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Experimental Design & Analysis. Further Within Designs; Mixed Designs; Response Latencies April 3, 2007. Outline. Mixed, or split-plot, designs Response latency designs, a special case for split plots. Mixed Designs.

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Experimental Design & Analysis

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experimental design analysis

Experimental Design & Analysis

Further Within Designs; Mixed Designs; Response Latencies

April 3, 2007


  • Mixed, or split-plot, designs
  • Response latency designs, a special case for split plots
mixed designs
Mixed Designs
  • The mixed factorial design is, in fact, a combination of a within-subjects design and a fully-crossed factorial design
    • A special type of mixed design, that is particularly common, is the pre-post-control design
      • All subjects are given a pre-test and a post-test, and these two together serve as a within-subjects factor
      • Participants are also divided into two groups
        • One group is the focus of the experiment (i.e., experimental group)
        • Other group is a base line (i.e., control) group.
mixed designs1
Mixed Designs
  • Also known as split-plot designs, mixed designs originated in agricultural research
    • Seeds were assigned to different plots of land, each receiving a different treatment
      • Subjects (ex., seeds) are randomly assigned to each level (ex., plots) of the between-groups factor (soil types), prior to receiving the within-subjects repeated factor treatments (ex., applications of different types of fertilizer)
mixed designs2
Mixed Designs
  • Partitioning the variance
    • Estimate between-groups effect
    • Estimate within-groups effect
    • Estimate interaction
  • Using error terms to estimate effects, significance
    • Between-subjects error term is used for between groups-effect
    • Within-subjects error terms is used for within-groups effect
    • Within-subjects error terms is used for the interaction since this includes a within-subjects effect
mixed designs3
Mixed Designs
  • Consider mixed design in which factor A is between-subject factor and B is within-subject factor: Ax(BxS)
    • Subjects factor is crossed with B but nested in A
    • Half of subjects see a1b1, a1b2 and half of subjects see a2b1, a2b2 conditions
    • Sources of variability: A, B, AxB, S(A), BxS(A)
    • To test effects: compare mean square of effects (A, B, AxB) with mean square for effects with subjects (MSS(A), MSBxS(A), MSBxS(A))
mixed designs4
Mixed Designs
  • Take Keppel’s example of kangaroo rats on p. 438-9
    • Between-subjects: 3 kinds of rats (A)
    • Within-subjects: number of landmarks (B)
    • Each subject is tested at 4 levels of B
mixed designs5
Mixed Designs
  • Another way to analyze the data is to look at multivariate analysis
    • Treats each rat’s scores as a vector
    • All the b scores for a rat represents a single multivariate observation
  • Assumptions for data
    • Sphericity: homogeneity of variances for within-subject data
    • Homogeneity of covariance: for within- and between-subject data
mixed designs6
Mixed Designs
  • We examine the effects of a new type of cognitive therapy on depression
    • Give a depression pre-test to a group of persons diagnosed as clinically depressed and randomly assign them into two groups (traditional and cognitive therapy)
    • After the patients were treated according to their assigned condition for some period of time, they would be given a measure of depression again (post-test)
    • This design consists of one within-subject variable (test), with two levels (pre- and post-), and one between-subjects variable (therapy), with two levels (traditional and cognitive)
within subject designs usefulness
Within-Subject Designs: Usefulness

Researchers using the pre-post-control design look for an interaction such that one cell in particular stands out, and that is the experimental group’s post test score. Ideally the pre-test scores will be equivalent.

It is the post-test score difference between the experimental and control that is important.    

pre test post test alternatives
Pre-test Post-test: Alternatives
  • One-way ANOVA on the posttest scores
    • Ignores pretest data and is not recommended
  • Split-plot repeated measures ANOVA
    • Between-subjects factor is the group (treatment or control) and the repeated measure is the test scores for two trials. The resulting ANOVA table will include a main treatment effect (reflecting being in the control or treatment group) and a group-by-trials interaction effect (reflecting treatment effect on posttest scores, taking pretest scores into account)
  • One-way ANOVA on difference scores
    • Difference is the posttest score minus the pretest score and is equivalent to a split-plot design if there is close to a perfect linear relation between the pretest and posttest scores in all treatment and control groups
    • This linearity will be reflected in a pooled within-groups regression coefficient of 1.0. When this coefficient approaches 1.0, this method is more powerful than the ANCOVA method.
  • ANCOVA on the posttest scores
    • Using the pretest scores as a covariate control. When pooled within-groups regression coefficient is less than 1.0, the error term is smaller in this method than in ANOVA on difference scores, and the ANCOVA method is more powerful.