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Lab 2: repeated measures ANOVA

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Inferior parietal involvement in long term memory

• There is a hypothesis that different brain regions are recruited during recall processes– A distinction between recognition -> I remember details of learning how to

calculate contrasts, like who taught me and why. and familiarity -> I have a vague notion that contrasts were described to me at some point.

• Experiment: Have people study a list of 150 words, wait 20min, then put them in the scanner and show them a list of 300 words, half old half new– Ask them to rate on a 4 point scale: 1 new word, 2 low confidence that they

studied it before, 3 high confidence but don’t remember any details, and 4 recognition with details.

– Record brain activity during memory test. Extract changes in blood flow from brain regions thought to be involved in memory processes.

– Classify brain activation by subjects’ ratings.

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Is inferior parietal cortex differentially involved in recognition and familiarity?

• Dependent variable?

• Independent variables?

• What type of design?

• How data organized?

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Assumptions: conditions of application

1. Independence of observations2. Normality within each factor level or group– Robust to violations as long as fully factorial -> no cells missing– If not, need to test with histograms

3. Homogeneity of variance: Replaced by compound symmetry (or sphericity) in RM ANOVA– Robust to violations as long as largest covariance is not more than 4

times the smallest and group sizes are approximately equal -> often get with repeated measures as all subjects complete each condition.

– If fail, should check for sphericity: variances of the difference of each pair of levels is identical (don’t need to check for two factor variable).

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Compound symmetry

• Correlate: Bivariate– Options• Cross-product deviations and covariances

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Compound symmetry

What about negative covariance numbers? Use absolute value

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Failed compound symmetry, now what?

• Continue on with analysis, but check Sphericity assumption within ANOVA

• Analyze: General linear model: repeated measures

• Setup factors: important to think about order

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Order of conditions potentially important• Make it easy on yourself – Set up conditions in order of columns of your data

if possible• Preserve/respect any natural ordering in

conditions– Control or neutral condition should be on the end so thatYou can use contrasts.

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Different windowsPlots Contrasts

Options

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Output: verify assumptions

• Mauchly’s test null hypothesis: variances of the differences all equal• Sphericity violated for interaction

– Greenhouse-Geisser value ranges from 0-1, closer to 1 means less deviation from 0. • Greater than .75, safe to use Huynh-Feldt, otherwise use GG

– Or use MANOVA, provided by SPSS automatically

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Results

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Main effect of recall

• Null hypothesis: all means the same• Can conclude that at least one of the means differ,

since there was a significant main effect of recall:– F3,24=13.26, p<.001

• But don’t know how differ– Need contrasts for this if there is a logical order– If no specific hypothesis, can do pairwise comparisons– Or if a very specific hypothesis can do paired t-tests

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Helps to look at your data

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Contrasts

• Linear contrast: is the last level sig different from first• Quadratic: If one of the middle conditions differs from what would be a

linear trend.• Implies a true linear relationship across all levels requires a sig linear

contrast with a non-sig quadratic

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Simple contrasts

• Chose simple contrasts comparing to last variable (correct reject)

• Recognition differs significantly from correct reject, collapsing across hemisphere (F1,8=16.36, p<.01)

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• Choice between LSD (lenient correction for multiple comparisons), Bonferroni (harsh correction), or Sidak (somewhere in between).

Pairwise comparisons

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Results

Fail to reject null hypothesis that the two hemispheres differ.(F1,8=1.09, p>.05)

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Results

Results show that there is a significant interaction between recall and hemisphere, using the Greehouse-Geisser correction (F1.45, 11.58=11.83, p<.01)

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Since violate sphericity, good to double check with MANOVA

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What does interaction mean?

• Results show that there is a significant interaction between recall and hemisphere, using the Greehouse-Geisser correction (F1.45, 11.58=11.83, p<.01)

• Get an interaction when linesdeviate from being parallel • Need to re-think main effectsBecause the story is not so simple

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Often gets tricky to investigate interactions with contrasts

• Can break apart analysis and investigate each independent variable separately for each level of the other (i.e. investigate simple effects)– Investigate recall for just left hemisphere, then repeat

for right hemisphere• Sometimes, if have a specific hypothesis, you can

also do a paired t-test to follow up – For instance, if you thought that only the left inferior

parietal cortex not right, was involved in recognition • Just what people do think!

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Now you try!!• A study was conducted to investigate how fMRI signals

varied by the hardware used to collect them (a 12 channel or 32 channel receiver coil) and by the amount of acceleration used (none, 2 factor or 3 factor).

• Each of 12 subjects completed each condition.• Its hypothesized that:– the signal will be greater when more channels are used– signal strength will decrease as more acceleration is

used.• These effects will be stronger for the 12 channel coil

compared to the 32.

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Should be able to answer:

• What are the independent and dependent variables?

• Are the conditions of application met?– Compound symmetry?– Sphericity?

• Are there main effects?• Interactions?• What can you conclude?