ANOVA lectures 7 and 8 Flashcards
R Squared = (in anova)
𝜂2=SSB/SST = proportion of variance in DV that is accounted for by both of the main effects + interaction
Tests of between subjects effects “corrected total”
SS for the ‘Corrected Total’ is SST
Tests of between subjects effects ‘Corrected Model’
SS for the ‘Corrected Model’ is SSB
Sig for two way anova
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.
Intercept in anova
Spss is testing whether the grand mean differs significantly from zero.
Anova Estimated Marginal Means
will be the same as the descriptive means in PSYC3010 because of equal n and no covariates.
Conclusion for main effect of A
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.
Conclusion for Interaction effect:
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
Can we ever assign direction to omnibus conclusions?
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.
How do you work out psy for multifactor design contrasts? Ho?
For the A family: psy = cjµj
B Family ckµk
Int Family cjkµjk
Ho = psys = 0
standard form for coefficients?
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)
If we have a full set of mututally orthogonal contrasts in one famkiily what happens?
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.
Product interaction
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)
How many coefficients and cell means are there?
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
Null hypothesis method of product int contrast
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
what is standard form for interaction coefficients?
Standard form Σ positive cjk = +2
Σ negative cjk = -2
How do you check the coefficients from cross multiplication are correct for product int via cross multiplication in two way anova contrasts?
0 1 -1 0 -1 1 => reflection in sign, shows you’ve done it right.
Why is the formula for interaction effect contrast = Interaction effect from anova? (SSAB)
Because all the sum of the ab1 and ab2 contrasts = (j-1)(k-1) mutually orth cntrasts.
In a 2 X 3 analysis of variance, how many null hypotheses are there?
three. main effect a, b, int
custom hyp test #4 =
interaction contrst for AB1 (assuming 2x3)
estimated marginal means
the bottom and side rows of the means from that table we made
EER vs FER vs DER
EER: alpha of .05 is ditributed across all the contrast in the experiement.
FER: .05 per family
DER. .05 per contrast quetsion
What do you have to think about to get F crit? (decide error rate)
what is k (bonf) what is v1 (sheffe).
V1 in sheffe is the df effect for that FAMILY.
Interpreting interaction contrasts
- What are the two ‘lots’ being compared in the A question?
- What are the two ‘lots’ being compared in the B question?
- 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)
Example of relaxing thoughts conclusion. Use (diff.).
Then can we provide another further direction of effect?
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
What do you do if you get a cross over interaction?
For cross over ones, you can’t say one is better/higher/greater than the other because they are going in opposite directions.
Simple effects
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?
when to interpret simple effects
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.
Why don’t we use FER for simple effects contrasts?
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)
How do you find critical F for a simple main effect contrast?
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
