Factorial ANOVAs Flashcards
what do ANOVAs help us to reduce?
type 1 errors (based on the use of multiple comparisons -> we want to avoid family wise error)
what is a Factorial Independent ANOVA?
has multiple independent variables
* different participants in all conditions
*one dependent/outcome variable
* you still need to run one ANOVA per dependent variable
what is a factorial design?
when you have several independent variables
what is a two-way factorial anova?
when there are two independent variables
i.e.
IV1: democratic status (4 levels)
IV2: GDP (3 levels)
DV: happiness score
what is a three-way factorial anova?
when there are three independent variables
what does a factorial design allow you to do?
allows you to look at interaction effects between variables
* the effect of one IV may depend on the level of another IV
what are the assumptions of a factorial anova?
- 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)
what should you do when assumptions are violated?
non-parametric alternative
how to structure your data (for a two-way factorial ANOVA)
IV1 (Coded)
IV2 (Coded)
DV
How to inspect your data for a One-Way Factorial ANOVA?
- 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
Running the Factorial ANOVA
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
â—‹ Plot Window allows you to draw a graph
â—‹ Drag IV with most levels to Horizontal axis
â—‹ Drag IV with fewest levels to separate lines
â—‹ Click Add > Continue
* Click Post-Hoc Tests (options same as ones in One-Way ANOVA)
â—‹ Post Hoc Window - Drag IVs to post-hoc box (select appropriate test(s))
* Click Options
â—‹ Drag your IVs and the interaction across to the Display means box
* Display
â—‹ Descriptive statistics, estimates of effect size, homogeneity tests
How should you interpret the output?
- Descriptive statistics box/table
- Levene’s Test of Equality of Error Variances
- Tests of Between-Subjects Effects
- Write up your results
descriptive statistics box/table
- check sample sizes are what you expected
Levene’s Test of Equality of Error Variances
homogeneity test -> we want Levene’s to be non-significant so we can assume equal variance
Test of Between-Subjects Effect
- main ANOVA summary table
- highlights main effects of your IVs -> interaction effect between the IVs
- Partial Eta Squared
what is Partial Eta Squared?
Effect Size
Writing up your results:
- 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)
how do we know if there’s a significant interaction?
if there isn’t then two variables do not influence one another -> main effect of IV1 is not influenced by the level of IV2
in what designs do interactions happen>
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
how do we know if there’s an interaction effect?
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)
what is not an interaction effect?
lines that are next to each other -> but not crossing over
when can we use planned contrasts?
if your ANOVA is significant, we can explore the effects more deeply through planned contrasts (i.e. planned comparisons) and compare every level specific
Planned Contrasts
- 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
How do planned contrasts actually work?
- 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
planned contrasts in the form of a cake analogy:
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
What are the Planned Contrasts that you can calculate?
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
Deviation
compared the means of each condition to overall mean
Simple
compares the mean of each condition to wither the first or last condition (i.e. compare with a control group
Helmert
compare the mean of one condition to the average of all other conditions
Difference
reverse of Helmet -> compares the mean of a condition to the average of all previous conditions
Repeated
compares sequential pairs of conditions
Polynomial
looks for trends in data
how do you run a planned contrast in SPSS?
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
how do your interpret your planned contrast findings?
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
what are custom contrasts?
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
How to calculate a custom contrast?
- 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)
what are the rules of custom contrasts?
- 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
K-1 (what does this mean for custom contrasts?)
you should always have one less contrast than the number of groups
e.g. 4 conditions with a simple contrast (1v2, 1v3, 1v4)
how do custom contrasts work?
- 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)
We can define some contrasts to compare different levels of the IV:
- 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
how to calculate contrasts in SPSS?
- 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
how to check outputs of a custom contrast?
- 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
there are two main types of effect size, what are these?
- 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
Eta Squared:
- used for one-way ANOVA
- same as R-squared
Partial Eta Squared:
- 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
