ANOVA/ANCOVA using the GLM Procedure

Question 1

Fixed factor(s)

Answer 1

Categorical IVs or treatment conditions that we can replicate; for example a dosage of a drug (e.g. low, medium or high).

Question 2

Random factor(s)

Answer 2

A treatment condition that is unique in space and time

Question 3

Covariate(s)

Answer 3

The continuous IVs in out study

Question 4

Corrected Model Significance

Answer 4

The overall significance of our model, including all factors

Question 5

Factor significance

Answer 5

The significance of that particular factor

Question 6

Total SS

Answer 6

Variation around the origin (zero). Meaningless.

Question 7

Corrected Total SS

Answer 7

Variation around the grand mean

Question 8

Unique Sum of Squares (Type III)

Answer 8

The SS as if each effect was the last one fitted in the model. The unique SS for each predictor or factor. Does not depend on order of the IV fit.

Question 9

Sequential Sums of Squares (Type I)

Answer 9

The SS when each factor is fitted in order to the model. Depends on order of IV fit.

Question 10

SStotal

Answer 10

SSbetween/treat + SSwithin/error

Question 11

SSbetween

Answer 11

Take a score, subtract the grand mean, square the result for every score and sum the result

Question 12

SSwithin/error

Answer 12

Take each group mean, subtract the grand mean, square and then sum the results and multiply the sum by n.

Question 13

SStotal

Answer 13

Take a score, subtract the mean of the group it belongs to, square the result and add up results

Question 14

dftotal

Answer 14

N-1

Where N = total sample size

Question 15

dfbetween/treat

Answer 15

K-1

Where K= number of groups

Question 16

dfwithin/error

Answer 16

N-K

Question 17

MSbetween

Answer 17

SSbetween/dfbetween

Question 18

MSwithin/error

Answer 18

SSwithin/dfwithin

Question 19

Number of possible pairwise comparisons formula

Answer 19

k(k-1)/2

Question 20

Planned contrasts

Answer 20

Specified in advance. Are orthogonal (sum of contrast coefficients equals zero); no part of model variance used more than once
NB there will always be one less orthogonal contrast than groups.
NB no group should occur in more than one contrast

Question 21

Post-hoc contrasts

Answer 21

Not normally specified in advance. May not be orthogonal (sum of contrast coefficients may not equal zero); some part of model variance may be used more than once (e.g. comparing A and B to B and C). All possible pairwise comparisons of group means

Question 22

Subcommand: posthoc

Answer 22

Simple contrast og group means.

Question 23

Subcommand: contrast

Answer 23

A selection of predefined contrast combinations.

Question 24

Subcommand: lmatrix

Answer 24

Allows you to hand code contrast specifications.

Question 25

Subcommand: emmeans

Answer 25

Compare marginal design means.

Question 26

Subcommand: profile

Answer 26

Plot of means.

Question 27

Rules for defining contrasts

Answer 27

1. Choose sensible contrasts
2. If A is compared to B, give A the positive weight and B the negative weight
3. Within a contrast, the weights must add to zero
4. Any group not logically involved in a contrast gets a weight of zero
5. In contrasts of multiple group contrasts, that total weights for each ‘chunk’ should be equal

Question 28

Contrast sub command: deviation

Answer 28

each group versus overall mean

Question 29

Contrast sub command: Simple

Answer 29

Each group versus the reference group

Question 30

Contrast sub command: Difference

Answer 30

Each group versus mean of preceeding groups

Question 31

Contrast sub command: Helmert

Answer 31

Each group versus mean of preceeding groups

Question 32

Contrast sub command: Repeated

Answer 32

Difference between consecutive groups

Question 33

Contrast sub command: Polynomial

Answer 33

Linear, quadratic, cubic

Question 34

Posthoc adjustment

Answer 34

Bonferroni: Most conserative adjustment.

Least Significant Adjustment - no adjustment for multiple comparisons

Question 35

Emmeans sub command

Answer 35

Compares and displays marginal means which is the difference in the values of means across a factor (or factors).

Question 36

Effect size: partial eta squared or Omega squared

Answer 36

“generally a better representation of effect size in a population rather than a sample”.

Question 37

One way ANOVA

Answer 37

IV: One categorical IV.
DV: Continuous numeric.
Design: between subjects
Syntax: GLM taste BY coffee_type.

Question 38

Two way ANOVA

Answer 38

IVs: Two categorical IVs
DV: Continuous numeric
Design: between subjects
Syntax for additive: 
GLM taste BY coffee_type size. 
Syntax for interaction model: 
GLM taste BY coffee_type size
/ DESIGN = coffee_type coffee_type*size
/ LMATRIX = 'dark coffees versus milk coffees across sizes' coffee_type*size -1 0.5 0.5 +1 0.5 0.5

Question 39

ANCOVA
Why ANCOVA?
Why include co-variates?

Answer 39

IVs: One categorical IV, plus one or more continuous IVs.
DV: Continuous numeric.
Design: between subjects.

Why ANCOVA? Why include co-variates?

1. Eliminates the influence of potentially confounding variables.
2. Reduce SSresidual/error making our test more powerful.

If something is a factor we put it after BY, if something is a covariate it goes after WITH.

Question 40

One Way Repeated Measures ANOVA

Answer 40

IVs: One categorical IV.
DV: Continuous numeric.
Design: Within subjects

Question 41

Assumptions of Repeated Measures ANOVA:

Answer 41

1. Independence within groups
2. Sphericity/compound symmetry
3. Normal distribution within groups

Question 42

Compound Symmetry

Answer 42

1. Equal variance across conditions - is the standard deviations approximately the same across for our IVs?
2. Equal correlation (or covariance) between all possible pairs of conditions - do our IVs correlate with each other fairly consisently?

Question 43

Sphericity

Answer 43

We use Mauchley’s test where we want a p>= 0.05. Informally, do we get similar standard deviations across participants for our DV?

Question 44

What happens when we fail Mauchly’s test of sphericity?

Answer 44

1. Look at the Epsilon output of Mauchly’s test and examine the values for Greenhouse-Geisser, Huynh-Feldt and Lower Bound.
2. If any measure is > 0.75 we can discard it and move onto the next, more conservative measure.

Question 45

Two Way Repeated Measures ANOVA

Answer 45

IVs: Two categorical IVs. 
DV: Continuous numeric. 
Design: Within subjects
Syntax: 
GLM cap_small cap_med cap_large mocha_small mocha_med mocha_large
/ WSFACTOR coffee 2 size 3
/ MMATRIX = "Cap vs..." 
/ WSDESIGN = coffee size coffee*size.

Question 46

Mixed Designs ANOVA

Answer 46

IVs: IVs that span between and within subjects.
DV: Continuous numeric.
Design: Between subjects and within subjects.
Syntax:
GLM cap exp mocha black size BY gender
/ WSFACTOR coffee 4 coffee_size 2.