Factorial Designs

• When analysing markets, a range of assumptions are made about the rationality of economic agents involved in the transactions
• The Wealth of Nations was written

  1776
• Rational


  (in classical economic theory) economic agents are able to consider the outcome of their choices and recognise the net benefits of each one
• Producers act rationally by


  Selling goods/services in a way that maximises their profits
• Workers act rationally by


  Balancing welfare at work with consideration of both pay and benefits
• Governments act rationally by


  Placing the interests of the people they serve first in order to maximise their welfare
• Groups assumed to act rationally


  • Consumers
  • Producers
  • Workers
  • Governments
• Rationality in classical economic theory is a flawed assumption as people usually don't act rationally
• If you add up marginal utility for each unit you get total utility
• Announcements


  • Test 2: Friday 9 June
  • Lab 2: Friday 16 June
  • Last workshop is on Monday
  • Last lecture is on Friday
• Aims


  • Rationale of factorial designs
  • Partitioning variance
  • Interaction effects
  • Interaction graphs
  • Interpretation
  • The beauty of these designs is their simplicity, but human behaviour is immensely complex
  • When a study includes more than a single independent variable, the result is called a factorial design, the focus of this lecture
• Factorial design


  More than one independent/predictor variable has been manipulated
• 1. way


  n predictors/independent variables
• Types of experimental designs

  • Two-way = 2 independent variables
  • Three-way = 3 independent variables
• Allocation of participants


  • Independent design = different entities in all conditions
  • Repeated measures design = the same entities in all conditions
  • Mixed design = different entities in all conditions of at least one IV, the same entities in all conditions of at least one other IV
• Main effect


  The overall effect of a single independent variable
• Interaction


  Shows how the effects of one predictor might depend on the effects of another
• Factorial ANOVA 2 x 2
• A factorial design involves all possible combinations of the levels belonging to two or more IVs
• Example of factorial design

  • Testing the effects of vitamin supplements and exercise on health
• Interaction effect


  When the effect of one independent variable differs depending on the level of a second independent variable
• Example of interaction effect


  • Vitamins much more effective when a person also exercises
• Testing the 'beer-goggles effect'
• Design: 3 x 2 ANOVA

  IV 1 (Alcohol dose): Placebo, Low dose, High dose

  IV 2 (Face type): Attractive, Unattractive

  Outcome variable: Median rating of attractiveness of 50 photos
• The data
• Sum of squares total (SST)


  Calculated as: ∑(xi - xgrand)^2 / (N-1)
• Sum of squares model (SSM)


  Calculated as: ∑ng(xg - xgrand)^2
• Sum of squares attractiveness (SSA)

  Calculated as: ∑ng(xg - xgrand)^2 for the face type factor
• Sum of squares alcohol (SSB)


  Calculated as: ∑ng(xg - xgrand)^2 for the alcohol factor
• Sum of squares interaction (SSA*B)


  Calculated as: SSM - SSA - SSB
• Sum of squares residual (error) (SSR)


  Calculated as: ∑sg^2(ng-1)
• Summary table
• Main effect of alcohol


  Significant effect of the amount of alcohol consumed on ratings of attractiveness of faces
• Main effect of face type

  Attractive faces rated significantly higher than unattractive faces
• Interaction effect


  Significant interaction between amount of alcohol and type of face on attractiveness ratings
• Interpreting main effects in the context of a significant interaction
• Combinations of main effects and interactions
• Example: Trajectory of mothers' perceived stress

  • 2 x 3 mixed factorial design
• Example: Children's anger/frustration


  • 2 x 3 mixed factorial design
• Labeling factorial designs


  Label: Size/Independence factorial design

  Example: 2 x 2 between-subjects factorial design, 2 x 3 within-subjects factorial design, 2 x 3 mixed factorial design