ANOVA lectures 7 and 8

Question 1

R Squared = (in anova)

Answer 1

𝜂2=SSB/SST = proportion of variance in DV that is accounted for by both of the main effects + interaction

Question 2

Tests of between subjects effects “corrected total”

Answer 2

SS for the ‘Corrected Total’ is SST

Question 3

Tests of between subjects effects ‘Corrected Model’

Answer 3

SS for the ‘Corrected Model’ is SSB

Question 4

Sig for two way anova

Answer 4

If α is controlled using a FER, p(obs|Ho) for each family can be compared against .05.

Each effect gets it’s OWN alpha of .05.

Question 5

Intercept in anova

Answer 5

Spss is testing whether the grand mean differs significantly from zero.

Question 6

Anova Estimated Marginal Means

Answer 6

will be the same as the descriptive means in PSYC3010 because of equal n and no covariates.

Question 7

Conclusion for main effect of A

Answer 7

Averaged over IVB (type of backup), mean number of DV (relaxing thoughts) was significantly higher after IVA level 1 (individual therapy) (M=32) than IVA level 2 (group therapy) (M=28), F(1, 66) = 20.01, p < .05.

Question 8

Conclusion for Interaction effect:

Answer 8

Differences in mean number of DV (relaxing thoughts) between those receiving (individual therapy) IVA level 1 and those receiving IVA level 2 (group therapy) differed significantly according to the type of assigned backup, F(2, 55) = 5.00, p < .05

Question 9

Can we ever assign direction to omnibus conclusions?

Answer 9

Yes if it is a main effect which is a 1 df question (2 groups) e.g. type of therapy ind vs group.
The OTHER effects (Main effect B and int.) require contrasts.

Question 10

How do you work out psy for multifactor design contrasts? Ho?

Answer 10

For the A family: psy = cjµj
B Family ckµk
Int Family cjkµjk

Ho = psys = 0

Question 11

standard form for coefficients?

Answer 11

sum of positive coefficients = 1, sum of neg coefficients = -1.
If this is the case, directly interpret the mean difference. (e.g. there is a four point difference)

Question 12

If we have a full set of mututally orthogonal contrasts in one famkiily what happens?

Answer 12

e.g. for B family, because there are (K-1) mutually orthogonal contrasts. (for A because j-1 orth conts.

SST has been partitioned into SSB and SSW. Of the SSB we partitoned it into two main effects and an interaction. Within those effects we further partitioned the SSs.

Question 13

Product interaction

Answer 13

product of an A main effect question and a B main effect question. It is the multiplication (timsing) of A question and b question.

Are the differences (in mean DV according to conditions in the A main effect question) different (according to conditions in the B main effect question)? (… or vice versa because all interaction effects are symmetrical)

Question 14

How many coefficients and cell means are there?

Answer 14

There is jxk coefficients. And there is one coefficient times each of the cell means. J times K coefficients and J x K cell means

Question 15

Null hypothesis method of product int contrast

Answer 15

The difference in relaxing thoughts between no backup and any backup (tape and pamphlet, on average) is the same (i.e., no different) for those receiving individual therapy and those receiving group therapy

Question 16

what is standard form for interaction coefficients?

Answer 16

Standard form Σ positive cjk = +2

Σ negative cjk = -2

Question 17

How do you check the coefficients from cross multiplication are correct for product int via cross multiplication in two way anova contrasts?

Answer 17

0 1 -1 0 -1 1 => reflection in sign, shows you’ve done it right.

Question 18

Why is the formula for interaction effect contrast = Interaction effect from anova? (SSAB)

Answer 18

Because all the sum of the ab1 and ab2 contrasts = (j-1)(k-1) mutually orth cntrasts.

Question 19

In a 2 X 3 analysis of variance, how many null hypotheses are there?

Answer 19

three. main effect a, b, int

Question 20

custom hyp test #4 =

Answer 20

interaction contrst for AB1 (assuming 2x3)

Question 21

estimated marginal means

Answer 21

the bottom and side rows of the means from that table we made

Question 22

EER vs FER vs DER

Answer 22

EER: alpha of .05 is ditributed across all the contrast in the experiement.

FER: .05 per family
DER. .05 per contrast quetsion

Question 23

What do you have to think about to get F crit? (decide error rate)

Answer 23

what is k (bonf) what is v1 (sheffe).

V1 in sheffe is the df effect for that FAMILY.

Question 24

Interpreting interaction contrasts

Answer 24

1. What are the two ‘lots’ being compared in the A question?
2. What are the two ‘lots’ being compared in the B question?
3. Is the difference (in the A question) the same for both ‘lots’ described in the B question?
   •Reduce the cell means to a 2x2 (JUST for interpretation)

Question 25

Example of relaxing thoughts conclusion. Use (diff.).

Then can we provide another further direction of effect?

Answer 25

The greater number of relaxing thoughts for any backup than no backup did not differ significantly between those receiving individual therapy (Diff=6) and those receiving group therapy (Diff=3), F(1,66)=2.5, n.s.

Yes. If the dotted line is always higher, the effect is the same for one level of the iV as the other level of the IV

Question 26

What do you do if you get a cross over interaction?

Answer 26

For cross over ones, you can’t say one is better/higher/greater than the other because they are going in opposite directions.

Question 27

Simple effects

Answer 27

Simple effects (or simple main effects) assess the effect of one IV on the DV at one specific level of the other IV.

e.g.• Is there a difference between individual therapy and group therapy in terms of the number of relaxing thoughts for those receiving no backup?

• Is there a difference between individual therapy and group therapy in terms of the number of relaxing thoughts for those receiving tape backup?
• Is there a difference between individual therapy and group therapy in terms of the number of relaxing thoughts for those receiving pamphlet backup?

Question 28

when to interpret simple effects

Answer 28

The presence of interaction limits the generalizeability
of main effects. This is because it is difficult to make
a general statement about a variable’s effect when the
size of the effect depends on the level of a second variable.
Testing simple effects is done following an interaction not to help understand the interaction, but rather to see
where the effect of the variable is significantly different from zero.

Question 29

Why don’t we use FER for simple effects contrasts?

Answer 29

Simple effects do not fall in the A, B or AB families, and its SS are confounded partitions of SS(A) and SS(AB), or SS(B) and SS(AB), so it not appropriate to control α for these contrasts using a FER of .05.

Instead, α must be controlled using an experiment-wise error rate (EER)

Question 30

How do you find critical F for a simple main effect contrast?

Answer 30

Under EER use either Bonferroni if it is planned (steson will get back to you about whther to check or not). Use sheffe for post hoc (MOST CASES). typically what happens is you get a sig int contrast, now let’s see if the difference on this side is sig or that side is sig.

FOR SHEFFE: v1 is (J x K) - 1, or number of groups in total for the experiment - 1. Say we get v1 = 5. Go to F tables, 5 and dfw (66) = 2.36. Now multiply 5x2.36 (AGAIN).
New Fc is 11.8.

For Bonferroni: dfb x anova f