Two-way repeated measures ANOVA FACTORIAL ANOVAS Flashcards
the three broad factorial ANOVA designs
- al IVs are between-subjects (p’s do only one condition)
- all IVs are within-subjects (p’s do all conditions)
- a mixture of between-subjects and within-subjects (p’s do more than on, but not all conditions)
reminder : 2*3
means 2 levels in main IV and 3 levels in secondary IV
example of two-way repeated measures condition
every level of main IV crossed with every level of secondary IV
what are main effects based on
marginal means
- two IVs
interaction effect
does main IV DEPEND in secondary IV
- based on cell means
e.g. that the influence of critters on fear, depends on nature of the trial
repeated measures - variance
- variance between IV levels does not include variance due to individual differences
- we can subtract variance due to individual differences from the variance within IV levels (removed from error variance)
- in repeated measures because each participant takes part in each IV level, we can calculate the degree of error associated with each factor separately
F ratio: two-way repeated measures ANOVA
- in repeated measures we have advantage of smaller error variance due to exclusion of individual differences
- therefore often get bigger F values
marginal means
mean scores for single IV levels ignoring other IV
picture for examples
data input SPSS two-way repeated measures
- every p gets own row
- separate columns for each condition that are clear for which level of main IV and which level for secondary IV e.g. critpresent_height
APA formatted table for factorial ANOVA - practice drawing
- include mean, SD, 95% CIs upper and lower
- One I separated by rows, other by columns
- main IV normally on vertical axis (left), secondary IV on horizontal axis (top)
assumptions for two-way repeated measures ANOVA
- normality
- sphericity (homogeneity of covariance)
- equivalent sample size
- NO PARAMETRIC EQUIVALENT if violate any of these
normality assumption
distribution of difference scores under each IV level pair should be normally distributed
sphericity assumption
homogeneity of covariance
- variance in difference scores under each IV level pair should be reasonably equal
- CHECK WITH MAUCHLY’S for repeated measures
equivalent sample size assumptions
sample size within each condition should be roughly equal
Mauchly’s
H0: no difference between covariances under each IV level pair
- if p < or = .05 we reject null (heterogeneity)
- use greenhouse-geisser
- not relevant for IVs with only 2 levels
write up factorial ANOVA: design
- IV: its levels, sunject design, steps taken to eliminate confounds (e.g. counterbalancing, random allocation)
- DV
factorial ANOVA results: step one: descriptive statistics in the table
- measure of central tendency: mean
- measure of spread: standard deviation
- interval estimate: CIs for upper and lower limit
factorial ANOVA: step 2: results write up + post hoc
- reference descriptive statistics table
- ANOVA test used
- main effect and if its significant and reported as (primary IV): F(dfM, dfR) = _.__, p = .___, partial eta sqaured.
- check marginal means graph if struggling to see directionality of significance
- post hoc if significant and if IV has more than 2 levels, Tukey HSD for between, Bonferroni for within
- p-values for each post hoc, if significant clarify direction of differences between IVs, if not just state no significance
- then report for secondary IV (still a main effect as stated in write up) in same format, clarify direction if significant, include post hoc if more than 2 IVs
DO NOT REPORT COHEN’S D FOR FACTORIAL ANOVAS MAIN EFFECT ONLY FOR PAIRWISE COMPARISONS AND FOR ONE-WAY ANOVA
factorial ANOVA: results write up: step 3: interaction
- test statistic and clarification of significance
Format: F(dfM, dfR) = _.__, p = .___, partial eta squared. - IF SIGNIFICANT, state how many PAIRED t-test were conducted to investigate the interaction and why )
e.g. to compare the heart rate of participants across the two levels of critters (absent vs present) (main IV), separately for each level of nature trial (secondary IV) (water, confined, and height). - based on these N pairwaise comparisons of simple effects, we applied bonferonni correction criterion for significance of p < X (- Bonferroni correction: dived 0.05 (alpha level) by the number of comparisons. (no need to check homogeneity in repeated measures) (significant if p < (less than) alpha from Bonferonni correction)
- report results of each simple effect as Format: (t(df) = _.__, p = .___, d = .)
- report direction if significant, attempt to group results e.g. where effect of main IV is consistent for all levels of secondary IV, those where main effect IV was different from secondary IV, and those where no effect was found
- CALCULATE COHEN’S D BY HAND
e.g. for when main IV has 2 levels, and secondary IV has 3 levels;
significantly higher HR when critters are present for water based and confinement trials. For height based trials we found no evidence that the presence of critters had any effect on HR.
Bonferroni corrected criterion for significance of p :
Bonferroni correction: dived 0.05 (alpha level) by the number of comparisons
- CORRECTED TO CONTROL FOR TYPE 1 ERRORS
how many pairwise comparisons (how many paired t-tests?)
largest number of levels of ONE IV (as all p’s take part in all levels)
- would be 3
Discussion repeated measures ANOVA - main IV 2 levels, secondary IV 3 levels
example
these findings provide evidence that participants in the presence of critters had higher HRs compared to when no critters were present. Those in trials involving water and confinement also experienced higher HRs in the presence of critters than when no critters were present. However, the greater increase in HR in the presence of critters compared to no critters was not seen in trials involving heights.
