Lecture 5 - repeated measures ANOVA

Question 1

When do you use a single factor repeated measures ANOVA?

Answer 1

When you have one independent variable with two or more levels, each produced by same group of people

Want to know if the means are really different or if the differences can be explained by error variability

Question 2

Why do we need to treat our between subjects data differently from our repeated measures data?

Answer 2

The amount of error we would expect to find in the data is affected by whether we are testing the same repeatedly or different groups of people and need to take this into account when calculating our error term

Question 3

What error term do we use for repeated measures?

Answer 3

Residual error

Question 4

What error term do we use for between subjects?

Answer 4

Within treatments variance

Question 5

In addition to random variation, what error variability does a between subjects ANOVA take into account?

Answer 5

Individual differences

Because of this we expect more error

Question 6

What is the f ratio in a between subjects design?

Answer 6

Treatment effects + (experimental error + individual differences) 
Divided by (experimental error + individual differences)

Question 7

What is the between treatment variance in a repeated measures design?

Answer 7

Treatment effects + experimental error only

Question 8

What is the f ratio for a repeated measures ANOVA?

Answer 8

Experimental error divided by experimental error and individual differences

Question 9

Why is a repeated measures ANOVA unbalanced?

Answer 9

It overestimates the total error variance. We need to subtract an estimate of the individual differences from the denominator

Question 10

How do we calculate error in a repeated measures ANOVA?

Answer 10

Calculate within treatment variance
Find an estimate of individual differences and minus this out (subjects variance = individual differences only)
(Residual error = experimental error only)

Question 11

How do you work out residual error SS?

Answer 11

Within treatments SS - subjects SS

Question 12

How do you work out the residual error df?

Answer 12

Within treatments df - subjects df

Question 13

How do you work out Residual error MS?

Answer 13

Residual error SS divided by Residual Error df

Question 14

What is the f ratio for repeated measures?

Answer 14

Between treatments MS divided by residual error MS

Question 15

Between treatment variance can be found where?

Answer 15

Treatment effects + error variability

Question 16

Residual error variance can be found where?

Answer 16

Error variability

Question 17

How do you hypothesis test in a repeated measures ANOVA?

Answer 17

Work out variability between the means predicted by the null hypothesis - how much expected if null is true measured by residual error
Compare obtained variability with this variability expected due to error
If this is 5% or less we reject null and support experimental

Question 18

What is the f ratio for a between subjects ANOVA?

Answer 18

Between treatment variability divided by within treatment variability

Question 19

How do you work out a repeated measures ANOVA f ratio?

Answer 19

Between treatment variability divided by residual error variability

Question 20

How do you work out the between treatments variance in a within subjects ANOVA?

Answer 20

MSbtw = SSbtw (sum of squares btw) divided by df btw (degrees of freedom btw)

Question 21

How do you work out the residual error variance in a within subjects ANOVA?

Answer 21

MSres = SSres (sum of squares residual error) divided by DFres (degrees of freedom residual error)

Question 22

Why are repeated measures ANOVA’s considered more powerful?

Answer 22

Because they eliminate a large source of variability - smaller error term than between subjects test

Question 23

What does the term between treatment mean?

Answer 23

That is our observed variance

Question 24

What does within treatment variability in a between subjects ANOVA mean?

Answer 24

It is the error term and includes error variance due to individual differences

Question 25

What does residual error variability mean in a repeated measures ANOVA?

Answer 25

It is an error term with experimental error only. Found by “minusing out” individual difference error (subject variability)