Factorial Designs Research Methods & Statistics Summer 2014 Kirstie Hawkey Example drawn from Ch. 12 of McBurney’s research methods textbook

Good tutorials Between subjects factorial design: – – – Mixed factorial design: – Interaction effects: –

Factorial Designs When you are manipulating more than one independent variable – Need to examine the impact of multiple IVs on the DVs – More efficient than running 2+ experiments – Can also examine interactions between the IVs – Must examine all possible cominations of the values of the variables

Terminology #levels of 1 st IV x # of levels of 2 nd IV – 2 IVs each with 2 levels: 2 x 2 – 3 IVs each with 2 levels: 2 x 2 x 2 – 2 IVs each with 3 levels: 3 x 3 Usually identify the levels when writing about it: – A 2 (interface: A, B) x 2 (screen size: small/large) factorial design – A 2 x 2 factorial design was used. Between subject factors were interface (A or B) and screen size (small or large) – Follow the conventions in papers in your domain

Simple 2 x 2 design Examining characteristics of a person that influence judgment of guilt – Facial expression (smiling person less guilty) – Attractiveness (attractive person less guilty) 2 IV’s each with 2 levels Need to have a condition for each combination of factors – Between subjects experiment – 4 groups of participants judging different sets of faces: unattractive neutral faces; unattractive smiling faces; attractive neutral faces; attractive smiling faces – Participants judge whether guilty or not

Simple 2 x 2 design Factor A1 (neutral face) Factor A2 (smiling face) Row Means (Effect of B) Factor B1 (unattractive) A1B1 88 A2B Factor B2 (attractive A1B2 16 A2B Column means (Effect of A) 5228 Main effect: The effect of a variable averaged over all values of another variable (or variables) Is there a main effect of Facial expression on the judgment of guilt? Is there a main effect of Attractiveness on the judgment of guilt?

Simple 2 x 2 design Factor A1 (neutral face) Factor A2 (smiling face) Row Means (Effect of B) Factor B1 (unattractive) A1B1 88 A2B Factor B2 (attractive A1B2 16 A2B Column means (Effect of A) 5228 Interaction effect: When the effect of one IV depends on the level of another IV Is there an interaction effect of facial expression and attractiveness on the judgment of guilt?

Graph it! Factor A1 (neutral face) Factor A2 (smiling face) Row Means (Effect of B) Factor B1 (unattractive) A1B1 88 A2B Factor B2 (attractive A1B2 16 A2B Column means (Effect of A) 5228 Interaction effect: When the effect of one IV depends on the level of another IV Is there an interaction effect of facial expression and attractiveness on the judgment of guilt? Easier to see if graph it: guilt on y axis, facial expression on x axis

What if you have an interaction? Report it Consider the impact on the main effects that you are observing What kind of interaction is it? – Antagonistic (the IV’s reverse each other’s effects) Lines cross, main effect can be flat – Synergistic (the IV’s reinforce each other’s effects) Steeper slopes – Ceiling-effect (one variable has a smaller effect when paired with higher levels of a second variable) Converging lines

Within Subjects Factorial Design 2 x 2 (each subject sees each of the 4 possible conditions) – E.g., Investigate whether the size of a handbag impacts our perception of its weight – Weight: 2 levels (heavy/light) – Size (volume): 2 levels (small/large) – Measure the apparent heaviness – Want to have a measure from each participant for each possible combination

Mixed Designs Some factors are between, some are within “A 2-factor mixed design was used: adaptive accuracy (Low or High) was a between-subjects factor and menu type (Control, Short-Onset or Long-Onset) was a within factor. Order of presentation was fully counterbalanced and participants were randomly assigned to condititions” – Findlater et al., “Ephemeral Adaptation: The Use of Gradual Onset to Improve Menu Selection Performance” CHI 2009

Assignment 4: Restate your research problem and your hypotheses. Briefly describe the study that you intend to run (an outline with open questions is fine) For each of your hypotheses, answer the following: 1.State your research hypothesis’s corresponding alternate and null hypotheses. 2.State whether it is one-tailed or two-tailed 3.If you had a type I error for this hypothesis, what would be the conclusion statement based on the error? 4.If you had a type II error, what would be the conclusion statement based on the error? 5.Where you will get your data 6.How you will rule out alternative explanations for the results (give an alternative and show why it is not viable What are the overall limitations to your study design?

Recap: hypothesis testing & p- values Zgg Zgg er_detailpage&v=eyknGvncKLw er_detailpage&v=eyknGvncKLw Type 1 and Type 2 error: – RM RM – Really good overview – last 10 minutes will help you talk about Q3 and Q4