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Factorial Designs

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Time in Instruction 1 hour per week 4 hours per week SettingIn-classPull-out A Simple Example RX 11 O RX 12 O RX 21 O RX 22 O Factor 1: Level 1: Level 2: Factor 2: Level 1: Level 2:

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A Simple Example Time in Instruction Setting

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A Simple Example Time in Instruction Setting Factors: Major independent variables

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A Simple Example Time in Instruction Setting 1 hour/week4 hours/week In-class Pull-out

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A Simple Example Time in Instruction Setting 1 hour/week4 hours/week In-class Pull-out Levels: subdivisions of factors

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A Simple Example Time in Instruction Setting 1 hour/week4 hours/week In-class Pull-out

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A Simple Example Time in Instruction Setting 1 hour/week4 hours/week In-class Pull-out A 2(rows) x 2 (columns) design

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A Simple Example Time in Instruction Setting 1 hour/week4 hours/week In-class Pull-out There are 4 (i.e., 2x2) groups.

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A Simple Example Group 2 average Group 4 average Group 1 average Group 3 average Time in Instruction Setting 1 hour/week4 hours/week In-class Pull-out Usually, averages are in the cells.

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Multiplicative Notation A 3 x 4 factorial design

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Multiplicative Notation A 3 x 4 factorial design The number of numbers tells you how many factors there are.

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Multiplicative Notation A 3 x 4 factorial design The number of numbers tells you how many factors there are. There are 2 factors because there are 2 numbers.

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Multiplicative Notation A 3 x 4 factorial design The number values tell you how many levels are in each factor.

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Multiplicative Notation A 3 x 4 factorial design The number values tell you how many levels are in each factor. Factor 1 has 3 levels. Factor 2 has 4 levels.

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The Null Case 55 55 5 5 55 1 hr4 hrs Out In Time Setting The lines in the graphs below overlap each other.

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A Main Effect l A consistent difference between levels of a factor l For instance, we would say there’s a main effect for setting if we find a statistical difference between the averages for the in-class and pull-out groups

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Main Effects 57 57 6 6 57 1 hr4 hrs Out In Time Setting Main Effect of Time

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Main Effects 55 77 5 7 66 1 hr4 hrs Out In Time Setting Main Effect of Setting

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Main Effects 57 79 6 8 68 1 hr4 hrs Out In Time Setting Main Effects of Time and Setting

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An Interaction Effect l When differences on one factor depend on the level you are on on another factor l An interaction is between factors (not levels) l You know there’s an interaction when can’t talk about effect on one factor without mentioning the other factor

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Interaction Effects 55 57 5 6 56 1 hr4 hrs Out In Time Setting The in-class, 4-hour per week group differs from all the others.

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Interaction Effects 75 57 6 6 66 1 hr4 hrs Out In Time Setting The 1-hour amount works well with pull-outs while the 4 hour works as well with in class.

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Advantages of Factorial Designs l Offers great flexibility for exploring or enhancing the “signal” (treatment) l Makes it possible to study interactions l Combines multiple studies into one

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