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Factorial Designs

Factorial Designs. A Simple Example. R X 11 O R X 12 O R X 21 O R X 22 O. Time in Instruction 1 hour per week 4 hours per week Setting In-class Pull-out. Factor 1: Level 1: Level 2: Factor 2: Level 1: Level 2:. A Simple Example. Time in Instruction. Setting.

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Factorial Designs

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  1. Factorial Designs

  2. A Simple Example R X11 O R X12 O R X21 O R X22 O Time in Instruction 1 hour per week 4 hours per week Setting In-class Pull-out 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 Factors: Major independent variables Setting

  5. A Simple Example Time in Instruction 1 hour/week 4 hours/week In-class Setting Pull-out

  6. A Simple Example Time in Instruction 1 hour/week 4 hours/week In-class Levels: subdivisions of factors Setting Pull-out

  7. A Simple Example Time in Instruction 1 hour/week 4 hours/week In-class Setting Pull-out

  8. A Simple Example Time in Instruction 1 hour/week 4 hours/week In-class Setting Pull-out A 2(rows) x 2 (columns) design

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

  10. A Simple Example Time in Instruction 1 hour/week 4 hours/week Group 1 average Group 3 average In-class Group 2 average Group 4 average Setting 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 Time 1 hr 4 hrs The lines in the graphs below overlap each other. 5 5 5 Out Setting 5 5 5 In 5 5

  17. A Main Effect • A consistent difference between levels of a factor • 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 Time 1 hr 4 hrs 5 7 6 Out Main Effect of Time Setting 5 7 6 In 5 7

  19. Main Effects Time 1 hr 4 hrs 5 5 5 Out Main Effect of Setting Setting 7 7 7 In 6 6

  20. Main Effects Time 1 hr 4 hrs 5 7 6 Out Main Effects of Time and Setting Setting 7 9 8 In 6 8

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

  22. Interaction Effects Time 1 hr 4 hrs 5 5 5 Out The in-class, 4-hour per week group differs from all the others. Setting 5 7 6 In 5 6

  23. Interaction Effects Time 1 hr 4 hrs The 1-hour amount works well with pull-outs while the 4 hour works as well with in class. 7 5 6 Out Setting 5 7 6 In 6 6

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

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