Factorial ANOVAs

Question 1

what do ANOVAs help us to reduce?

Answer 1

type 1 errors (based on the use of multiple comparisons -> we want to avoid family wise error)

Question 2

what is a Factorial Independent ANOVA?

Answer 2

has multiple independent variables
* different participants in all conditions
*one dependent/outcome variable
* you still need to run one ANOVA per dependent variable

Question 3

what is a factorial design?

Answer 3

when you have several independent variables

Question 4

what is a two-way factorial anova?

Answer 4

when there are two independent variables

i.e.
IV1: democratic status (4 levels)
IV2: GDP (3 levels)
DV: happiness score

Question 5

what is a three-way factorial anova?

Answer 5

when there are three independent variables

Question 6

what does a factorial design allow you to do?

Answer 6

allows you to look at interaction effects between variables
* the effect of one IV may depend on the level of another IV

Question 7

what are the assumptions of a factorial anova?

Answer 7

• independence (each participant contributes one data point)
• normality (K-S, Shapiro Wilk and observe your graphs)
• homogeneity of variance (Levene’s Test and observe your graphs Q-Q Plots)

Question 8

what should you do when assumptions are violated?

Answer 8

non-parametric alternative

Question 9

how to structure your data (for a two-way factorial ANOVA)

Answer 9

IV1 (Coded)
IV2 (Coded)
DV

Question 10

How to inspect your data for a One-Way Factorial ANOVA?

Answer 10

• drag the type of graph you need (multiple line graphs)
• drag one IV to the x-axis -> choose the one with the most levels first
• drag the second IV to set colour
• drag the DV to the y-axis
• Element Properties -> Error Bars -> SE +/- 1
• Click OK to generate your graph

Question 11

Running the Factorial ANOVA

Answer 11

Analyse > General Linear Model > Univariate
* use this option for any factorial independent ANOVA (two-way, three-way etc.)
* Drag IVs to fixed factors box
* Drag DV to to dependent variable box
* Click Plots
○ Plot Window allows you to draw a graph
○ Drag IV with most levels to Horizontal axis
○ Drag IV with fewest levels to separate lines
○ Click Add > Continue
* Click Post-Hoc Tests (options same as ones in One-Way ANOVA)
○ Post Hoc Window - Drag IVs to post-hoc box (select appropriate test(s))
* Click Options
○ Drag your IVs and the interaction across to the Display means box
* Display
○ Descriptive statistics, estimates of effect size, homogeneity tests

Question 12

How should you interpret the output?

Answer 12

• Descriptive statistics box/table
• Levene’s Test of Equality of Error Variances
• Tests of Between-Subjects Effects
• Write up your results

Question 13

descriptive statistics box/table

Answer 13

• check sample sizes are what you expected

Question 14

Levene’s Test of Equality of Error Variances

Answer 14

homogeneity test -> we want Levene’s to be non-significant so we can assume equal variance

Question 15

Test of Between-Subjects Effect

Answer 15

• main ANOVA summary table
• highlights main effects of your IVs -> interaction effect between the IVs
• Partial Eta Squared

Question 16

what is Partial Eta Squared?

Answer 16

Effect Size

Question 17

Writing up your results:

Answer 17

• Descriptive for graphs
• Results of assumptions tests
• Test statistics (F)
• Degrees of Freedom (model, error)
• P Value
• Effect Size (n2)

(if there’s a significant main effect, the graph should technically show us)

Question 18

how do we know if there’s a significant interaction?

Answer 18

if there isn’t then two variables do not influence one another -> main effect of IV1 is not influenced by the level of IV2

Question 19

in what designs do interactions happen>

Answer 19

deigns where there are more than one IV
* the effect of IV1 changes depend on IV2
* can suggest ideas and future research of interactions -> help aid critical analyses

Question 20

how do we know if there’s an interaction effect?

Answer 20

if they cross, there’s likely a interaction effect happening (or you can extrapolate the line to see if they’ll eventually cross over -> visualising the data)

Question 21

what is not an interaction effect?

Answer 21

lines that are next to each other -> but not crossing over

Question 22

when can we use planned contrasts?

Answer 22

if your ANOVA is significant, we can explore the effects more deeply through planned contrasts (i.e. planned comparisons) and compare every level specific

Question 23

Planned Contrasts

Answer 23

• most systematic -> used for testing specific hypotheses
• make a smaller number of comparisons and can include multiple conditions in each comparison
• useful for examples if you compare your group against a control -> or if you expect an effect to get larger as the level of treatment increases

IN THIS CASE, you don’t have to be as conservative in your corrections to avoid specific family wise errors -> running fewer tests is often preferred but only works if you have a specific hypothesis

Question 24

How do planned contrasts actually work?

Answer 24

• general idea that you’re further dividing the variance explained by the model (comparing the amount of variance that can be attributed by your IV with any variance left over)
• allow us to further divide these control groups to find out which comparisons is driving the effect we saw -> chunks of variance explained by your variables

Question 25

planned contrasts in the form of a cake analogy:

Answer 25

This slice of the cake will be significantly different from the rest of the cake, and the planned contrast allows us to do that by comparing it with a different slice (or two) or even the whole cake, that are explained by other parts of our experiment -> take chunks and pair them to see where our differences are arising from

Question 26

What are the Planned Contrasts that you can calculate?

Answer 26

You can change the type of contrast which you want to make -> allowing you to compare different versions of the slices * deviation * simple * helmert * difference * repeated * polynomial

Question 27

Deviation

Answer 27

compared the means of each condition to overall mean

Question 28

Simple

Answer 28

compares the mean of each condition to wither the first or last condition (i.e. compare with a control group

Question 29

Helmert

Answer 29

compare the mean of one condition to the average of all other conditions

Question 30

Difference

Answer 30

reverse of Helmet -> compares the mean of a condition to the average of all previous conditions

Question 31

Repeated

Answer 31

compares sequential pairs of conditions

Question 32

Polynomial

Answer 32

looks for trends in data

Question 33

how do you run a planned contrast in SPSS?

Answer 33

click on contrasts in the univariate window * for some contrasts you must specify which group to compare (first or last) -> change this if the control condition is indeed the first one (default tends to be last- depends on spss version) * this will depend on how you set up your data i.e. which variable is your control variable * once you've chosen a specific contrast, you must click change (if you don't it'll run the default) * you must do this for each of the IVs (and click change) * the contrast will appear next to your IV variable in the bracket i.e. IV name (simple) * click continue

Question 34

how do your interpret your planned contrast findings?

Answer 34

Contrast Results (K Matrix) * as usually, we're mostly interested in the p-value given in the sig row * all tests control for multiple comparisons -> no need to worry about family wise error

Question 35

what are custom contrasts?

Answer 35

sometimes you want to compare things in a way that built in contrasts don't * for one-way ANOVAs, SPSS allows you to specific your own contrasts

Question 36

How to calculate a custom contrast?

Answer 36

* One-way ANOVA window -> Drag Variable Across -> Contrasts -> Specify Co-Efficients ( * you're forcing SPSS to take two groups and give us a comparison of those two things)

Question 37

what are the rules of custom contrasts?

Answer 37

* contrasts must be independent (must test unique hypotheses and no double dipping) * only 2 chunks can be compared at once -> once you've compared the chunk, you then have to discard it, you can't compare it again in that particular set of contrast

Question 38

K-1 (what does this mean for custom contrasts?)

Answer 38

you should always have one less contrast than the number of groups e.g. 4 conditions with a simple contrast (1v2, 1v3, 1v4)

Question 39

how do custom contrasts work?

Answer 39

* assign each group a 'weight' (coefficient) * + weights compared to - weights * sum of weights for a comparison should equal 0 (should cancel each other out and be equal on both sides) * to remove a group from a contrast, you give it a weight of 0 (doesn't put it on the scale for the comparison) * once a group is singled out in a comparison, it should not be used in any subsequent contrasts (no double dipping)

Question 40

We can define some contrasts to compare different levels of the IV:

Answer 40

* we assign weights called coefficients to each level of the independent variable * these weights must sum to 0, so half should be positive and half negative * to be able to tell SPSS we want to compare these two things, we assign 1s and -1s - so coefficients add up to 0

Question 41

how to calculate contrasts in SPSS?

Answer 41

* type the weights into the box one at a time pressing 'add' after each one (coefficient total should be 0) * coefficients are added to the list * click next to define the next contrast * press continue

Question 42

how to check outputs of a custom contrast?

Answer 42

* check contrasts were defined correctly then find t and p values for each contrast (to see if there are any differences (i.e. 1 and 1 vs. -1 and -1 together) SPSS has be controlled for multiple comparisons * you can indicate the significance of your contrasts on a graph (through an *) * discuss these in your discussion section

Question 43

there are two main types of effect size, what are these?

Answer 43

* effect size based on the differences in means as scaled by the variance * Effect sizes that tell you what proportion of variance has been explained by the test

Question 44

Eta Squared:

Answer 44

* used for one-way ANOVA * same as R-squared

Question 45

Partial Eta Squared:

Answer 45

* use for factorial ANOVAs * gives you this in your ANOVA table (via selection in option) * tells you the proportion of variance that is uniquely explained * both scaled between 0 and 1 (0 means it doesn't explain any of the variance, 1 means it explains all of the variance -> tends to be between 0.3 and 0.6) * can find them in tests of between-subject effects tables and within-subject effects table dependent on whether it's a between-subject or within-subject ANOVA