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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

Quantitative Methods

Random Effects

slide2

Random Effects

What are random effects?

slide3

Random Effects

What are random effects?

Criterion:

Fixed effects

Random effects

slide4

Random Effects

What are random effects?

Repetition:If the experiment were repeated:

Criterion:

Fixed effects

Random effects

slide5

Random Effects

What are random effects?

Repetition:If the experiment were repeated:

Same levels would be used

Criterion:

Fixed effects

Random effects

slide6

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

slide7

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:

slide8

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

slide9

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

slide10

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?

slide11

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?

slide12

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

slide13

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

slide14

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?

slide15

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

slide16

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

slide17

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?

slide18

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

slide19

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

slide20

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

slide21

Random Effects

What are random effects?

slide22

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

slide23

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

slide24

Random Effects

New concepts: expected mean square

slide25

Random Effects

New concepts: expected mean square

slide26

Random Effects

New concepts: nesting

slide27

Random Effects

New concepts: appropriate denominators

slide28

Random Effects

New concepts: appropriate denominators

slide29

Random Effects

A one-way ANOVA with a random factor

slide30

Random Effects

A one-way ANOVA with a random factor

slide31

Random Effects

A one-way ANOVA with a random factor

slide32

Random Effects

A one-way ANOVA with a random factor

slide33

Random Effects

A one-way ANOVA with a random factor

slide34

Random Effects

A one-way ANOVA with a random factor

slide35

Random Effects

A one-way ANOVA with a random factor

slide36

Random Effects

A one-way ANOVA with a random factor

(2) + 4(1) = 0.01076+4*0.02072

= 0.09362

slide37

Random Effects

A one-way ANOVA with a random factor

(2) + 4(1) = 0.01076+4*0.02072

= 0.09362

slide38

Random Effects

A one-way ANOVA with a random factor

(2) + 4(1) = 0.01076+4*0.02072

= 0.09362

LEAF MS = 0.09362

slide39

Random Effects

A two-level nested ANOVA

slide40

Random Effects

A two-level nested ANOVA

slide41

Random Effects

A two-level nested ANOVA

slide42

Random Effects

A two-level nested ANOVA

slide43

Random Effects

A two-level nested ANOVA

slide44

Random Effects

A two-level nested ANOVA

slide45

Random Effects

A two-level nested ANOVA

slide46

Random Effects

Mixing random and fixed effects

slide47

Random Effects

Mixing random and fixed effects

slide48

Random Effects

Mixing random and fixed effects

slide49

Random Effects

Mixing random and fixed effects

slide50

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