2. ANOVA + contrasts Flashcards
When can Fisher’s LSD be used?
It is a protected t-test, meaning it can only be used after a significant omnibus F-test.
What does Fisher’s LSD do?
Compares all pairs of groups, with no adjustment to DER.
Does Fisher’s LSD work?
No, don’t use it.
What does Tukey’s HSD do and when can it be used?
Used regardless of significance of omnibus ANOVA. It tests pairwise comparisons. So it’s limited as can’t group IVs together.
When can the contrast estimate be interpretable as a mean difference?
When the contrast coefficients are in standard form, i.e. 1/3 + 1/3 + 1/3 + 1
When is it acceptable to run multiple contrasts without controlling for DER?
When the contrasts are planned and orthogonal
In a complete set of orthogonal contrasts, the sum of SS from each contrast should equal what?
The SSB from the overall ANOVA, as it has been completely partitioned into the contrasts
How many is a complete set of contrasts?
k = J-1
When is orthogonality satisfied for a pair of contrasts?
If the sum of the cross products is zero.
How do you deal with contradictions in the results of orthogonal contrasts?
There ARE no contradictions, dipshit! They’re orthogonal, asking different questions.
When can trend analysis be used in ANOVA?
When IV is quantitative and has evenly spaced intervals.
What does the presence of a linear AND quadratic trend indicate?
There is an increase or decrease in the DV as IV increases, but there is a change in the rate of change.
How does the Bonferroni procedure control EER at .05?
By dividing α by k (number of contrasts).
When can the Scheffé procedure be used?
For planned AND post hoc analyses.
How is critical F for Scheffé calculated?
Critical F from the omnibus ANOVA multiplied by degrees of freedom between (also from omnibus ANOVA).
If the omnibus ANOVA is not significant, is it worth running Scheffé to test the contrasts?
Hell no! If the ANOVA is not significant, none of the contrasts will be significant.
When is Bonferroni ALWAYS more powerful than Scheffé?
When k < (J-1) Bonferroni is always more powerful than Scheffé.
Which procedure should be used when k>(J-1)?
Could be either. Check critical values of each and go with the more powerful.
Which fun parks do Bonferroni and Scheffé prefer?
Bonferroni likes Luna Park – only pay for rides you go on
Scheffé likes Australia’s Wonderland – pay an entry fee, then as many rides as you like
Can Bonferroni be used for both planned and unplanned (post hoc) contrasts?
No, just for planned.
Why can’t Bonferroni be used for post-hoc contrasts?
Bonferroni is based on the rationale that the tests are planned and randomly selected values of the F distribution if H0 is true. Post-hoc contrasts are clearly NOT randomly selected values of the F distribution if H0 is true.
If H0 is rejected, does that mean there must be at least one statistically significant contrast?
Yes.
What’s the definition of a contrast?
A linear combination of weighted means whose coefficients sum to zero.
What is the maximal contrast?
The “at least one” contrast that accounts for all of the groups’ variability (SSB).
Is the maximal contrast usually interpretable?
Nah, usually not interpretable.
What are the contrast coefficients for the maximal contrast?
The c for each group is the same as the α for each group. (i.e. group mean minus grand mean)
