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Factorial Designs. 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.

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Presentation on theme: "Factorial Designs. 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."— Presentation transcript:

1 Factorial Designs

2 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:

3 A Simple Example Time in Instruction Setting

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

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

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

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

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

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

10 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.

11 Multiplicative Notation A 3 x 4 factorial design

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

13 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.

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

15 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.

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

17 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

18 Main Effects hr4 hrs Out In Time Setting Main Effect of Time

19 Main Effects hr4 hrs Out In Time Setting Main Effect of Setting

20 Main Effects hr4 hrs Out In Time Setting Main Effects of Time and Setting

21 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

22 Interaction Effects hr4 hrs Out In Time Setting The in-class, 4-hour per week group differs from all the others.

23 Interaction Effects 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.

24 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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