Factorial Designs Q560: Experimental Methods in Cognitive Science Lecture 11

U2 has a concert that starts in 17 minutes, and they must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them get across to the other side, and there is only one torch. A maximum of two people can cross the bridge at any one time. Any party who crosses, either one or two people, must have the torch with them. The torch must be walked back and forth, it cannot be thrown etc. Each band member walks at a different speed. A pair must walk together at the rate of the slower man’s pace: Bono - 1 minute to cross Edge - 2 minutes to cross Adam - 5 minutes to cross Larry - 10 minutes to cross

Verbal vs. Visual Processing Conditions: Item match (2): Same/Diff Material (2): Geometic/Verbal Configuration (2): Same Linear Verbal vs. Visual Processing Santa (1977) presented items that were either geometric objects or words referring to them, and tested in either the same or different configuration. Task is to identify if the test display has the same items as at study Triangle Circle Study Square Test Triangle Circle Triangle Circle Square Square

Factorial Designs Factorial Design: More than one factor (IV) is manipulated in the same experiment This can produce main effects of either factor, and an interaction effect between the factors This is the most comprehensive design, since factors interact with one another to produce behavior in the real world The downside…you need far more subjects, time, and effort

Main Effects and Interactions Main effect: Mean differences along the levels of one factor (oneway F-ratio) In addition to the two factors alone, we can evaluate mean differences that result from unique combinations of the two factors. An interaction between two factors occurs whenever mean differences between individual treatment conditions (combinations of two factors) are different from the overall mean effects of the factors “The effects of one factor vary as a function of the other”

Two-factor ANOVA will do three things: Examine differences in sample means for humidity (factor A) Examine differences in sample means for temperature (factor B) Examine differences in sample means for combinations of humidity and temperature (factor A and B).  Three F-ratios.

Main effect for humidity (Factor A) Main effect for temperature (Factor B) The differences among the levels of one factor are referred to as the main effect of that factor.

Evaluation of main effects  two out of three hypothesis tests in two-factor ANOVA. Hypotheses: H0: A1 = A2 H1: A1  A2 F-ratio: F = variance between means (factor A) variance expected by chance/error

H1: At least one  is different. F-ratio: Factor B: Hypotheses: H0: B1 = B2 = B3 H1: At least one  is different. F-ratio: F = variance between means (factor B) variance expected by chance/error

Main Effects and Interactions In addition to the two factors alone, we can valuate mean differences that result from unique combinations of the two factors. An interaction between two factors occurs whenever mean differences between individual treatment conditions (combinations of two factors) are different from the overall mean effects of the factors.

Are there any interactions in this example?

How about this one?

H1: There is an interaction between factors A and B Hypotheses: H0: There is no interaction between factors A and B. (all mean differences are explained by main effects) H1: There is an interaction between factors A and B F-ratio: F = variance not explained by main effects variance expected by chance/error

In a graph, lines that are non-parallel indicate the presence of an interaction between two factors.

Main Effects and Interactions Two-factor ANOVA consists of three hypothesis tests. All combinations of outcomes are possible (see next slide)

Notation and Formulas Three hypothesis tests  three F-ratios  four variances!! Schematic view:

Spotting Interactions Main effects: Averaging across levels of the other factor, the means differ between the levels of the factor you are looking at Interaction effect: Differences in the individual cell means are inconsistent with the results when you average over those levels (non-parallel lines) Simple main effect: Difference in the levels of one factor conditional on the level of the other factor

Source SS df MS F Between treatments 240 5 Factor A (difficulty) 120 1 120.0 24.00 Factor B (arousal) 60 2 30.0 6.00 A x B interaction Within treatments 24 5.0 Total 360 29

Terminology CR design: Completely Randomized. Multiple between-subjects factors (e.g., CR23) RBF design: Randomized Block Factorial. Multiple within-subjects factors (e.g., RBF223) SPF design: Split-Plot Factorial (aka: Mixed Design). At least one between and one within-subjects variable. Between variables come before the dot, within after (e.g., SPF2.3, SPF22.4)

Spotting Effects in Line Graphs Parallel lines = no interaction Non-parallel lines = interaction Main effects: Average the two points on the same colored lines and compare to each other, or average the two points from the different colored lines and compare to each other An Excel example…