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Experimental Design & Analysis

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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  1. Experimental Design & Analysis Further Within Designs; Mixed Designs; Response Latencies April 3, 2007 DOCTORAL SEMINAR, SPRING SEMESTER 2007

  2. Outline • Mixed, or split-plot, designs • Response latency designs, a special case for split plots

  3. 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.

  4. 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)

  5. 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

  6. 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))

  7. 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

  8. 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

  9. 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)

  10. 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.    

  11. 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.

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