Repeated Measures ANOVA Flashcards
COMPARING DIF GROUPS
- non-repeated measures
- between-participants
- between-groups
- between-subjects
- independent
COMPARING SAME GROUP
- repeated measures
- within-pps
- within-groups
- within-subjects
- non-independent
BETWEEN-PPS (HYPOTHETICAL) AKA. ONE-WAY ANOVA
- scores not linked
- unable to calculate decline scores
- can only compare mean scores
- no sign dif revealed between groups
ONE-WAY ANOVA IMPLICATIONS
- dubious as based on assumption that scores in dif groups = independently sampled aka. unlinked in any way
- aka. assumes samples are also independent
- violated is same pp tested 2+ occasions as each pps scores = NOT independent
- aka. T1/T2 scores = paired as come from same pps
WHEN TO USE BETWEEN/NON-REPEATED?
- when data for each experimental condition is collected via testing completely dif/independent pp sets
WHEN TO USE WITHIN/REPEATED?
- when pps are tested on REPEATED occasions (ie. 2+ times)
- apply special purpose ANOVA here
RELATION BETWEEN “T” & “F”
- t-value = from paired t-test
- F value = from repeated ANOVA
- ie. t(6) = 7.07; F (1,6) = 50.00
- t = ALWAYS STATSIG whenever F is; vice versa
- w/2 lvls, both tests = dif versions of SAME test
- BUT… F-test (aka. ANOVA) = more general as can be applied in exactly same way when factor being tests = 2+ lvls
- can also be used in 2/3+ factor designs when other factors = either RM/NRM/both
AKA. NON-REPEATED MEASURES
- assumes scores from dif groups = independent/unrelated to one another
- no particularly important statistical assumptions affect reliability/F-ratios
AKA. REPEATED MEASURES
- assumes scores from dif conditions = links aka. probably correlations across group lvls
- reliability of F-ratios depends on extent to which data meets sphercity assumption
THE ASSUMPTION OF SPHERCITY
- ANOVA relies on certain assumptions about data (ie. this)
- for sphercity to exist, SDs of dif columns must be equal
- aka. we assume the affect of manipulation (ie. delay) at each step = approximately the same for all pps
ASSESSING SPHERCITY
MAUCHLEY’S
- routinely given as first SPSS output step
- sig Mauchly’s W indicates that sphercity assumption = violated (aka. sig W = TROUBLE)
- BUT… Mauchly’s = inaccurate aka. ignore
- do “Lower Bound” instead
DEALING W/SPHERCITY DEPARTURES
WORST CASE SCENARIO
- assumes that violation = as bad as possible
- aka. each pp = affected entirely dif by dif stages of manipulation
- so… -> “Lower Bound”
- 4 dif F-ratios/p-values reported for RM ANOVA:
1. Sphercity Assumed (high sig = no violation)
2. Greenhouse-Geiser (intermediate)
3. Huynh-Felt (intermediate)
4. Lower-bound (JUST statsig = WCS)
- only dif lies in DoF
- no difs in F-ratios
- BUT reducing dfs = ^ crit value of F-ratio -> reduces p-value
SPSS CALC FOR SPHERCITY ADJUSTMENTS
BEST CASE SCENARIO
- all pps equally affected by all lvls of IVs
WARNING SIGN
- if 4 p-values = dif in table ->
WORST CASE SCENARIO
- v rare
- LB/G-G usually ^ Type 2 error chance unnecessarily
INTERMEDIATE SCENARIO
- more common
- H-F test offers best compromise between likelihood of making Type 1/2 errors
SPSS SPHERCITY OUTPUT
- 3 “sphercity violated” tests carried out automatically by SPSS; appear as part of RM output
- Huynh-Feldt agreed as best compromise
- also includes live giving F-ratios based on assumption that there’s NO sphercity issue
- aka. “sphercity assumed”
HAND CALCS FOR SPHERCITY ADJUSTMENTS
- all take form of REDUCING dfs used to assess statsig of calc F-ratio
- reducing dfs = sig more difficult to achieve
- calc involves multiplying usual dfs by epsilon (E)
- Greenhouse-Geisser/Huynh-Feldt estimates of E = designed to accurately estimate correction needed to compensate for issues w/sphercity
- SEE CHEAT SHEET
- BUT… don’t need calcs for course
- just report SPSS calcs + full dfs
SPHERCITY ADJUSTMENTS FOR CONTRASTS
- contrast tests (planned/unplanned) can be carried out on RM factors just like on NRM
- BUT… SPSS syntax = dif
- BUT… sphercity for contrasts?
- NO; for sphercity to exist, SDs of dif columns must be equal
- aka. sphercity assumption CANNOT be violated as there’s only 1 dif column aka. SD inequalities = impossible
POLYNOMIAL/PLANNED CONTRAST EFFECTS
- dif values for dfs for all 4 tests = violation w/sphercity assumption
- SPSS automatically calculates contrast effects for within-pps variable
ADVANTAGE - if contrast is needed you don’t have to worry about typing in syntax
DISADVANTAGE - meaningless for non-quantitative variables so “help” may be misleading
CONCEPT OF ANOVA I: SIGNAL TO NOISE RATIO
- ANOVA tries to identify difs in DV score (group variance) that vary systematically w/group/condition membership
- compares difs w/random variations in score (error variations) that DON’T vary systematically w/group membership
- when group variance = high & error variance = low -> grouping variable effect = detectable
- when error variance = high & group variance = low -> grouping effect variable = undetectable
- aka. signal to noise ratio; if signal = stronger than background noise -> signal = detectable
- if background noise = too high, signal = undetectable
CONCEPT OF ANOVA II: WITHIN-GROUPS VARIANCE
- difs in scores (variance) explained by factor (ie. difs between groups)
- difs between scores (variance) that CANNOT be explained by factor (ie. difs within groups)
- within-groups variance = error
- F-ratio = between-groups variance divided by within-groups variance (mean square of error)
- must make sure that correct error terms are used for calc
