Summary
- ANCOVA can:
o Reduce error variance (increase power of the test). Then covariate is related to the
dependent measure.
o Correct for a confound (increase accuracy (and power) of the test). Then covariate
is systematically related to both the dependent and the independent variable.
- Original effect of IV can:
o Become stronger (through reduced error or by increased accuracy).
o Disappear (through adjusted means) → then covariate explains the effect →you can
be happy (mediation) or unhappy (uninteresting other variable) with this result.
- Covariate can also be used as another IV
o Effect of manipulations depend on covariate (interaction).
o Use it in a regression (continuous variable): spot-light analyses.
Lecture 6 – Repeated measures mixed design
Repeated measures
Within-subject design: why?
- Advantage:
o Less participants needed (more power)
o Measure changes in time
o Increased comparability of conditions
- Disadvantage:
o Carry over effects (e.g., mood manipulation)
o Expectation effects: effect of surprise/novelty of task is lost
o Practice/maturation effects (learning, familiarity, boredom, fatigue)
Repeated measures: variance revisited
- When we have different measures on the same people, we use the “repeated measures”
ANOVA.
- Now the systematic variance is between measures, not between groups.
32
,Repeated measures: T-test
- Participants recall of positive vs. neutral words
- Valence is the within-participants IV
- DV is recall of words per valence condition
- H0: no difference in recall across different conditions
One-way ANOVA
- 1 within-participants IV, > 2 levels (conditions)
- Participants assigned to all levels of the IV
- Example: evaluation of copycats with low, moderate and high similarity
33
,Variance partitioning
- Systematic variance (SSIV) = sum of squares of the difference from the mean of the
conditions to the grand mean
- Error variance (SSerror) = SStotal – SSIV – SSbetween participants
o SStotal = sum of squared differences of all scores from the grand mean
o SSIV = sum of squared differences of each condition’s mean from the grand mean
- When we have a within design, we can also correct for individual differences (overall mean
of the participant)!
o SSbetween participants = sum of squared differences of each participant’s mean (across
conditions) from the grand mean
Mauchly sphericity assumption test
- Variances of differences between the conditions should be equal.
- You need at least 3 conditions for sphericity to be an issue.
- Should (like Levene’s test) not be significant (p > .05).
- If significant: higher chance Type I error (you confirm the hypothesis while you shouldn’t).
34
, What if sphericity is violated?
- Use adjusted F-test
- Look at Greenhouse-Geisser estimate (epsilon) in SPSS output:
o When ε < .75 then use the Greenhouse-Geisser correction
o When sphericity (ε) > .75 then use the Huynh-Feldt correction
→ significant → not good. Look at Greenhouse-Geisser >.75 → not good. Look at Huynh-Feldt
>.75 → good. Look at the results fron the Huyn-Feldt test.
Example
- Hypothesis: Ads with strong arguments lead to more favorable product attitudes than ads
with weak or no arguments.
- Each participant 3x advertisement with different argument strength
o Strong (condition = 1)
o Weak (condition = 2)
o No (condition = 3)
- DV = attitude (1-7)
- Three group (argument strength: no, weak, strong), within-subject design
35
- ANCOVA can:
o Reduce error variance (increase power of the test). Then covariate is related to the
dependent measure.
o Correct for a confound (increase accuracy (and power) of the test). Then covariate
is systematically related to both the dependent and the independent variable.
- Original effect of IV can:
o Become stronger (through reduced error or by increased accuracy).
o Disappear (through adjusted means) → then covariate explains the effect →you can
be happy (mediation) or unhappy (uninteresting other variable) with this result.
- Covariate can also be used as another IV
o Effect of manipulations depend on covariate (interaction).
o Use it in a regression (continuous variable): spot-light analyses.
Lecture 6 – Repeated measures mixed design
Repeated measures
Within-subject design: why?
- Advantage:
o Less participants needed (more power)
o Measure changes in time
o Increased comparability of conditions
- Disadvantage:
o Carry over effects (e.g., mood manipulation)
o Expectation effects: effect of surprise/novelty of task is lost
o Practice/maturation effects (learning, familiarity, boredom, fatigue)
Repeated measures: variance revisited
- When we have different measures on the same people, we use the “repeated measures”
ANOVA.
- Now the systematic variance is between measures, not between groups.
32
,Repeated measures: T-test
- Participants recall of positive vs. neutral words
- Valence is the within-participants IV
- DV is recall of words per valence condition
- H0: no difference in recall across different conditions
One-way ANOVA
- 1 within-participants IV, > 2 levels (conditions)
- Participants assigned to all levels of the IV
- Example: evaluation of copycats with low, moderate and high similarity
33
,Variance partitioning
- Systematic variance (SSIV) = sum of squares of the difference from the mean of the
conditions to the grand mean
- Error variance (SSerror) = SStotal – SSIV – SSbetween participants
o SStotal = sum of squared differences of all scores from the grand mean
o SSIV = sum of squared differences of each condition’s mean from the grand mean
- When we have a within design, we can also correct for individual differences (overall mean
of the participant)!
o SSbetween participants = sum of squared differences of each participant’s mean (across
conditions) from the grand mean
Mauchly sphericity assumption test
- Variances of differences between the conditions should be equal.
- You need at least 3 conditions for sphericity to be an issue.
- Should (like Levene’s test) not be significant (p > .05).
- If significant: higher chance Type I error (you confirm the hypothesis while you shouldn’t).
34
, What if sphericity is violated?
- Use adjusted F-test
- Look at Greenhouse-Geisser estimate (epsilon) in SPSS output:
o When ε < .75 then use the Greenhouse-Geisser correction
o When sphericity (ε) > .75 then use the Huynh-Feldt correction
→ significant → not good. Look at Greenhouse-Geisser >.75 → not good. Look at Huynh-Feldt
>.75 → good. Look at the results fron the Huyn-Feldt test.
Example
- Hypothesis: Ads with strong arguments lead to more favorable product attitudes than ads
with weak or no arguments.
- Each participant 3x advertisement with different argument strength
o Strong (condition = 1)
o Weak (condition = 2)
o No (condition = 3)
- DV = attitude (1-7)
- Three group (argument strength: no, weak, strong), within-subject design
35
