Repeated measures one-way ANOVA Flashcards
How do you calculate the F value with a t value?
F = t^2
Used when we have 1 IV with more than 2 levels, within participants
One-way repeated measures ANOVA
What contributes to variance between IV levels in repeated measures designs?
- Manipulation of IV (treatment effects)
- Experimental error (random error and potentially constant error)
Variance between IV levels due to individual differences is absent
a. Independent designs
b. Repeated measures design
b. Repeated measures design
What contributes to variance within IV levels in repeated measures designs?
- Experimental error (random error)
Variance within IV levels due to individual differences is absent
a. Independent designs
b. Repeated measures design
b. Repeated measures design
Total variance is the sum of…?
List 3 things
- Variance between IV levels
- Variance within IV levels
- Individual differences
What is the formula for the t/F ratio for repeated measures designs?
t/F = variance between IV levels / (variance within IV levels - variance due to individual differences)
or
t/F = MSM / MSR
The variance ‘caused’ by
our manipulation of the IV and error variance is known as…?
Variance between IV levels
Includes only error variance
This is known as…?
Variance within IV levels (excluding variance due to individual diffs)
Variance between IV levels
a. includes only error variance
b. includes the variance ‘caused’ by our manipulation of the IV and error variance
b. includes the variance ‘caused’ by our manipulation of the IV and error variance
Variance within IV levels (excluding variance due to
individual diffs)
a. includes only error variance
b. includes the variance ‘caused’ by our manipulation of the IV and error variance
a. includes only error variance
When F value is close to 0, is the variance between IV
levels relative to within IV levels small or large?
Small
When F value is far from 0, is the variance between IV
levels relative to within IV levels small or large?
Large
Small variance between IV
levels relative to within IV levels
a. F value far from 0
b. F value close to 0
b. F value close to 0
Large variance between IV
levels relative to within IV levels
a. F value far from 0
b. F value close to 0
a. F value far from 0
A dating website wants to find out if certain date locations result in better match success rates. They send 10 website members
on 4 dates each (with 4 suitable matches, randomly allocated to pair them on each date).
The different dates take place in a restaurant, a pub, a bowling alley and a cinema.
After each date, the participants are asked to rate their match in terms of
levels of attraction (a likert scale where 1 = no attraction and 7 = lots of attraction)
What are the:
a. IVs
b. IV levels
c. DV
d. Subjects design
e. Type of test
a. Date location
b. 4 (restaurant, pub, bowling alley, cinema)
c. Levels of attraction on a likert scale
d. Within subjects
e. Repeated measures one-way ANOVA
What are the 3 assumptions of repeated measures one-way ANOVA?
- Normality
- Sphericity (homogeneity of covariance)
- Equivalent sample size
What is the normality assumption for a repeated measures one-way ANOVA?
The distribution of difference scores under each IV level pair should be normally distributed
What is the sphericity (homogeneity of covariance) assumption for a repeated measures one-way ANOVA?
The variance in difference scores under each IV level pair should be reasonably equivalent
How do we check for Sphericity (homogeneity of covariance) on SPSS?
Mauchly’s test of sphericity
How do we correct for Sphericity (homogeneity of covariance) on SPSS?
Greenhouse-Geisser
What is the non parametric equivalent for a repeated measures one-way ANOVA?
Friedman Test
Friedman Test is a non parametric equivalent for…?
Repeated measures one-way ANOVA
What do we do when Mauchly’s test shows p < .05?
We reject H0, the data is not homogenous
Where on SPSS do we look for Mauchly’s W statistic?
On the ‘Mauchly’s Test of Sphericity’ table under the ‘Mauchly’s W’ column
Where on SPSS do we look for Mauchly’s p-value?
On the ‘Mauchly’s Test of Sphericity’ table under the ‘Sig.’ column
Where on SPSS do we look if Mauchly’s p-value is not significant (homogenous)?
‘Sphericity Assumed’ row
Where on SPSS do we look if Mauchly’s p-value is significant (heterogenous)?
‘Greenhouse-Geisser’ row
How do you present the F value for repeated measures one-way ANOVA?
F(dfM,dfR) = F-value, p = p-value
Variance between IV levels (incl. variance due to manipulation of the IV and error)
a. Model Sum of Squares (SSM)
b. Residual Sum of Squares (SSR)
a. Model Sum of Squares (SSM)
Variance within IV levels (incl.
only error variance, but not variance due to individual differences)
a. Model Sum of Squares (SSM)
b. Residual Sum of Squares (SSR)
b. Residual Sum of Squares (SSR)
What is the formula for Model Mean Square (MSM)?
MSM = SSM / dfM
or
MSM = Model Type III Sum of Squares / Model df
What is the formula for Residual Mean Square (MSR)?
MSR = SSR / dfR
or
MSR = Residual Type III Sum of Squares / Residual df
How do you calculate the F value based on SPSS output?
F = MSM / MSR
or
F. = Model Mean Square / Residual Mean Square
How many d.p. do you present the F value in?
2 d.p.
How many dfs are there for a repeated measures one way ANOVA?
2
- between IV level (model) variance
- within IV level (error/residual) variance
What is the formula to calculate the df for between IV levels for a repeated measures one-way ANOVA?
dfM = k - 1
or
dfM = number of IV levels - 1
What is the formula to calculate the df for within IV levels for a repeated measures one-way ANOVA?
dfR = dfM x (n - 1)
or
dfR = (number of IV levels - 1) x (sample size - 1)
What post-hoc test is used for repeated measures one-way ANOVA?
Bonferroni
What post-hoc test is used for independent one-way ANOVA?
Tukey HSD
What is the formula for partial eta^2 / partial n^2?
partial n^2 = SSM / SSM + SSR
How many d.p. do we report partial n^2 in?
3 d.p.
Do we include a 0 before the decimal point when reporting partial n^2?
No
Calculate the Cohen’s d for all comparisons
Data:
Restaurant
M = 5.35
SD = 0.99
Pub
M = 6.00
SD = 1.03
Bowling
M = 4.40
SD = 1.14
Cinema
M = 3.90
SD = 0.79
Restaurant - Pub
d = 5.35 - 6.00 / ((0.99 + 1.03) / 2)
d = 0.65
Restaurant - Bowling
d = 5.35 - 4.40 / ((0.99 + 1.14) / 2)
d = 0.89
Restaurant - Cinema
d = 5.35 - 3.90 / ((0.99 + 0.79 ) / 2)
d = 1.63
Pub - Bowling
d = 6.00 - 4.40 / ((1.03 + 1.14) / 2)
d = 1.47
Pub - Cinema
d = 6.00 - 3.90 / ((1.03 + 0.79) / 2
d = 2.32
Bowling - Cinema
d = 4.40 - 3.90 / ((1.14 + 0.79) / 2
d = 0.52
What are the 3 main advantages of repeated measures designs?
- Recruitment: needs fewer participants to gain the same number of measurements
- Error variance (within IV levels) is reduced
- More power with the same number of participants
One advantage of repeated measures design is that error variance (within IV levels) is reduced
How?
- Remove variance due to individual differences from
error variance - Because this variance is eliminated from our model variance (each participant acts as his/her own control)
One advantage of repeated measures design is that there is more power with the same number of participants
Why is this an advantage?
- Easier to find significant difference (avoid Type II error)
- Because with the same variance due to IV manipulation, the resulting F/t value is larger
- Recruitment: needs fewer participants to gain the same number of measurements
- Error variance (within IV levels) is reduced
- More power with the same number of participants
Are these advantages of independent or repeated measures designs?
Repeated measures designs
What are the 3 disadvantages of repeated measures design?
- Order effects
- Counterbalancing
- Alternatives where counterbalancing not possible
What are the 4 types of order effects?
- Practise effects
- Fatigue effects
- Sensitisation
- Carry-over effects
- Practise effects
- Fatigue effects
- Sensitisation
- Carry-over effects
These are examples of…?
Order effects
How can we control for order effects?
Counterbalancing
How do we control for practice effects where counterbalancing is not possible?
Extensive pre-study practise
How do we control for fatigue effects where counterbalancing is not possible?
Short experiments
How do we control for sensitisation effects where counterbalancing is not possible?
Intervals between exposure to IV levels
How do we control for carry-over effects where counterbalancing is not possible?
Include a control group
Instead of counterbalancing, extensive pre-study practise is used to control for…?
a. Practise effects
b. Fatigue effects
c. Sensitisation
d. Carry-over effects
a. Practise effects
Instead of counterbalancing, a control group is used to control for…?
a. Practise effects
b. Fatigue effects
c. Sensitisation
d. Carry-over effects
d. Carry-over effects
Instead of counterbalancing, short experiments are used to control for…?
a. Practise effects
b. Fatigue effects
c. Sensitisation
d. Carry-over effects
b. Fatigue effects
Instead of counterbalancing, intervals between exposure to IV levels are used to control for…?
a. Practise effects
b. Fatigue effects
c. Sensitisation
d. Carry-over effects
c. Sensitisation
One-way ANOVA can be applied to situations where there are ______ IV levels
a. 2 IV levels
b. 3 or more IV levels
b. 3 or more IV levels
More post-hoc comparisons means _____ Cohen’s d calculations
a. More
b. Less
a. More
