there? How many effects would we be testing (how many null hypotheses are being evaluated)?
This is a three-way factorial ANOVA
There are three IVs, one has 3 levels, one has 4 levels, and one has 2 levels.
By multiplying through we can determine how many conditions exist in the study = 24 conditions
We will test for 3 main effects and 4 interactions.
What are the two primary advantages of factorial experiments?
- Modest gain in efficiency
2. The ability to test joint effects of IVs (additive versus non-additive)
Provide three different definitions of an interaction
- Interactions indicate that the effect of one IV differs across levels of another IV
- Interactions can be referred to as “moderator” effects in the sense that a moderator (one IV) regulates the effect of another IV
- Interactions can be thought of us a test of the difference between differences
What is the equation for the F statistic? From this, which part of this equation changes when dealing with factorial compared with one-way ANOVAs? (Slides 21-24) What is the primary difference between the calculation of F for one-way and factorial ANOVAs? What does an F value of 1 indicate and why?
F = variance between treatments/ variance within treatments
The numerator of this equation changes when dealing with factorial compared with one-way ANOVAs. This is because between treatment variance is divided into three components now: factor A between treatment variance, factor B between treatment variance, and factor AxB between treatment variance
An F value near 1 indicates that a given treatment effect is 0.
An F value larger than 1 indicates that a given treatment effect exists
How many effects need to be followed up when dealing with a 2x2 ANOVA in which all effects are significant why?
For main effects with two levels (such as in this case) no follow-up tests are required.
Since the interaction is significant we must conduct a planned follow-up test (simple effect analysis)
What are simple effects? Explain this conceptually and mathematically
A simple effect is the effect of one IV at a specific level of the other IV
This involves computing the between treatment MS across levels of one IV at a single level of the other IV
The simple effect MS is then divided by the overall ANOVA MS within to produce an F test
How many simple effects are there in a 2x2 design? What about a 2x3? What is a common simple effects analysis for a 2x3 design?
In a 2x2 design there are 4 simple effects.
In a 2x3 design there are 5 simple effects.
A common simple effects analysis for a 2x3 design would involve testing the simple effect of the first IV at each of the three levels of the second IV.
The 3 means versus 1 mean pattern is a common pattern that is tested for in medicine. Can you think of why this is? Draw two graphs that represent support for the null and alternative hypotheses for this test.
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What are Abelson’s three claims? Define each and provide examples of each within a 2x2 ANOVA write up
Ticks
- Detailed statements of distinct research results
- In a 2x2 ANOVA, a main effect would be an example of a tick
Buts
- Statements that qualify or constrain ticks
- In a 2x2 ANOVA, an interaction would be an example of a but
Blobs
- A cluster of undifferentiated research results
- In a 2x2 ANOVA the omnibus f-tests would be an example of blobs
Why is it a problem that alpha is not adjusted in factorial ANOVA? What is the argument/practice that is used as justification for this?
Given the multiple omnibus f-tests that are conducted in factorial ANOVA and given that alpha is not adjusted, the possibility of family wise error is evident and even a greater risk.
The justification for not adjusting alpha is that it is hard to balance alpha and beta in complex designs. Thus, there is an emphasis on follow-up analyses.
What is the main difference between alpha and power calculations for factorial and one-way ANOVAs?
Alpha is not adjusted for in factorial ANOVAs like it is in one-way ANOVAs so the cumulative risk of making a type I error increases.
Power can be computed separately for each of the omnibus f-tests in factorial ANOVA, thus, power will not always be the same across the effects like it is in a one-way ANOVA.
What are the two principles for specifying beta in the context of multiple tests?
- Power study based on the weakest anticipated effect
OR
- Power study based on the most important effect(s)
Compare the calculation of partial eta squared to F
What is the difference?
How do you think this affects the values/range of the statistics?
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