20_anova3

# 20_anova3 - Two-way ANOVA I 9.07 No class Thursday • •...

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Unformatted text preview: Two-way ANOVA, I 9.07 4/27/2004 No class Thursday • • – way ANOVA – comparisons) • Based upon how we are coming along on the material. You shouldn’t need the next class to complete the final homework (just posted on the web) Don’t need to know how to do post-hoc testing on two- Just read the handout on what post-hoc tests you’re allowed to do (confounded vs. unconfounded Turn in your Thursday HW to one of your TAs Two-way ANOVA • variable) • • Factorial design only 2 Cups of coffee (Factor B) only 1 only Neither (Control) 0 Yes No did one-way ANOVA. Each square in the table, representing a particular combination cell . So far, we’ve been talking about a one-way ANOVA, with one factor (independent But, one can have 2 or more factors Example: Study aids for exam – how do they affect exam performance? – Factor 1: workbook or not – Factor 2: 0, 1, or 2 cups of coffee Workbook + 2 cups coffee 2 cups coffee Workbook + 1 cup coffee 1 cup coffee Workbook Workbook (Factor A) Note different levels of Factor A in columns, as when we Different levels of Factor B in rows. of a level of Factor A and a level of Factor B, is called a 1 Why do a two-factor • – dependent variable is called a main effect • – experimental design Interactions • independent variable. • E.G. Look at the effects of aspirin and beta (or multi-factor) design? Such a design tells us everything about an individual factor that we would learn in an experiment in which it were the only factor The effect of an individual factor, taken alone, on the The design also allows us to study something that we would miss in a one-factor experiment: the interaction between the two factors We talked a bit about interactions when we talked about An interaction is present when the effects of one independent variable on the response are different at different levels of the second Interactions (from an earlier lecture) carotene on preventing heart attacks – Factors (i.e. independent variables): 1. aspirin, 2. beta carotene – Levels of these factors that are tested: 1. (aspirin, placebo), 2. (beta carotene, placebo) 2 Placebo Factor 1: Aspirin Factor 2: Beta Carotene Yes Yes No No Beta Carotene Aspirin Beta Carotene Placebo Placebo Aspirin Placebo Figure by MIT OCW. Outcomes of a factorial design • – – • – – preventing heart attacks? • rates depend upon the level of the beta Main effects What effect does aspirin have on heart attacks, independent of the level of beta carotene? What effect does beta carotene have on heart attacks, independent of the level of aspirin? Interaction(s) The influence that two or more independent variables have on the dependent variable, beyond their main effects How does beta carotene interact with aspirin, as far as Does the effect of aspirin on heart attack carotene factor?...
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20_anova3 - Two-way ANOVA I 9.07 No class Thursday • •...

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