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##### Experimental Design: Factorial

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**Experimental Design: Factorial**Psych 231: Research Methods in Psychology**Announcements**• In labs: • Turn in checklist (in PIP packet) with paper • Only social security numbers please • Journal summary due in two weeks • Exam coming up soon (1 week)**B1**B2 B3 B4 A1 A2 Factorial experiments • Two or more factors • Factors - independent variables • Levels - the levels of your independent variables • 2 x 4 design means two independent variables, one with 2 levels and one with 4 levels • “condition” or “groups” is calculated by multiplying the levels, so a 2x4 design has 8 different conditions**Factorial experiments**• Two or more factors (cont.) • Main effects - the effects of your independent variables ignoring (collapsed across) the other independent variables • Interaction effects - how your independent variables affect each other • Example: 2x2 design, factors A and B • Interaction: • At A1, B1 is bigger than B2 • At A2, B1 and B2 don’t differ**Results**• So there are lots of different potential outcomes: • A = main effect of factor A • B = main effect of factor B • AB = interaction of A and B • With 2 factors there are 8 basic possible patterns of results: • 1) No effects at all • 2) A only • 3) B only • 4) AB only • 5) A & B • 6) A & AB • 7) B & AB • 8) A & B & AB**A1**A2 Condition mean A1B1 Condition mean A2B1 B1 mean B1 Main effect of B Condition mean A1B2 Condition mean A2B2 B2 B2 mean A1 mean A2 mean Marginal means Main effect of A 2 x 2 factorial design**A**Main Effect A2 A1 of B B1 30 60 B1 B Dependent Variable B2 B2 30 60 Main Effect A1 A2 of A A 45 45 30 60 Main effect of A Main effect of B Interaction of A x B **A**Main Effect A2 A1 of B B1 60 60 B1 B Dependent Variable B2 B2 30 30 Main Effect A1 A2 of A A 60 30 45 45 Main effect of A Main effect of B Interaction of A x B **A**Main Effect A2 A1 of B B1 60 30 B1 B Dependent Variable B2 B2 60 30 Main Effect A1 A2 of A A 45 45 45 45 Main effect of A Main effect of B Interaction of A x B **A**Main Effect A2 A1 of B B1 30 60 B1 B Dependent Variable B2 B2 30 30 Main Effect A1 A2 of A A 45 30 30 45 Main effect of A Main effect of B Interaction of A x B **main effect**anxiety of difficulty easy low mod high medium 50 hard hard test performance 35 80 35 70 Test difficulty medium 65 65 80 80 easy 80 80 80 low mod high 60 80 60 main effect anxiety of anxiety Anxiety and Test Performance Example Let’s add another variable: test difficulty. Yes: effect of anxiety depends on level of test difficulty Interaction ?**Factorial Designs**• Advantages • Interaction effects • One should always consider the interaction effects before trying to interpret the main effects • Adding factors decreases the variability • Because you’re controlling more of the variables that influence the dependent variable • This increases the statistical Power of the statistical tests • Increases generalizability of the results • Because you have a situation closer to the real world (where all sorts of variables are interacting)**Factorial Designs**• Disadvantages • Experiments become very large, and unwieldy • The statistical analyses get much more complex • Interpretation of the results can get hard • In particular for higher-order interactions • Higher-order interactions (when you have more than two interactions, e.g., ABC).**Describing your design**• You need to describe: • How many factors • How many levels of each factor • Whether the factors are within or between groups • e.g., 2 (categorical/alphabetical) x 2 (read to/read by) completely between groups factorial design**Pres**Main Effect RB RT of Order Al 9.5 8.3 Order Cat 9.8 10.9 Main Effect of Presentation Class experiment • Main effect of Presentation • Main effect of Order • Interaction 8.9 10.4 9.1 10.2 9.5 - 8.3 = 1.2 10.9 - 9.8 = 1.1 Interaction