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Complex Analytic Designs

This text provides an overview of complex analytic designs in research, focusing on factorial ANOVA with two or more factors. It also covers the concepts of moderators, mediators, and modeling techniques such as hierarchical regression.

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Complex Analytic Designs

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  1. Complex Analytic Designs

  2. Outcomes (DVs)

  3. ANOVA • “Factorial” = 2 or more factors that have at least 2 levels each • Example of a 2x2 design: Factor 1 Level 1 Level2 Factor Level A mean A1 mean A2 2 Level B mean B1 mean B2

  4. Main effect of Treatment Main effect of Gender Example Treatment Gender males females Row mean Experimental 5 15 10 Control 5 5 5 Column Mean 5 10 7.5 (grand mean) Note: Cell means are a combined effect of row effects, column effects, the grand mean and the interaction.

  5. Female teacher Female teacher score Male teacher score Male teacher Male Female Male Female Female teacher score Male teacher Male teacher score Female teacher Male Female Male Female Interactions A B Design Main Effect Interaction A none yes B both no C both yes D one yes D C

  6. More complex factorial designs • 2 factors, many levels: 3x2, 3x3, 6x8…. • >2 factors: 2x2x2, 3x4x2 • Nested designs: levels within levels • Repeated measures: multiple values per subject • Mixed (Between-within) designs: some factors are groups of different subjects and some are repeated measures on the same subjects

  7. Mediators and Moderators A moderator is variable that affects the direction and/or strength of the relation between the IV and DV (i.e. sex, gender, level of reward) A mediator is a variable that accounts for the relation between the IV and DV.

  8. Mediator b c Mediation Independent Variable Dependent Variable a Criteria for mediator: Before mediator inclusion: path a is significant After mediator inclusion: paths b and c are both significant but a is not

  9. Models and modeling • Hypothesize the data structure by specifying the model • “Fit” the data to the model • Test the fit of the data • Easiest example: simple regression is a linear model (i.e. is a straight line a good approximation of the data)

  10. Regression on more than one IV • Predictor is a combination, typically linear (aka additive) of several IV. • Y = a + bX1 + bX2 + bX3 + …. + ε • Same principles apply, but also some new ones emerge…

  11. Weak correlation Strong correlation X1 X1 X3 X2 X1 X2 X1 X3 Y Y Y Y Linear combination with multicolinearity Linear combination

  12. Hierarchical Regression • You can add or subtract terms to make a new model and test differences Model 1: Y = a + bX1 + ε R2 Model 2: Y = a + bX1 + bX2 + ε R2change R2 is the proportion (%) of variance in Y that is explained by the model. R2 change is the proportion (%) of variance in Y that is explained by the model over and above the previous model.

  13. Teen Depression Stressful events Adult Depression Example: 1: adult depression  teen depression 2: adult depression  teen depression + stressful events Change in R2 : proportion of variance in adult depression explained by stressful events after controlling for previous levels of depression

  14. What has not been covered • Use of categorical variables in regression (i.e. dummy coding) • Loglinear analysis (linear contrasts of frequency data) and Discriminant Function Analysis (DFA). • Person-centered approaches and cluster analysis • Factor Analysis, Principle Components Analysis (PCA) • Structural Equation Modeling (SEM), Hierarchical Linear Modeling (HLM), and other more difficult or esoteric analyses.

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