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2 (or more)-way ANOVA is used when one has...

2 or more fixed categorical IVs and 1 or more continuous random DV


2-way ANOVA hopes to find

1. Interactions 2. Main effects


"2 way ANOVA" indicates _____ whereas "2 x 2 ANOVA" indicates

1. That we have 2 IVs 2. That we have 2 IVs, each with 2 levels.


What does "Factorial design" mean?

More than one IV


What is the goal of 2-way ANOVA?

Add second IV that strengthens first IV and reduces E


What is an interaction?

Second IV affects the levels of 1st IV differently


How can one examine interaction graphically?

1. Parallel lines means there is no interaction
2. Test of interaction is test of parallelism. Not testing if means are significantly different
3. Examination of slope (how regression works)


What should one do statistically upon finding a significant interaction?

Do not pursue main effects.


What are the 3 hypotheses of 2-way ANOVA?

1. Interaction 2. Main effect A 3. Main effect B


What is the effect of adding a 2nd IV on power?

1. Doubles number of participants one needs to have in order to achieve sufficient power
2. Because power is based on cells-- the smallest breakout that one will compare


What questions does one ask in 2-way ANOVA?

1. Is there a significant effect? 2. Where is it? 3. How big is it?


What are assumptions of 2-way ANOVA?

1. n 4:1 ratio
2. N - Normality of error term (not normal distribution of subjects). Error term = that for which is not accounted.
3. I - Independence - participants can be in only 1 cell at a time. Cannot randomly assign to a tx group and then a second tx group.
4. H - Homogeneity - Equivalent variances (SDs) of all cells. Across IVs and also across interactions
5. R - Random


What does ATI stand for?

Attribute-Treatment Interaction


What is Attribute-Treatment Interaction?

* Uses both experimental and ex post facto methods:
* Treatment-Control = experimental variable
* M/F or SES = organismic variable
* Can manipulate one variable but not the other.


How is Attribute-Treatment Interaction conducted?

* Randomly assign to treatment (experimental variable).
* Randomly select from attribute (organismic variable).
* May have control and treatment or multiple treatments
* May have control organismic variable.
* Main objective is to assess interaction.


What does it mean when lines of interaction graph cross?

1. There is an interaction effect. 2. Termed "Disordinal Interaction"


What does it mean when lines of interaction graph change slope but do not cross?

1. There is an interaction effect. 2. Termed "Ordinal Interaction"


What does it mean when lines of interaction graph are parallel?

No interaction


Interaction hypothesis is addresses through



Main effect hypotheses are addressed through

Post-hoc tests (if interaction is not demonstrated)


What is included in 2-way ANOVA source table?

* Source SS df MS F
* IV (by name)
* IV 2 (by name)
* Interaction
* Error
* Total