ANOVA lectures 3 and 4 Flashcards
how do you work out the SE from the SPSS contrasts output?
How do you work out F if it is not provided?
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.
what is R squared in ANOVA? what is it’s other name?
proportion of DV accounted for by your different levels of the IV. AKA eta sqaured.
SSB/SST
where are the real coefficients?
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
what is hypothesised value?
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)
What are estimated marginal means?
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.)
Independent questions are?
the answer to one question doesn’t tell you or depend on the answer to another question.
non independent questions are?
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.
Orthogonality
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.
Are all orthogonal contrasts independent?
Yes, but not all independent contrasts are orthogonal.
how can you declare a set orthogonal?
For a set of k contrasts, all possible pairs must be considered before the set can be declared mutually orthogonal
how many mutually orth contrasts can there be in a set?
With J levels of an IV, there can be a maximum of (J – 1) = dfB mutually orthogonal contrasts in the set
Why is the ssb sometimes the same as the sum of the SS contrasts?
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
are orth contrasts consistent?
yes but can contradictory answers are possible with non-orthogonal contrasts if there is tyoe 1 error etc
other name for trend contrasts
Trend analysis (orthogonal polynomials)
when do we use trend analyses?
Appropriate when the IV is quantitative with equally spaced intervals.
Nominal/Categorical, ordinal -> mean diff contrasts
Interval, Ratio -> trends
what is the interpretation for all trend contrasts?
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
Negative linear trend
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)
Do we write the quadratic trend inflection point?
we don’t specify precisely where the optimal point is if you only have data from a sample of participants.
Best example of cubic trends
life spans. hours of sleep goes up, down, up, down. Also facial recognition across lifespan
Linear + Quadratic Trend
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?
if given trend coefficients, how do you work out if it’s linear, cubic or quadratic?
sketch them out.
why do we use EER? k times alpha?
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
Problem with EER for planned orth contrasts
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
why is Fisher’s LSD protected? problem with it
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.
The Tukey HSD test for contrasts better tha Fisher’s LSD?
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,
when do you use bonferroni procedure?
Only for PLANNED contrasts = BEFORE looking at the results of the analysis. BASED ON THEORY. not data
How to do the Bonferroni adjustment
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
how to use bonf F table
k runs across the page, v2 (N-J) is down the page.
How to do sheffe.
2 Positives of sheffe
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.
Which critical value? sheffe vs bonf
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
questions to ask for EER
is K equal to or smaller than j-1? Sheffe.
If k is larger than j-1, check.
