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Factorial Design: Multiple Independent Variables and Interactions

In this lecture, we explore factorial design and how multiple independent variables (IVs) interact to impact behavior. We discuss terminology, design notation, main effects, and interactions. We also learn about effect size and its measure, partial eta squared.

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Factorial Design: Multiple Independent Variables and Interactions

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  1. Lecture 12 - Chapter 12 Factorial Design (Multifactor) More than one IV Most frequently used design Terminology IV = Factors One way…. Two way, Three way …

  2. Why?

  3. In real world/natural setting not Just one variable impacts behavior! Variables combine to impact behavior Interact  interaction

  4. Interaction: the effect of one Factor (IV) on the DV changes depending on the level of the other factor (IV) Artificial variable weather & temperature Running speed

  5. Design Notation: Matrix of Cells How many Factors (IVs) How many levels 2 X 2 3 X 2 5 X 2 Levels of A Levels of A Levels of A Levels of B Levels of B Levels of B

  6. Testing more than one Hypothesis • No difference bwt the levels of A If difference… MAIN EFFECT • No difference bwt the levels of B If difference… MAIN EFFECT 3. No significant interaction of factor A & B…signif interaction

  7. Possible Outcomes

  8. Possible Outcomes

  9. Whether you are using a t-test, one-way ANOVA, Factorial Did you get an effect???? • Significance level  (p value) • Ex: F ratio…you found sign. difference and with 95% confidence (0.05) not just due to chance and F ratio represents  F= 67.01…67 times more variance between the groups than expected by chance …very dependent on sample size…power Large F may represent sample size…so..

  10. We need some measure that • Index of the STRENGHT of the experimental effect 2. Independent of Sample Size Effect Size (Magnitude of Effect) Proportion of the variance “explained”, “accounted” for by the treatment… “treatment effect”… Does this ring a bell

  11. Whether you are using a t-test, one-way ANOVA, Factorial Effect Size: Partial Eta Squared (h2p) SS Main Effect or Interaction / SS Main Effect or Interaction+SS Error …notice n not a part of the formula Number ranges from .00 to 1.00 (correlation between the effect and the DV) Small:? Med:? Large:? Depends on the area of interest .40 .25 .10 ANOVA t-test

  12. Other tests out there in the world… Extension of ANOVA MANOVA: Multivariate Analysis More than one DV

  13. Examples… For the main effect of ATTRACT partial Eta squared was .90, therefore the variable of ATTRACT accounted for 90% of the overall (effect+error) variance. 30 % of the variation in time spent in conversation can be attributed to the type of the approach… The interaction accounted for 41% of the total variance….

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