2. ANOVA + contrasts

Question 1

When can Fisher’s LSD be used?

Answer 1

It is a protected t-test, meaning it can only be used after a significant omnibus F-test.

Question 2

What does Fisher’s LSD do?

Answer 2

Compares all pairs of groups, with no adjustment to DER.

Question 3

Does Fisher’s LSD work?

Answer 3

No, don’t use it.

Question 4

What does Tukey’s HSD do and when can it be used?

Answer 4

Used regardless of significance of omnibus ANOVA. It tests pairwise comparisons. So it’s limited as can’t group IVs together.

Question 5

When can the contrast estimate be interpretable as a mean difference?

Answer 5

When the contrast coefficients are in standard form, i.e. 1/3 + 1/3 + 1/3 + 1

Question 6

When is it acceptable to run multiple contrasts without controlling for DER?

Answer 6

When the contrasts are planned and orthogonal

Question 7

In a complete set of orthogonal contrasts, the sum of SS from each contrast should equal what?

Answer 7

The SSB from the overall ANOVA, as it has been completely partitioned into the contrasts

Question 8

How many is a complete set of contrasts?

Answer 8

k = J-1

Question 9

When is orthogonality satisfied for a pair of contrasts?

Answer 9

If the sum of the cross products is zero.

Question 10

How do you deal with contradictions in the results of orthogonal contrasts?

Answer 10

There ARE no contradictions, dipshit! They’re orthogonal, asking different questions.

Question 11

When can trend analysis be used in ANOVA?

Answer 11

When IV is quantitative and has evenly spaced intervals.

Question 12

What does the presence of a linear AND quadratic trend indicate?

Answer 12

There is an increase or decrease in the DV as IV increases, but there is a change in the rate of change.

Question 13

How does the Bonferroni procedure control EER at .05?

Answer 13

By dividing α by k (number of contrasts).

Question 14

When can the Scheffé procedure be used?

Answer 14

For planned AND post hoc analyses.

Question 15

How is critical F for Scheffé calculated?

Answer 15

Critical F from the omnibus ANOVA multiplied by degrees of freedom between (also from omnibus ANOVA).

Question 16

If the omnibus ANOVA is not significant, is it worth running Scheffé to test the contrasts?

Answer 16

Hell no! If the ANOVA is not significant, none of the contrasts will be significant.

Question 17

When is Bonferroni ALWAYS more powerful than Scheffé?

Answer 17

When k < (J-1) Bonferroni is always more powerful than Scheffé.

Question 18

Which procedure should be used when k>(J-1)?

Answer 18

Could be either. Check critical values of each and go with the more powerful.

Question 19

Which fun parks do Bonferroni and Scheffé prefer?

Answer 19

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

Question 20

Can Bonferroni be used for both planned and unplanned (post hoc) contrasts?

Answer 20

No, just for planned.

Question 21

Why can’t Bonferroni be used for post-hoc contrasts?

Answer 21

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.

Question 22

If H0 is rejected, does that mean there must be at least one statistically significant contrast?

Answer 22

Yes.

Question 23

What’s the definition of a contrast?

Answer 23

A linear combination of weighted means whose coefficients sum to zero.

Question 24

What is the maximal contrast?

Answer 24

The “at least one” contrast that accounts for all of the groups’ variability (SSB).

Question 25

Is the maximal contrast usually interpretable?

Answer 25

Nah, usually not interpretable.

Question 26

What are the contrast coefficients for the maximal contrast?

Answer 26

The c for each group is the same as the α for each group. (i.e. group mean minus grand mean)