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
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
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
Calculating MSbetween
  • Just like in between subjects ANOVA
    • = SSbetween/df between
      • SSbetween = SStotal – SS within groups
      • df between = df total – df within
calculating mserror
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
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
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
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
What about post hocs?
  • Still needed
  • Can use Tukey and Scheffe, just using MS error instead of MS within
bottom line
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
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
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
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
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
Be sure you know
  • When to use repeated measures ANOVA
  • When to use factorial ANOVA
  • The general logic of each
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