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Quantitative Methods

Quantitative Methods. Random Effects. Random Effects. What are random effects?. Random Effects. What are random effects?. Criterion: Fixed effects Random effects. Random Effects. What are random effects?. Repetition: If the experiment were repeated:. Criterion: Fixed effects

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Quantitative Methods

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  1. Quantitative Methods Random Effects

  2. Random Effects What are random effects?

  3. Random Effects What are random effects? Criterion: Fixed effects Random effects

  4. Random Effects What are random effects? Repetition:If the experiment were repeated: Criterion: Fixed effects Random effects

  5. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Criterion: Fixed effects Random effects

  6. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects

  7. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to:

  8. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used

  9. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample

  10. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random?

  11. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another?

  12. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another? The strain The barley plant

  13. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another? The strain The barley plant

  14. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another? The strain The barley plant Do guppies swim faster at higher temperatures?

  15. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another? The strain The barley plant Do guppies swim faster at higher temperatures? Temperature Guppy

  16. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another? The strain The barley plant Do guppies swim faster at higher temperatures? Temperature Guppy

  17. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another? The strain The barley plant Do guppies swim faster at higher temperatures? Temperature Guppy Do starlings learn faster with higher rewards?

  18. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another? The strain The barley plant Do guppies swim faster at higher temperatures? Temperature Guppy Do starlings learn faster with higher rewards? Starling Reward

  19. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another? The strain The barley plant Do guppies swim faster at higher temperatures? Temperature Guppy Do starlings learn faster with higher rewards? Starling Reward

  20. Random Effects What are random effects? Repetition:If the experiment were repeated: Same levels would be used Different levels would be used Criterion: Fixed effects Random effects Desired inference:The conclusions refer to: The levels used A population from which the levels used are just a (random) sample Applying the criteria: Fixed or random? Does one strain of barley grow faster than another? The strain The barley plant Do guppies swim faster at higher temperatures? Temperature Guppy Do starlings learn faster with higher rewards? Starling Reward The problem is a random effect produces an extra random term

  21. Random Effects What are random effects?

  22. Random Effects Why do random effects matter? 1. More than one random term 2. While the error is different for each datapoint, a random effect is not

  23. Random Effects New concepts: components of variance Example: 10 starlings, each set 5 different foraging tasks and the time to learn was measured. Model formula is LEARNTIME = STARLINGS There are 50 random error terms, but 10 random starling terms. The EMS measures the size of the error variation. We also want to measure the size of the starling variation

  24. Random Effects New concepts: expected mean square

  25. Random Effects New concepts: expected mean square

  26. Random Effects New concepts: nesting

  27. Random Effects New concepts: appropriate denominators

  28. Random Effects New concepts: appropriate denominators

  29. Random Effects A one-way ANOVA with a random factor

  30. Random Effects A one-way ANOVA with a random factor

  31. Random Effects A one-way ANOVA with a random factor

  32. Random Effects A one-way ANOVA with a random factor

  33. Random Effects A one-way ANOVA with a random factor

  34. Random Effects A one-way ANOVA with a random factor

  35. Random Effects A one-way ANOVA with a random factor

  36. Random Effects A one-way ANOVA with a random factor (2) + 4(1) = 0.01076+4*0.02072 = 0.09362

  37. Random Effects A one-way ANOVA with a random factor (2) + 4(1) = 0.01076+4*0.02072 = 0.09362

  38. Random Effects A one-way ANOVA with a random factor (2) + 4(1) = 0.01076+4*0.02072 = 0.09362 LEAF MS = 0.09362

  39. Random Effects A two-level nested ANOVA

  40. Random Effects A two-level nested ANOVA

  41. Random Effects A two-level nested ANOVA

  42. Random Effects A two-level nested ANOVA

  43. Random Effects A two-level nested ANOVA

  44. Random Effects A two-level nested ANOVA

  45. Random Effects A two-level nested ANOVA

  46. Random Effects Mixing random and fixed effects

  47. Random Effects Mixing random and fixed effects

  48. Random Effects Mixing random and fixed effects

  49. Random Effects Mixing random and fixed effects

  50. Random Effects Last words… • Nested and crossed. • Fixed or random? is a vital question. Tell by desired inference and repetition. • Be prepared for the complications... Categorical Data Read Chapter 13

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