1.6 Factorial Analysis of Variance (ANOVA) Flashcards
In a one-way ANOVA how many and what type of factors and dependent variables are there?
one discrete factor and one continuous dependent variable
In a factorial ANOVA how many factors and dependent Variables are there?
at least two factors and one dependent variable
A two-way ANOVA includes how many factors? How many levels can it have?
two factors and each factors can have two or more levels
A 2x2 ANOVA has how many factors and levels? A 2x3 has how many factors and levels
2x2 has two factors, each with two levels
2x3 has two factors where one factor has two levels and one factor has three levels
There are many different factorial combinations that can be studied with factorial ANOVA
three way anova such as (blank x blank x blank)
3x2x2
What is the General Linear Model (GLM)?
a mathematical framework that describes the estimated components of the analysis. it is the foundation for several stats test including, ANOVA, ANCOVA, and regression analysis
In a two way ANOVA how many measurable effects (F tests) are there? what are they?
Main Effect of A: intervention (training versus control)
Main effect of B: age group (young versus old)
Interaction between AB: intervention x age group
When do interaction effects occur?
when the effect of levels of one factor on the dependent measure scored depend on the levels of a second factor
A affect the scores on B and vise versa
The two factors interact with each other such that having both caffeine and sugar speed up reaction times more than you would expect if you simply added the effects together
Having both caffeine and sugar results in a
synergistic effect
Partitioning of variance for two-way ANOVA (withing subjects)
The total variance in the dependent variable scores can be partitioned into:
Variance for main effect A (SSA)
Variance for main effect B (SSB)
Variance for the interaction (SSAB)
Variance for the error (SSE) which is SSwithin
SStot = SSA + SSB + SSAB + SSE
Statistics associated with factorial ANOVA
F rations and p values for three different F tests
—Main effect of Factor A
—Main effect of Factor B
—Interaction between factors A and B
Eta squared effect sizes for each of the three F tests
Powerful of each F test?
Factorial means, standard deviations, standard errors, and 95% confidence intervals?
Graphical representation of means including error bars
T or F: Each F test has its own null and alternative hypothesis,
true
when entering data for a two-way ANOVA for between subjects data what do you enter in the columns and what does each row represent?
you enter the dependent variables in n a column and each row of the data file represents a different participant
when entering data for a two-way ANOVA what do factors act as. The levels of a factor are entered where?
Factors as grouping variables where the levels of a factor are entered in a column
In a source table for a two way ANOVA;
A is the…
B is the…
AB is the
Error is a…
SS is…
K and K are the…
A is the main effect
B is the main effect
AB is the AB interaction
Error is a measure of within groups variation
SS is sum of squared
K and K are the number of levels for factors A and B, respectively
Follow-up Analyses to a Significant Omnibus Main Effect: Perform follow-up analyses to tease out differences for main effects. You run a…
Run simple Bonferroni contrasts, where the weights will be:
1, 0, -1
0, 1, -1
Interactions can be explored by running factorial or pairwise comparisons, such as:
Running simpler factorial ANOVAs with the goal of isolating the interaction
Running a series of t test comparing the levels of one factor to one another where the t test is computed at each level of the second factor
That is, a simple effect is the effects of one independent variable within one level of a second independent variable
What is a simple effect?
Can you remember the caffine/sugar example?
the effect of one independent variable within one level of a second independent variable
For example, selecting cases for the no sugar condition and then running three t tests comparing 1) no caffeine to 10g, 2) no caffeine to 20g, and 3) 10g to 20g
Next selecting cases for the 30g sugar condition and running the same three t tests
You can also work to isolate interaction by performing simplified factorials.
can you remember the caffeine/sugar example for this one?
For example, running to 2x2 factorial with the two levels of sugar and two levels of caffeine (no caffeine and 10g)
Then running a second 2x2 factorial with the two levels of sugar and two levels of caffeine (10g and 20g).
This procedure provides the possibility to isolating the interaction.
