Factorial ANOVA (independent) Flashcards
What is the purpose of including more than one IV in the study?
We can explore the effects of
each IV on the DV and the interactions between the IVs
Used to test for differences
when we have more than one IV
Factorial ANOVA
What are the three broad factorial ANOVA designs?
- Independent
- all IVs are between-subjects - Repeated Measures
- all IVs are within-subjects - Mixed
- a mixture of between-subjects and within-subjects IVs
True or False?
The terms ‘IV’ and ‘factor’ are not interchangeable
False
The terms ‘IV’ and ‘factor’ are interchangeable
ANOVAs with more than one IV are called…?
Factorial ANOVAs
How many IVs/factors are present in a 2-way independent ANOVA?
2 IVs
How many IVs/factors are present in a 4-way independent ANOVA?
4 IVs
How many IVs/factors are present in a 3-way repeated measures ANOVA?
3 IVs
How many IVs/factors are present in a 2-way mixed ANOVA?
2 IVs
2-way independent ANOVA, 4-way independent ANOVA, 3- way repeated measures, 2-way mixed ANOVA etc…
What does the number mean?
The number of IVs/factors
IVs/factors in a factorial NAOVA have at least ___ levels
2
What does a 2*2 ANOVA mean?
- 2 IVs/factors
- One IV with 2 levels
- One IV also with 2 levels
What does a 2*4 ANOVA mean?
- 2 IVs/factors
- One IV with 2 levels
- One IV with 4 levels
What does a 4* 2 *2 ANOVA mean?
- 3 IVs/factors
- One IV with 4 levels
- One IV with 2 levels
- One IV also with 2 levels
Used when there are 2 or more IVs, between subjects
Two-way independent ANOVA
Used when there are 2 or more IVs, within subjects
Two-way repeated measures ANOVA
Used when there are 2 or more IVs, at least one IV that is between subjects and at least one IV that is within subjects
Two-way mixed ANOVA
A two-way factorial ANOVA tells us 2 things
What are they?
- Main effects
- Interaction
Do gender effects depend on
texture?
Is this an example of:
a. Main effects
b. Interaction
b. Interaction
Is there a texture effect?
Is this an example of:
a. Main effects
b. Interaction
a. Main effects
Is there a gender effect?
Is this an example of:
a. Main effects
b. Interaction
a. Main effects
Instead of running separate one-way ANOVAs (or t-tests) to learn about main effects, we use factorial ANOVAs to control for…?
Familywise error rate
What do factorial ANOVAs control for…?
Familywise error rate
The dependency of one factor (or IV) on another
factor (or IV)
This is known as…?
Interaction effects
True or False?
Factorial ANOVA does not tell us about interaction effects
False
Factorial ANOVA tells us about interaction effects
What makes up the variance between IV levels in a two-way independent ANOVA?
- IV 1 variance
- IV 2 variance
- Interaction variance
What makes up the variance within IV levels in a two-way independent ANOVA?
- Error
(incl. individual diffs and experimental error)
The combined effects of multiple IVs/factors on the
DV
This is known as…?
Interaction effects
What are interaction effects?
The combined effects of multiple IVs/factors on the
DV
What does a significant interaction effect indicate?
The effect of manipulating one IV depends on the level of the other IV
True or False?
Where an interaction is present, it is always meaningful to draw conclusions from the main effects
False
Sometimes where an interaction is present, it’s not meaningful to draw conclusions from the main effects
A researcher is interested in whether the way individuals’
experience sport influences it’s impact on their mood.
She also wants to consider whether any influence of sport experience is dependent on gender.
She randomly assigns participants to either participate in a team sport, solo exercise or to watch
sport on TV.
Half the participants in each group are male and half are female. Having completed the sport experience, they
rate their level of positivity on a scale between 1-100.
What are the:
a. IVs
b. IV levels
c. DV
d. Subjects design
e. Type of test
a. Sport experience, Gender
b. 3 (team, solo, TV), 2 (male, female)
c. Level of positivity
d. Between subjects
e. Two-way independent ANOVA
For factorial ANOVAs, the first IV referred to as the…?
‘Main IV’
For factorial ANOVAs, the second IV referred to as the…?
‘Secondary IV’
What are the 4 assumptions for a two-way independent ANOVA?
- Normality
- Homogeneity of variance
- Equivalent sample size
- Independence of observations
What is the non parametric equivalent for factorial ANOVA?
There are none
Instead, we can attempt to fix or simplify the design
What is the normality assumption for a two-way independent ANOVA?
The DV should be normally distributed, within each condition
What is the homogeneity of variance assumption for a two-way independent ANOVA?
The variance in the DV, within
each condition, should be (reasonably) equivalent
What is the equivalent sample size assumption for a two-way independent ANOVA?
Sample size within each
condition should be roughly equal
What is the independence of observations assumption for a two-way independent ANOVA?
Scores within each condition should be independent
How do we check for homogeneity on SPSS for a two-way independent ANOVA?
Look at the ‘Levene’s Test of Equality of Error Variances’ table and look at the ‘Based on Mean’ row
Is there a correction value / Welch’s values of F for factorial ANOVA?
No
How do you present the F value of a two-way independent ANOVA?
F(df IV 1, df IV 1 error) = F-value IV 1, p = p-value IV 1
What is the formula for F value for a two-way independent ANOVA?
F = Mean Square IV 1 (MSM) / Mean Square Error IV 1 (MSR)
What is the formula for partial eta^2 or partial n^2?
Partial n^2 = SSM / SSM + SSR
or
Partial n^2 = Model Type III Sum of Squares / (Model Type III Sum of Squares + Error/Residual Type III Sum of Squares)
What is the formula for classical eta^2 or n^2?
n^2 = SSM / SST
Proportion of the total variance attributable to the
factor
This is known as…?
Classical eta^2 or n^2
What is classical eta^2 or n^2?
Proportion of the total variance attributable to the
factor
The calculation of ______ only takes into account the variance from one IV at a time
a. classical eta^2 or n^2
b. partial eta^2 or partial n^2
b. partial eta^2 or partial n^2
The calculation of partial eta^2 only takes into account
…?
The variance from one IV at a time
Proportion of the total variance attributable to the
factor, partialling out (excluding) variance due to other factors
This is known as…?
Partial eta^2 or partial n^2
What is partial eta^2 or partial n^2?
Proportion of the total variance attributable to the factor, partialling out (excluding) variance due to other factors
What is the formula for partial eta^2 or partial n^2 in terms of classical eta^2 or n^2?
Partial n^2 = SSM 1 / SST - (SSM 2 + SSM 1 x SSM 2)
Post hoc tests are only relevant when…?
List 2 points
- Main effect of IV is significant
- IV has more than 2 levels
Report Cohen’s d alongside post hoc results
a. One-way ANOVA only
b. One-way ANOVA and Two-way ANOVA
c. Two-way ANOVA only
d. Neither One-way ANOVA or Two-way ANOVA
a. One-way ANOVA only
Cohen’s d not reported alongside post hoc results
a. One-way ANOVA only
b. One-way ANOVA and Two-way ANOVA
c. Two-way ANOVA only
d. Neither One-way ANOVA or Two-way ANOVA
c. Two-way ANOVA only
True or False?
Cohen’s d is reported alongside post hoc results for factorial ANOVA
False
Cohen’s d is not reported alongside post hoc results for factorial ANOVA
True or False?
Cohen’s d is reported alongside post hoc results for one-way ANOVA
True
Interaction effect size is reported by…?
partial n^2
Effect size for simple effects is known as…?
Cohen’s d
Effect size for simple effects
a. Partial n^2
b. Cohen’s d
b. Cohen’s d
Interaction effect size
a. Partial n^2
b. Cohen’s d
a. Partial n^2
If the SPSS output contained a ‘Tests of Between-Subjects Effects’, what does this suggest about the data?
It follows a two-way independent ANOVA and we are looking for an interaction
How do we report the F-value for an interaction?
F (df interaction, df error/residual) = F-value interaction, p = p-value interaction
The ANOVA looks for differences between marginal means to determine …?
Main effects
The ANOVA looks for differences between _____ to determine main effects
Marginal means
True or False?
The ANOVA deals with one IV at a time, ignoring the other IV
True
The presence of an interaction suggests we need to consider …?
Differences at the level of cell means (simple effects)
Simply = The effect of the main IV at different levels of the secondary IV
The effect of an IV at a single level of another IV
This is known as…?
Simple effects
What are simple effects?
The effect of an IV at a single level of another IV
How do we determine whether simple effects are significant?
Conduct t-tests between individual cell means
We conduct t-tests between individual cell means in order to…?
Determine whether simple effects are significant
To determine whether simple effects are significant,
we conduct t-tests between individual cell means
This is only appropriate when…?
The interaction is significant
Repeated testing increases the risk of…?
a. Type 1 error
b. Type 2 error
a. Type 1 error
How do we correct simple effects following Bonferroni correction?
Divide required alpha level
(e.g. α = .05) by the number of comparisons
e.g. 4 comparisons: .05/4 = .013
So, we’d conclude the paired comparison is significant
IF p < .013
Males
team vs. solo: t(18) = 6.50, p < .001
team vs. watch: t(18) = 7.60, p < .001
solo vs. watch: t(18) = 1.24, p = .230
Females
team vs. solo : t(18) = 2.68, p = .015
team vs. watch : t(18) = 3.61, p = .002
solo vs. watch : t(18) = 0.97, p = .345
Which are significant after applying Bonferroni correction?
Comparisons are significant if:
p = .05 / 6 comparisons
p < .008
Males:
- team vs. solo: t(18) = 6.50, p < .001
- team vs. watch: t(18) = 7.60, p < .001
Females:
- team vs. watch : t(18) = 3.61, p = .002
We need to correct our
alpha level in simple effects to control for …?
Type 1 errors
Because the simple effects tests are run as t-tests, the appropriate effect size measure is …?
Cohen’s d
Why is Cohen’s d the appropriate effect size measure for simple effects?
Because the simple effects tests are run as t-tests
