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Lecture 16

# Lecture 16 - Factorial Experiments.docx

5 Pages
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Department
Psychology
Course Code
Psychology 2800E
Professor
Doug Hazlewood

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Description
Factorial Experiments - “Multiple factor experiments” - Experiments with more than one independent variable (or “factor”) - Allow us to study the effects of more than one “cause” Part 1: The Notation System  - 3 basic features: o Each factor (IV) is identified by a number o The numerical values indicate the ”levels” of each factor (e.g., “2” = 2 levels) o Create all possible combinations of levels by “crossing” each factor (symbol = “x” = “by”)  Each unique combination of factors and levels defines a “condition”  Number of conditions = product of levels (multiply the levels of each factor) - Examples: 1. 2x2 factorial (simplest design) o Two factors (IV’s) o Each factor has two levels – if it doesn’t have 2 levels, there’s no variability  4 conditions (2x2=4) 2. 3x3 factorial o Two factors (IV’s); each factor has 3 levels  9 conditions (3x3=9) 3. 2x3x2 factorial o Three factors, with 2, 3, and 2 levels  12 conditions (2x3x2=12) - Note typo on p.284 (W&M): A 3x3x3 factorial has 27 conditions, not 9 - It’s possible to have any number of factors (with any number of levels): 2x4x3x7… - BUT, as design becomes more complex, it’s more difficult to interpret the results o Limit the number of factors/levels to address the specific questions that you want to answer o Science grows by examining a few causes at a time Part 2: The “Factorial Cell Matrix” Notation System - Assign a capital letter to each factor (A, B…) - Assign numerical subscripts to represent the levels of each factor (e.g., A1, A2…) o Numbers should preserve “quantity” (e.g., low = 1; high = 2) o If categorical, numbers are arbitrary (e.g., gender: M = 1, F = 2 or F = 1, M = 2) - Create factorial matrix that represents all combinations of factors/levels o Each “cell” represents a condition - Example: 2x2 Factorial Factor A A1 A 2 Factor B B 1 A1B1 A 2 1 B 2 A1B2 A 2 2 - Concrete Example: 2x2 factorial (p. 274) - DV = judged “guilt” of defendant - Factor A: facial expression o A1 = “neutral” o A2 = “smiling” - Factor B: physical attractiveness o B1 = unattractive o B2 = attractive - Note: This design could be expanded to include: 1. A third level of each factor. E.g., o neutral (A1); small smile (A2); big smile (A3) o unattractive (B1); neutral (B2); unattractive (B3) 2. More than two factors (IV’s). E.g., o Gender of def (C1 = male; C2 = female) o Trust (D1 = untrustworthy; D2 = trustworthy) o 3x3x2x2 =36 conditions - Remember, more factors = more complexity (or more possible outcomes) Part 3: Outcomes of Factorial Experiments A. Main effects: allow us to examine the separate effects of each factor - Easy to examine main effects by focusing on “marginal means” in matrix (e.g., 2x2) o Main effect of A (column means, p. 274); table 11.4 p274 W&M  Compare A1 (averaged over B1 and B2) and A2 (averaged over B1 and B2) o Main effect of B (ro
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