advantages of RM designs
- Economy of participants
Sensitivity is enhanced by separating individual differences from experimental error.
disadvantages of RM designs
- Cant use with all IVs
○ If the variable cannot be measured with repeated measures (i.e. nationality).- Order effects (practice, fatigue, carryover).
cannot use if there is absolutely no way to ensure these effects can be removed.
- Order effects (practice, fatigue, carryover).
RM design and matching
- A repeated measures analysis may also be conducted if the participants in each condition are precision matched.
○ Where each participant is directly matched with others in the other levels of the IV e.g. age and gender matched.
○ i.e. different people at each level but the participants are heavily matched and thus considered equal.
problems with RM designs
- Several methodological confounds MUST be addresses that are particular to RM designs:
○ Difficult to repeatedly measure participants
§ Drop outs
§ There will be less drop out if people are invested in the deign.
○ Maturation
○ History
○ Attrition/mortality
○ Order effects
§ Practice effects
§ Fatigue effects
§ Carry over effects
remedies to order effects
- Practice and fatigue effects can be controlled by design;
○ Counterbalance or randomise the order to treatments across participants.
○ Prior exposure to measurement before exposure to experimental conditions may reduce practice effect.- Carry over effects
○ Can seldom be controlled ( a long delay between testing each level of the IV can help).
Should use a BG design if you suspect that they will operate with the IV you are doing.
- Carry over effects
counterbalancing
Seek to mitigate the effect of order effects.
- Randomisation
○ Each participant gets exposed to each level of the IV randomly.
- Counterbalancing
Each conditions appear in a given order an equal number of times. (i.e. diagonal matrix).
RM design and control for individual differences
- In independent groups analyses we compare groups to each other and individual differences to contribute to our error.
- In RM analyses we can control for these individual differences as we compare each participant to themselves across conditions.
- Statistically this has the effect of removing variability due to individual differences which reduce the error.
- Can partition the SStotal even further.
THEREFORE DF ALSO CHANGES
In within groups you only have treatment, total and error variability. In RM designs you also have subject variability.
RM design more sensitive
- The F ration will always be larger in a repeated measures design than a comparable IG design. The error term will be smaller as we are removing all the variability due to individual differences from the error term.
testing significance with RM designs
- Logical exactly the same as the IG ANOVA.
- Testing to see what is more probable explanation of F ratio… error or effect of IV>
- If the F is larger than the cut off, can retain the research hypothesis and state that the IV had an effect.
assumptions for RM ANOVA
- Normality: as in IG.
- Independence: is not a problem because while the scores are not independent in a RM design, there participant effect have been portioned out.
- Sphericitiy: as an assumption specific to RM designs.
○ Def: essentially refers to homogeneity across conditions and participants, so homogeneity of the variance and co-variance matrix.
○ For designs with more than 2 levels, violations of sphericity can inflate type 1 error.
Sphericity is often breached and there are two ways to fix this.
traditional model
Traditional Model:
- If Mauchley’s sphericity test is significant then the sphericity assumption is breached.
○ Significance is bad and then the assumption is violated.
- Corrections for breaching the Sphericity assumption.
○ Can no longer use the normal F distribution as it assumed we have met the sphericity assumption. If you use this, the type 1 error will not be as expected (wont be 0.05).
○ Therefore we need to adjust our degree of freedom in line with the magnitude of the breach of sphericity to account for inflated type 1 error.
○ Epsilon values show how much the data has breached sphericity, 1=not breaches, 0=very breached.
§ Df are multiplied by the epsilon value.
○ If sphericity is breached we need to use these adjusted df to test the F ration.
§ This adjustment only alters the Fcrit not Fobtained.
- In SPSS, know how to identify Sign and Greenhouse-Geisser (epsilon value).
- Greenhouse-geisser methods is the method to reduce the df.
not recommended
multivariate approach
- Extends the difference scores analysis we used in RM t-tests to within subjects factors with 3 or more levels.
- Based on difference scores.
- By analysing difference scores, we can ‘partial out’ the consistency in scores for each person from one level of the IV to another.
- Essentially treats each set of difference scores as a separate DV. Therefore, we are testing using separate error terms for each pair of conditions rather than a pooled error terms, which means we don’t have to worry about sphericity.
- The traditional approach and multivariate approach are identical when there are only 2 levels of the IV.
error and power in RM designs
- The error term is smaller for RM ANOVA. MSerror is smaller than Mswithin as variance due to individual differences are portioned out.
- Power will be greater in a repeated measures design than between groups given the same effect size.
- We can get effect size statistics from SPSS in the same way as for between groups ANOVA (either manually calculating or via General Linear Model).
follow up tests in RM deisgns
- Still need to do a priori or post hoc tests.
- Can do these using the dependent samples t test procedure and use a Bonferoni adjustment to maintain an EW type 1 error rate.
SPSS will not produce post hoc for RM designs but we can get Bonferoni adjusted post hoc pairwise comparisons through the display mean function in options.
- Can do these using the dependent samples t test procedure and use a Bonferoni adjustment to maintain an EW type 1 error rate.
to find F crit
need df between and df subjects
