Stats Lecture 9 Repeated measures anova

Question 1

Disadvantages

Answer 1

Carryover effects?
•Practice, fatigue, order, etc
•Counterbalancing may be possible solution

Question 2

Advantages

Answer 2

(Possibly) greater internal validity

Question 3

What is the difference score formula as a related (paired) samples t-test?

Answer 3

D (difference/change score) is X1-X2.

Question 4

What is the difference score formula as a contrast?

Answer 4

= (1)X2 + (-1)X1 = CONTRAST [-1 1] across repeats

Question 5

Ho and Ha?

Answer 5

Mean of the difference scores is zero, contrast coefficient = 0 Alternative is mean doesn’t equal zero.

Question 6

How to conclude F = sentence from repeated measures anova

Answer 6

F(1,4) = 6.3252 = 40.00, p = .003

Look at the line on spss that is not the error, ignore that

Question 7

What is SS condition?

Answer 7

Averaged over subjects, we can obtain an estimate of systematic differences on the DV between conditions (substances):
𝐒𝐒𝐂𝐨ndition =𝑛 SUM OF (J=1) (Ybar𝑗−Ybar) sqaured
= 5 x [(-5)squared + (-1)sqaured + (6)sqaured]
=310

Question 8

What is SS subject?

Answer 8

Averaged over conditions, we can obtain an estimate of overall differences on the DV between subjects to remove from analysis:
𝐒𝐒(Subject) =SUM OF Ji=1 (Sbar 𝑖−Ybar)sqaured
= 3 x [(-5)2 + (-3)2 + (-2)2 + (3)2 + (7)2]
= 288

Question 9

What is SS error?

Answer 9

The effect of condition (treatment) can also fluctuate between subjects (subject x treatment interaction) because of individual differences or error. This error variance can also be estimated:
𝐒𝐒Error 𝐄=SUM OF n SUM OF j (Y𝑖𝑖 −Ybar𝑗−S
bar 𝑖+Ybar) sqaured
= [(3-7-7+12)2 + … + (0)2 ]
= 88

Question 10

In SPSS what does the table with the Type III Sums of Squares mean?

Answer 10

top line = SS(Condition): Systematic variability on the DV between conditions
bottom line = SS(Error): Non-systematic variability on the DV after removing systematic differences between conditions and subjects

Different table labelled error = SS(Subjects): Systematic variability on the DV between subjects

Question 11

Between vs. Within-subject designs bottom line

Answer 11

Repeated measures designs can be more powerful, all other things being equal, because there is less error variance (i.e., variability in the DV that we cannot account for).
•Using a repeated measures ANOVA, SS(Subjects) is estimated and then partitioned away in the ‘Test of Between Subjects Effects’ where it is removed from the analysis.
•However, if mistakenly analysed as a between-subjects design, (three conditions, three diffreent groups of participants) SS(Subjects) becomes part of the error term.

Question 12

df condition

Answer 12

J-1

Question 13

df subjects

Answer 13

n-1

Question 14

Suppose experiment incorrectly analysed using Between-Subjects ANOVA (condition = group) what would happen?

Answer 14

Larger SSW => SS(Error) => Larger MSE => Smaller F =>Less power
If we correctly used a repeated measures anova, the variability is partitioned away, locled away because we have accounted for SS Subjects.

Question 15

Suppose the researcher planned the following contrasts ahead of time what happens?

Answer 15

the sum of the SS contrasts in either interger or standard form, is SS Condition. This is because they are a full set of mutually orthogonal contrasts

Question 16

why would a wrong between subbjects design give les spower?

Answer 16

pooled error term includes the between subjects error, in within subjects designs they aren’t compared against each other, just between groups

Question 17

difference score vs contrast score

Answer 17

they mean the same thing

Question 18

what is Ybar contrast?

Answer 18

mean = psy hat = Ybar contrast

Question 19

Why does F value stay the same whether normalised or not?

Answer 19

ratio is the same. all in same scale

Question 20

if you want to compare variability across contrasts or for the anova effect:

Answer 20

all have to be in the same scale (we are setting the normalised scale)

Question 21

Why separate error term for each of the contrasts?

Answer 21

Each of the represents variability in how people’s driving skills (DV) changes on that dimension (contrast) of interest
•
These separate error terms are sensitive to differences in variability in how people’s scores change

Multivariate approach in spss. Each repeat has it’s own error. Subtract each person’s contrast score from the mean of the contrast scores.

Question 22

larger MSE wil give what F?

Answer 22

smaller F

Question 23

What uses the pooled error term?

Answer 23

univariate approach

Question 24

what is pooled error term?

Answer 24

SSW or average error variance across all the levels of the IV. not sensitive to variablity in contrast scores so overestimates or underestimates variability in ind poeple’s contrasts (difference) scores.
UNderestimate = type 1 error risk
overestimate = type 2 error risk

Question 25

ifi we wrongly use pooled error term (when we want seperate errors for repeats) what happens?

Answer 25

obs F is larger, because MSE has been underestimated for one contrast (type 1 error. rejecting ho)

Question 26

Sphericity

Answer 26

Sphericity is assumed when using the univariate (pooled) error term: variability in contrast scores is the same across all possible pairwise comparisons between conditions

Question 27

omnibus questions for within subjects designs

Answer 27

all about change. do changes (differences) differ between two conditions.

Question 28

spss output test of within subject effects

Answer 28

anova table with three families but with seperate error terms.