5. Repeated Measures ANOVA Flashcards by Cate Paterson

Q

What is repeated measures?

A

It is an extension of paired observations that are made on the same “individual” or “experimental unit” for a given random variable of interest.

i.e. the same X is observed repeatedly on the same individual, at different times or on different parts of it, or both.

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

In a repeated measures data table, what do the rows represent?

A

The individuals

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

In a repeated measures data table, what do the columns represent?

A

The levels of the repeated measures factor(s)

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

What are the two ways to do the analysis of repeated measures?

A

Between-subjects (row by row) and within-subject (column by column)

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

ANOVA model equation for repeated measures

A

Xijt = μ + ai + εij(1) + ct + (a c)it + εijt(2)

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

In the equation Xijt = μ + ai + εij(1) + ct + (a c)it + εijt(2):

What does μ represent?

A

μ is the population mean

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

In the equation Xijt = μ + ai + εij(1) + ct + (a c)it + εijt(2):

What does ai represent?

A

ai are the between-subjects effects

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

In the equation Xijt = μ + ai + εij(1) + ct + (a c)it + εijt(2):

What does εij(1) represent?

A

εij(1) is the error term for the between-subjects effects (ai)

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

In the equation Xijt = μ + ai + εij(1) + ct + (a c)it + εijt(2):

What does ct represent?

A

ct is the main effects

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

In the equation Xijt = μ + ai + εij(1) + ct + (a c)it + εijt(2):

What does (a c)it represent?

A

(a c)it is the interaction

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

In the equation Xijt = μ + ai + εij(1) + ct + (a c)it + εijt(2):

What does εijt(2) represent?

A

εijt(2) is the error term for within-subject effects (so for ct and (a c)it )

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

What SAS procedure can be used for repeated measures?

A

PROC GLM

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

What are the 5 different approaches to the analysis of repeated measures?

A

First Univariate approach (U1)
Multivariate approach (M)
Second Univariate approach (U2)
Third Univariate approach (U3)
Fourth Univariate approach (U4)

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

What is the first univariate approach (U1)?

A

It is based on separate univariate ANOVAs perfomed for a given level of the repeated measures factor(s) (i.e. using one column Xijt of the repeated measures data table for a given t)

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

What is the multivariate approach (M)?

A

It uses a multivariate ANOVA (MANOVA) model built on the rows of the repeated measures data table, alias profile vectors

How well did you know this?

1

Not at all

2

3

4

5

Perfectly

Q

What is the second univariate approach (U2)?

Study These Flashcards

A

The between-subjects effects (ai) are assessed using the means calculated across all levels of the repeated measures factor(s) for each of the individuals

Q

What is the third univariate approach (U3)?

Study These Flashcards

A

The within-subject effects are tested; the corresponding means are used to calculate the sum of squares

Q

What is the fourth univariate approach (U4)?

Study These Flashcards

A

Contrasts are used to perform specific comparisons between two or more levels of the repeated measures factor(s)

Q

In the SAS code, what does PRINTE do?

Study These Flashcards

A

It prints the Error SSCP Matrix
SSCP = sums of squares and cross products

Q

When doing a repeated measures in SAS, what type of model must you write under the MODEL statement?

Study These Flashcards

A

a multivariate model (more than one variable on the left side of the equation)

Q

What do you have to write under the REPEATED statement?

Study These Flashcards

A

The definition of repeated measures factors and their levels

Q

When writing the SAS code, how should you arrange the data under the INPUT statement?

Study These Flashcards

A

Such that each profile vector can be read with one statement

Q

How do you find signs of heteroscedasticity in the Error SSCP Matrix?

Study These Flashcards

A

In the ratio of the minimum and maximum diagonal elements

Q

How do you find signs of autocorrelations (i.e. correlation between errors)?

Study These Flashcards

A

In the partial correlations; partial correlations close to 1.0 in absolute value indicate strong autocorrelation

What is circularity?

The independence and homoscedasticity of orthonormalized contrasts

Under the circularity condition, what happens to the classical ANOVA F-tests for within subjects?

They are valid, so they need not be modified. (their p values dont need to be adjusted)

What is Box's epsilon?

It is how we measure any discrepancy of the variance-covariance matrix of orthonormalized contrasts from the circularity condition

What are the bounds of Box's epsilon

1/(R-1) < Box's epsilon < 1 where R is the number of repeated measures

When is the circularity condition satisfied? (in terms of Box's epsilon)

When Box's epsilon = 1

What is the value of Box's epsilon when R = 2?

1

What are the bounds of Box's epsilon when R = 3?

0.5 < BOX < 1

What does CONTRAST(1) mean on the line of the REPEATED statement in a SAS code?

CONTRAST(1) means that comparisons are made with respect to the first year, or the first level of the repeated measures factor in general