Week 11 - Mixed ANOVA Flashcards
• Explain what types of factors are included in mixed/split-plot ANOVA (x2)
o WP - within participant
o BP - between participant
• What types of research questions can be addressed with mixed ANOVA?
Those where manipulation of both IVs impossible/unethical, e.g. brain injury
• Explain how mixed ANOVA is different from mixed model within-participants ANOVA (x1, x2)
- Mixed anova has a BP factor and a WP factor.
- Mixed model within-participants ANOVA is the normal way of doing WP ANOVA (where you evaluate sphericity and report an adjusted F, such as GG) – in contrast to MANOVA
• Explain the main strengths of mixed ANOVA (x2)
Can include factors in RM design that are unethical to manipulate
And exclude potential carry-over effects with BP factor_
• Explain the difference between fixed and random factors in mixed ANOVA
Both within-Ps and between Ps IVs are fixed factors (levels chosen by us)
While the Ps factor is still random (not pre-selected for particular combination of factors)
• Explain what is meant by: One factor is nested under another factor (x1)
The (random) Ps factor is nested under/within levels of the between-Ps factor (independent group factor)
• Explain what is meant by: One factor is crossed with another factor (x1)
The (random) Ps factor is crossed with levels of the within-Ps factor (RM factor)
• In a 2-way mixed factorial ANOVA, indicate the sources of systematic and error variance for each effect (3 levels. x1, x3, x4)
SStotal divided into:
SSbetweenPs (independent groups factor)
- SSgroup (treatment)
- SSpswithingroups (error)
SSwithinPs (RM factor)
- SSblock (factor effect)
- SSbxg (interaction of block and group)
- SSbxpswithing (block by Ps within groups - error)
Explain the diffs in error terms in between-groups, RM and Mixed ANOVA (x3)
o In between Ps ANOVA, we had one error term – deviations from cell means
o RM factor has three separate error terms, for each omnibus effect (TR x Ps interaction)
o While in mixed ANOVA, we have two error terms – one for between groups factor, and other for main effect of RM factor and the interaction
What omnibus tests do you do in a 2-way Mixed ANOVA? (x3)
o Main effect of group
o Main effect of block
o Group x block interaction
What 2 error terms are need for omnibus tests in 2-way mixed ANOVA? (x3, x3)
One for between-Ps factor (Ps within groups)
*Deviations of P’s mean from group mean - variability within the group
One for within-Ps factor and the 2-way interaction (interaction between block and participants within groups)
*Inconsistencies in effect of the within-subjects/RM/block factor across Ps, adjusted for between-group diffs in Ps
• Explain how the F ratio is calculated in a 2-way mixed factorial design for:
o The effect of the between-participants factor
Ratio of variability among group means divided by variability within groups
(the familiar ANOVA: MStreat/MSerror)
• Explain how the F ratio is calculated in a 2-way mixed factorial design for:
o The effect of the within-participants factor
Ratio of variability among means for within-Ps factor levels divided by variability in within-Ps factor effect
• Explain how the F ratio is calculated in a 2-way mixed factorial design for:
o The interaction of the between-participants factor and the within-participants factor
Ratio of variability among cell means for WPF levels within each group (adjusted for MEs) divided by variability in WP effect
• Indicate the formulae for degrees of freedom for:
o Total effects
o All between-participants effects
o All within-participants effects
g = number of groups b = number of levels of block/RM factor n = number of Ps
df-total = gbn - 1
df-betweenPs = gn - 1
- df-group = g - 1
- df-Pswithing = df-betweenPs - df-group
df-withinPs = df-total - df-betweenPs
*df-block = b - 1
*df-bg (interaction) = (b - 1)(g - 1)
df-bxPswithing (error) = df-withinPs - df-block - df-bg
• When following up the main effect of a between-participants factor in a mixed ANOVA:
o Explain what scores you are comparing
Means of group (main effect comparisons if 3+ levels)
• When following up the main effect of a between-participants factor in a mixed ANOVA:
o Indicate the type of test you would use
Could use linear contrast,
But generally pair-wise comparisons (t-tests)
• When following up the main effect of a between-participants factor in a mixed ANOVA:
o Indicate which error term you would use
Original error term from between-Ps main effect test
*MS-Pswithing
• When following up the main effect of a within-participants factor in a mixed ANOVA:
o Explain what scores you are comparing
Block means
• When following up the main effect of a within-participants factor in a mixed ANOVA:
o Indicate the type of test you would use
Could use linear contrast,
But generally run a 1-way within-Ps ANOVA on each pair of comparison blocks
• When following up the main effect of a within-participants factor in a mixed ANOVA:
o Indicate which error term you would use
We have to get the error term for each comparison based upon only the data involved in that comparison:
SS-BcomparisonxPs
• When following up a significant 2-way interaction in a mixed ANOVA with the simple effects of the within-participants factor:
o Explain what scores you are comparing
The cell means of block, at each level of group (are the simple effects of block)
• When following up a significant 2-way interaction in a mixed ANOVA with the simple effects of the within-participants factor:
o Indicate the type of test you would use
Always run a 1-way within-Ps ANOVA on block, separately for each group
• When following up a significant 2-way interaction in a mixed ANOVA with the simple effects of the within-participants factor:
o Indicate which error term you would use
Individual ANOVAs on block for each group creates a new error term that only considers the data involved in the simple effect we’re analysing
o Which is best because pooled error might overestimate error, even when df are adjusted
• When following up a significant 2-way interaction in a mixed ANOVA with the simple effects of the between-participants factor:
o Explain what scores you are comparing
The cell means of group, at each level of block (are the simple effects of group)
• When following up a significant 2-way interaction in a mixed ANOVA with the simple effects of the between-participants factor:
o List the two approaches that you could use
Run four 1-way between-participants anovas to compare groups at each of the four blocks (ie using separate errors) OR Use same (new, special, pooled) error for all - averages error variance across all cells
• When following up a significant 2-way interaction in a mixed ANOVA with the simple effects of the between-participants factor:
o Explain the strengths of the two approaches (x2, x2)
Separate 1-way ANOVAs is more precise - not homogenising the variance in groups
But using single pooled error tests all simple effects with same power, and applies logic familiar for between-groups ANOVA
• When following up a significant 2-way interaction in a mixed ANOVA with the simple effects of the between-participants factor:
o Explain the weaknesses of the two approaches
Separate is damn time consuming!
Pooled error can conceal (often seen) heterogeneity of variances across the RM factor
• When following up a significant simple effect of a between-participants factor with simple comparisons:
o Explain what scores you are comparing
If any of the simple effects of group at each level of block was significant, need to compare the block levels
• When following up a significant simple effect of a between-participants factor with simple comparisons:
o Indicate the type of test you would use
Linear contrasts
• When following up a significant simple effect of a between-participants factor with simple comparisons:
o Indicate which error term you would use
The same as the original 1-way ANOVA simple effect test (that we did for each block):
MS-Pwithing(@ block#)
What are assumptions re DV and between-Ps factor in Mixed ANOVA? (x1, x1)
DV normally distributed
Homogeneity of variance (as with all between-Ps designs)
What are assumptions re within-Ps factor in Mixed ANOVA? (x1, x1)
Homogeneity of variance: assume WPFxP interactions constant at all levels of between participant factor
o Interaction of Ps and within participants factor is consistent… Group factor doesn’t change the error term for the RM factor
Variance-covariance matrix same at all levels of WPF
Pooled (average) variance-covariance matrix exhibits compound symmetry (c.f. sphericity)
• Usual epsilon adjustments apply when within-Ps assumptions violated
• In a two by three mixed ANOVA in which gender (male; female) serves as a between-participants variable and time of test (start of semester, mid-semester, end of semester) serves as a repeated measures variable, participant is crossed with ______ and nested within _______ .
Time of test
Gender
