# Module 12.docx - Module 12 Two-Factor ANOVA 12.1 Two-Factor...

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Module 12- Two-Factor ANOVA 12.1 Two-Factor ANOVA One-Factor vs Two-Factor Differences Expanding ANOVA from one factor to two factor introduces some complexities Explanation of Two-factor ANOVA A two-factor analysis of variance table lets us ask three different kinds of questions: 1. Is there an effect of Factor A? Known as ‘main effects Factor A’ For example, if we average across of cells (or in this case diet effect) These are questions called main effect questions and has to do with where there’s an overall effect of different levels within the drug factor 2. Is there an effect of Factor B? Known as ‘main effects Factor B’ 3. Does the response to Factor A depend on Factor B Known as interaction between A and B Practice Question 1. An investigator randomly assigns 30 college students into three equal size study groups (early-morning, afternoon, late-night) to determine if the period of the day at which people study has an effect on theory retention. What type of test is most appropriate for this study? o Two-Sample t-test o Correlation o Regression o Singe-factor ANOVA o Two-factor ANOVA
2. Which of the following statements is TRUE about a 2 X 2 factorial design?
Two-factor ANOVA Visualization Graphing along a single factor makes it difficult to see the main effects and interaction Better to graph an interaction plot: boxplot moved to interaction plot In interaction plot o One factor is shown along the x axis and then the other factor is shown using different symbols or lines to represent the other levels in the factor o X-axis is one factor, symbols or lines are the other Building a Interaction Plot On the x axis we have just the insect treatment, either absent or present First dot is insect absent and toads absent The second one is insects present and toads absent
Connect the two with the line that represents toad absence Another dot for insects absents and toads present Then another point where both the insects and the toads are present The two new blue dots are joined with a solid line that represent the toads are present Then the interaction plot is created It is the same information as out box plot, but its organized into the different factors that’s easier to see the main effects of the factors in the interaction Questions to ask about the Interaction Plot 1. Main effects of insects o Is there a difference if the insects are absent verses present on tadpole mass? o Key thing to remember for this question is we’re averaging across what the toads are doing o Orange dot added to the interaction plot for insects absent and for insect’s present o You then are able to look to see if there is a difference between the orange dots in the absence or the presence of insects 2. Main effects of toads o Involves taking the average across the treatment groups o