Test 2: Factorial ANOVA Flashcards
Factorial ANOVA
Examining the simultaneous effects of several (two or more) factors on the dependent variable. (ANOVA simultaneously analyze two or more factors)
Example of a Factorial ANOVA
Does the effect of Factor A on our dependent variable depend on the level of Factor B?
Factorial ANOVA is the same thing as…
two-way ANOVA models
How many factors are in a Two-Way ANOVA?
There are two factors/IVs (Factor A & Factor B); factors can be between-subjects factors, within-subjects factors, or a combination of the two
Between-Between Design
Occur when both Factor A and Factor B are between-subjects factors; ex. effects of age (young or old) and obesity (healthy weight or obese) on knee extensor strength. (2x2 between-subjects factorial ANOVA)
Between-Within (or mixed) Designs
Occur when Factor A is a between-subjects factor and Factor B is a within-subjects factor; ex. effects of age (2 groups, young or old) and leg dominance (measured 2x, dominant or non-dominant) on knee strength (2x2 mixed-model factorial ANOVA)
Within-Within Designs
occur when both Factor A and Factor B are within-subjects factors; ex. effects of leg dominance (dominant & non-dominant) and protein supplementation (low dose & high dose) on knee-extensor strength (1 group measured 4 times)
Between-Subjects Factor
Cannot be a member of more than one group
Within-Subjects Factor
Same subjects are being tested on each variable across each group
Main Effect
What is the effect of Factor A independent of Factor B? (vice versa)
Interaction Effect
What is the simultaneous/joint effect of Factors A and B? (are the differences in population means on the dependent variable among levels of Factor A the same across levels of Factor B?); Factor A x Factor B
Interaction Plot
Factor A on the x-axis; Means of the DV on the y-axis; Separate lines for each level of Factor B
The interaction can be thought of as a measure of whether the lines describing the effects of two factors are…
Parallel; If the lines are parallel (regardless of the shape of that line) the interaction effect is NOT statistically significant• If the lines are not parallel, then the interaction is statistically significant (it doesn’t matter what it looks like)
What do Interaction Plots infer about Main Effect for Factor A?
If the levels of Factor A are along the X-axis, the slope of the line indicates if a main effect of Factor A is present (no slope = no effect);
What do Interaction Plots infer about Main Effect for Factor B?
If levels of Factor B are on separate lines, the offset (or separation) of the lines indicate if a main effect for Factor B is present (close together = no effect)
If values change between the levels of Factor A?
Main effect of Factor A
If Lines are parallel for Factor A or B?
No interaction effect
If lines are close together for Factor A?
Little difference between the levels of Factor B = no main effect for Factor B
If lines are separated for Factor B?
Indicates a main effect for Factor B
If there is little to no slope in the lines?
Mean values do not change much between levels of Factor A, no main effect of Factor A
If lines have slope?
Main effect of Factor A
H0: μA1 = μA2 =
… μAa (a = # of levels of A)
H0: μB1 = μB2 =
… μBb (b = # of levels of B)
H0: μA1,B1 = μA1,B2 =
… μAa, μBb
The alternative hypotheses for each of these is that…
at least 2 means differ (if only two levels, it means the IV has an effect)
Variance due to the treatment effect of A
Deviation of marginal means of factor A from grand mean
Variance due to the treatment effect of B
Deviation of marginal means of factor B from grand mean
Variance due to the combined effects of A & B
Deviation of group mean from respective marginal mean of Factor A, marginal mean of Factor B, and the grand mean
Unexplained variance (error)
Deviation of observation from group mean
these 4 sources combine to make up the total variance
Deviation of observation from the grand mean
ANOVA table: Factor A
Sum of Squares: SSA, df: a-1, Mean Square: MSA = SSA/dfA, F: MSA/MSE
ANOVA table: Factor B
Sum of Squares: SSB, df: b-1, Mean Square: MSB = SSB/dfA, F: MSB/MSE
ANOVA table: A*B Interaction
Sum of Squares: SSAxB, df: (a-1)(b-1), Mean Square: MSAxB = SSAxB/dfA, F: MSAxB/MSE
ANOVA table: Error
Sum of Squares: SSE, df: (N-ab), Mean Square: MSE = SSE/dfE
ANOVA table: Total
Sum of Squares: SST, df: N-1
What do the variables a, b, and N mean in an ANOVA table?
a = # of levels of A, b = # of levels of B, N = total # of participants
