PSYC3010 Exam Prep

Lecture 1

Interaction

When the effect of an IV on a DV, changes at levels of the second IV

Interactions expanding understanding of established effects

Tells us the conditions that the effect will be (stronger, weaker, reversed)

Factorial design

Used when there are two or more factors affecting the DV

Main effect

The effects of each factor (IV) on the DV

Advantages of factorial design

- Examines both IV's effects on the DV

- Examines interaction between both IV's

Research questions in two -way factorial design.

Main effect of Factor A

Main effect of Factor B

A x B Interaction

Significant interaction moderating main effect

whether the effect of one factor (IV) on the DV is changed by the other factor (IV)

Does it become stronger weaker etc.

Grand mean

Mean of all scores across all levels.

Marginal Means

Means of scores at each level of one factor (IV)

Marginal Mean calculation

Averaging scores of each level of one factor, disregarding input from the other factor.

Significant Main effect?

1. There is a difference somewhere between the marginal means.

2. Run Main comparisons (Pairwise comparisons)

Significant Main comparisons (Pairwise comparisons)?

Significant difference between specific sets of marginal means

What type of test examines significant Main Effects?

F-test

What type of test examines significant Main Comparisons?

protected t-test

Cell Means

Average of all scores within each cell, combining both factors (IV)

Significant Interaction

1. Relationship of one IV on the DV, changes at levels of the second IV

2. Run Simple effects test

Significant Simple effects test?

1. There is a difference somewhere between the cell means

2. Run Simple comparisons

Significant Simple Comparisons (Pairwise Comparisons)?

Significant difference between specific sets of cell means

What type of test examines significant Simple Effects?

F-test

What type of test examines significant Simple Comparisons?

t-test

No interaction (Graph plotting)

Parallel Lines

May be Interaction (graph plotting)

Non-parallel lines

Crossed lines (graph plotting)

Disordinal interaction

Lines do not cross (graph plotting)

Ordinal Interaction

Identifying simple effects (graph plotting)

Isolate one line, identify whether values of plots are different from each other.

Difference - Yes

No Difference - No

Main effect (graph plotting)

Identify whether averages of each IV (Marginal means) are different from each other.

Difference - Yes

No Difference - No

Between-groups

Factors have different people in each condition

Within-groups

all factors have same people in each condition

Mixed groups

Mix of between and within participants.

Lecture 2

One-Way Anova Research Question

Is there an effect of the IV on the DV.

MS treatment

Between groups variance

MS error

Within groups variance

SS treatment

Between-groups variability

SS error

Within-groups variability

MS treatment =

SS treatment/df treatment

MS error

SS error/df error

F =

between groups variance/within groups variance OR MS treatment/MS error

One-Way ANOVA Structural Model

Score of person i in group j = grand mean + treatment effect of group + error associated

Two-Way ANOVA Research Questions

Main effect of Factor A on DV?

Main effect of Factor B on DV?

Factor A x B interaction?

Two-Way between-groups ANOVA portioned variance

Between groups - Factor A variance, Factor B variance, A x B variance

Within groups variance

Factor A F-test

Omnibus test that assess whether there is a difference among the group means

Factor B F-test

Omnibus test that assess whether there is a difference among the group means

Factor A x B F-test

Omnibus test that assess whether there is a difference among the group means

Two-Way ANOVA Structural Model

Two-Way ANOVA Assumptions

-Normal distribution

-group populations have same variance

Lecture 3

Omnibus Test

A test that looks for all possible differences among levels of a factor (IV)

Omnibus tests in two-way ANOVA

1. Main effect tests

2. Interaction tests

3. F-tests (Significance)

Following up main effects

Pairwise comparisons OR linear contrasts

Pairwise comparisons

Compares two means at a time

Linear contrasts

Compare one mean OR set of means to another mean OR set of means

Protected t-tests

Only run after significant main effect has been found in omnibus test

What test is used to follow up a significant two-way interaction?

simple effects test

Simple effects test

Test conducted after finding significant interaction between factors

Main effects would need to be followed up when,

1. there are >2 levels of that factor

2. the test is significant

(through Main effect comparisons)

significant t test for main effect comparison tell us,

which differences between marginal means are significant

significant F test for a simple effect tells us?

there is a statistically significant difference between cell means

Maximum number of simple effects tested

equal to the number of levels of opposing factor

Specify the circumstances in which simple effects would need to be followed up

1. if the simple effect was significant

2. If there are >2 levels

types of comparisons following up significant simple effects

simple comparisons

simple comparisons

test that tells us EXACTLY which means differ

main comparisons vs simple comparisons

main comparisons assess marginal means, simple comparisons assess cell means

what does a significant t test for a simple comparison tell us

which differences between cell means are significant

How can variance be re-partitioned

Sum of simple effects of factor (IV) x = Sum of main effect of factor x + interaction

Eta-squared (η2)

proportion of total variance in the samples DV scores. (accounted for by the effect).

Omega-squared (ω2)

estimated proportion of total variance in the populations DV scores. (accounted for by the effect)

Partial eta-squared (ηp2)

proportion of residual variance (left over, not accounted for by other factors) in the sample's DV scores (accounted for by the effect).

Eta-squared (η2) vs Omega-squared (ω2)

(η2) - observed variability in the sample (may be biased)

(ω2) - estimated variability in the population

Eta-squared (η2) vs Partial eta-squared (ηp2)

η2 - proportion of total variance explained by a given factor

ηp2 - proportion of residual variance explained by any factor after removing variance from other factors.

Cohen's d

how many standard deviations apart two groups are

Confidence intervals

range of values we believe contains true values of what is being measured (usually with 95% confidence).

Lecture 4

Higher-order designs

Factorial design with >2 factors

Omnibus effects in a three way ANOVA

1. Main effects x3

2. Two-way interactions x3

3. Three way interaction

Three-way ANOVA research questions

1. Main effect of factor A (IV) on the DV?

2. Main effect of factor b (IV) on the DV?

3. Main effect of factor C (IV) on the DV?

4. Factor A x B Interaction?

5. Factor A x C interaction?

6. Factor B X factor C?

7. Factor A x B x C Interaction?

Structural Model of Three-way ANOVA

omnibus two-way interactions

1. tests interaction between two factors (IV), ignoring the third factor.

2. (e.g. A x B Interaction, AVERAGING ACROSS LEVELS of Factor C)

simple two-way interactions

1. tests interaction between two factors at each level of the third factor.

2. (e.g. A x B Interaction AT EACH LEVEL of Factor C)

Simple simple effects

1. follow up from significant simple two way interactions

2. test of one factor, at each level of the second factor, at the level(s) of the third factor, given the simple two way interaction was significant

3. (e.g. effect of Factor A, at each level of Factor B, at each level for Factor C)

Simple Comparisons vs Simple simple comparisons

1. SC's - Compare levels of Factor A at each level of Factor B

2. SSC's - Compare levels of Factor A at each level of Factor B, at each level of Factor C

Lecture 5

Correlation

Tests relationships between continuous variables (Standardised)

Covariance

1. reflects the degree to which two variables vary together

2. how much a score on a variable deviates from the variables mean

Covariance limitations

1. Unstandardised measurement between two variables

2. Scale dependent

3. Can vary drastically depending on scale used

Correlation coefficient

Pearsons "r"

Names for Pearson's r

1. Pearson's correlation

2. Bivariate correlation

3. Zero-order correlation

Pearson's r

1. Standardised measure of covariance

2. indicates strength/magnitude and direction of a relationship

3. can be converted into a correlation coefficient

Pearson's r vs covariance

expresses the relationship in terms of standard deviations, rather than raw deviations (covariance)

r range

-1 to +1, closer r is to zero, the weaker the relationship

when testing r for significance,

we see whether it is likely to reflect an actual relationship in the population. (confirmation)

coefficient of determination

r2

r2

indicates proportion of variance in one variable that can be explained by the other.

error/residual variance =

1-r2

SSy (Total variability)

SS regression + SS residual

SS regression

Variability in Y explained by X

SS residual

Variability in Y that cannot be explained by X

r2 vs r2 adj

variance in Y accounted for by all predictors.

adjusted less biased

b

unstandardised regression coefficient