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## PowerPoint Slideshow about 'repeated measures and two-factor anova' - Mia_John

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### Repeated measures and two-factor ANOVA

Chapter 14

Two extensions of ANOVA

- Repeated measures: comparable to paired samples t-test
- Used with within-subjects design
- Factorial ANOVA: used when there is more than one predictor variable

Repeated measures ANOVA

- Captures variability between conditions, compared to error
- MSbetween/MSerror
- MSerror = variability within groups, with variability due to individual idiosyncrasies removed

Calculating MSbetween

- Just like in between subjects ANOVA
- = SSbetween/df between
- SSbetween = SStotal – SS within groups
- df between = df total – df within

Calculating MSerror

- Variability within groups, minus variability due to individual people
- SS within (calculated just like in between subjects ANOVA) minus…
- SS between people (calculate mean for each person, across all treatments, and then calculate SS for those means)
- SS error = SS within – SS between

What about df error?

- df error = df within – df between participants
- df within = sum of df within each condition
- df between participants = number of participants - 1

So, MS error =…

- SS error/df error
- Bottom line: captures how much variability there is in scores that’s not just due to participants being unique weird people
- MS error < MS within
- F = MS between/MS error
- repeated measures ANOVAs will have a better chance at detecting variability that’s due to condition

What about effect size?

- Still measured by h2
- Calculated by SS between conditions/(SS total – SS between participants)
- Sometimes called partial h2, since individual differences are removed

What about post hocs?

- Still needed
- Can use Tukey and Scheffe, just using MS error instead of MS within

Bottom line

- Repeated measures ANOVA captures the same idea as between subjects ANOVA
- However, since the same participants are in each condition, individual differences can be removed from the equation
- more ability to detect differences due to condition

The power of interactions

- Sometimes one variable isn’t enough to capture what’s going on
- Sometimes the role of one variable may differ, depending on the value of another variable
- interaction

Types of interactions

- Especially if: an effect is especially pronounced in some circumstances
- Only if: an effect is only present in some circumstances
- But if: the direction of an effect changes, depending on circumstances

Three things to look for

- Main effect: role of one variable in the dependent variable
- Main effect (2): role of the other variable in the dependent variable
- Interaction: does the role of one variable depend on the value of the other variable?

To keep in mind

- Once you have a significant interaction, you cannot interpret the main effects without taking that interaction into account

Be sure you know

- When to use repeated measures ANOVA
- When to use factorial ANOVA
- The general logic of each

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