Repeated measures and two factor anova
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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.

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Two extensions of anova l.jpg
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 l.jpg
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 l.jpg
Calculating MSbetween

  • Just like in between subjects ANOVA

    • = SSbetween/df between

      • SSbetween = SStotal – SS within groups

      • df between = df total – df within


Calculating mserror l.jpg
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


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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 l.jpg
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


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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


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What about post hocs?

  • Still needed

  • Can use Tukey and Scheffe, just using MS error instead of MS within


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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


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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


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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


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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?


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To keep in mind

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


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Be sure you know

  • When to use repeated measures ANOVA

  • When to use factorial ANOVA

  • The general logic of each


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