ANOVA lectures 3 and 4

Question 1

how do you work out the SE from the SPSS contrasts output?

How do you work out F if it is not provided?

Answer 1

In the ‘contrasts tests’ box of the output: you see the ‘value of contrasts’ column (=psy hat), the SE, t, df (dfw from anova) and sig.

psy hat/SE = t

t sqaured = F.

Question 2

what is R squared in ANOVA? what is it’s other name?

Answer 2

proportion of DV accounted for by your different levels of the IV. AKA eta sqaured.
SSB/SST

Question 3

where are the real coefficients?

Answer 3

custom hypothesis tests. L1 column is first cont question vertically now. L2 and L3 are the others.

Could have calculated t by dividing psy hat by SE

Question 4

what is hypothesised value?

Answer 4

second line of table after contrast estimate.
Hypothesised value is always equal to 0 for a contrast, so the ‘difference’ is always equal to psy hat. (mean difference)

Question 5

What are estimated marginal means?

Answer 5

The means for each group will be printed (again) if the EMMs have been requested (in the Options tab).

In PSYC3010, the EMMs will always be the same as the Descriptive sample means because we will equal n and no covariates. (They will not always be the same in more advanced analyses.)

Question 6

Independent questions are?

Answer 6

the answer to one question doesn’t tell you or depend on the answer to another question.

Question 7

non independent questions are?

Answer 7

Dependency means there is some degree of theoretical overlap between the two questions that have been asked and because of this overlap the sum of the ss contrasts will never add up to SSB from the anova.

Question 8

Orthogonality

Answer 8

two contrasts are orthogonal to each other they are uncorrelated, or at right angles. Can be tested by seeing if the sum of the cross products of coefficients (cxc) each to zero.
If they add to zero the pairwise contrast is orthogonal. A is orth to B, B is orth to A.

Question 9

Are all orthogonal contrasts independent?

Answer 9

Yes, but not all independent contrasts are orthogonal.

Question 10

how can you declare a set orthogonal?

Answer 10

For a set of k contrasts, all possible pairs must be considered before the set can be declared mutually orthogonal

Question 11

how many mutually orth contrasts can there be in a set?

Answer 11

With J levels of an IV, there can be a maximum of (J – 1) = dfB mutually orthogonal contrasts in the set

Question 12

Why is the ssb sometimes the same as the sum of the SS contrasts?

Answer 12

A FULL set of (J – 1) mutually orthogonal contrasts accounts for ALL of the SSB in the analysis of variance because
• Each of the (J – 1) mutually orthogonal contrasts partition and account for independent parts of the SSB (without overlap)

SSB won’t equal sum of SS contrasts if the set of contrasts are not mutually orthogonal

Question 13

are orth contrasts consistent?

Answer 13

yes but can contradictory answers are possible with non-orthogonal contrasts if there is tyoe 1 error etc

Question 14

other name for trend contrasts

Answer 14

Trend analysis (orthogonal polynomials)

Question 15

when do we use trend analyses?

Answer 15

Appropriate when the IV is quantitative with equally spaced intervals.
Nominal/Categorical, ordinal -> mean diff contrasts
Interval, Ratio -> trends

Question 16

what is the interpretation for all trend contrasts?

Answer 16

Each is designed to ask focussed questions about the quantitative aspects of the IV, so the results cannot be interpreted as mean differences
•
Instead, the correct interpretation for all trend contrasts is as a trend in DV means as a function of quantitative changes in IV

Question 17

Negative linear trend

Answer 17

Increase in IV leads to decrease in DV.
(e.g.Cognitive performance appears to be poorer among those with more hours of sleep deprivation)

Pos is the more the more

Use overall patterns, (not comparing time points of IV etc. that would be mean diff)

Question 18

Do we write the quadratic trend inflection point?

Answer 18

we don’t specify precisely where the optimal point is if you only have data from a sample of participants.

Question 19

Best example of cubic trends

Answer 19

life spans. hours of sleep goes up, down, up, down. Also facial recognition across lifespan

Question 20

Linear + Quadratic Trend

Answer 20

Change in the rate of change
–Does the rate of increase/decrease in DV means change with increasing/decreasing levels of the IV?

Learning curve, therapy curve. Concavity as well. Rate of anxiety changes. Linear = more the more, or more the less. Quadratic is rate slows or increases?

Question 21

if given trend coefficients, how do you work out if it’s linear, cubic or quadratic?

Answer 21

sketch them out.

Question 22

why do we use EER? k times alpha?

Answer 22

The probability of making at least 1 Type I error inflates when the number of questions (k) tested on the same data exceeds 1. With k independent questions/contrasts, the experiment-wise error rate (EER) is: 1-alpha to the power of k.
Each question is give a DER of alpha and k refers to the number of questions that’s being asked. a x k

Question 23

Problem with EER for planned orth contrasts

Answer 23

if your contrasts are planned and orthogonal, Current practice allows use of a DER of .05 for planned, orthogonal contrasts (i.e., no control over the EER)

We know that the EER (= FER when there is only 1 IV) is inflating, to a maximum of .15 with k = 3 questions, but running the risk because the questions are orthogonal, and have been planned in advance.
We don’t want to run this risk of inflating the EER -> bonferroni and sheffe

Question 24

why is Fisher’s LSD protected? problem with it

Answer 24

Tests all pairwise contrasts between levels of the IV

Considered a ‘protected’ t-test because it uses a more stable estimate of error (MSW, which is based on all J groups) than an independent samples t-test.

But the protection only extends to DER level. The ind samples t test gives a higher p value than Fisher’s.

•Generally, Fisher’s doesn’t adequately control for the EER.

Question 25

The Tukey HSD test for contrasts better tha Fisher’s LSD?

Answer 25

Tests all pairwise contrasts between levels of the IV
•
Effectively controls the EER at .05 by adjusting p(obs|H0) based on J.
We need it to give us power to detect effects without running too high a risk of making a type 1 error,

Question 26

when do you use bonferroni procedure?

Answer 26

Only for PLANNED contrasts = BEFORE looking at the results of the analysis. BASED ON THEORY. not data

Question 27

How to do the Bonferroni adjustment

Answer 27

rather than using an a of .05 per contrast (inflate EER), you use alpha divided by K.
Crit F with a/k; v1(1), v2 (dfw anova)
Use the Bonferroni F table

Question 28

how to use bonf F table

Answer 28

k runs across the page, v2 (N-J) is down the page.

Question 29

How to do sheffe.

2 Positives of sheffe

Answer 29

Do an anova, make the F crit bigger by multiplying anova crit F with dfb.
Doesn’t depend on K, so unlimited questions possible.
You save time by doing omnibus anova first, as no contrast can be sig through sheffe if the ANOVA wasn’t sig to start with.

Question 30

Which critical value? sheffe vs bonf

Answer 30

compare the bonf and sheffe and use smaller crit F.

When k ≤ (J-1), Bonferroni is more powerful than Scheffé
•When k > (J-1), you need to check the critical F value for each procedure and then use the more powerful of the two

Question 31

questions to ask for EER

Answer 31

is K equal to or smaller than j-1? Sheffe.

If k is larger than j-1, check.