contrasts

Question 1

what do treatment / simple contrasts do

Answer 1

compare all treatments to first, or last, in alphanumeric order)
eg A vs B, A vs C, A vs D, A vs E)
OR
A vs E, B vs E, C vs E, D vs E

Question 2

sum to zero

Answer 2

first two groups are compared to grand mean

Question 3

when to use polynomial contrasts

Answer 3

if the IV is not an arbitary ordered set of categories but an increasing set of values, eg if dose A B C is actually 0.5, 1, 2. Here we are interested in whether the response to the drug is linear or non linear.

If you had 3 groups, you’d get a linear and then a quadratic. if you have 4 groups you’d get a linear, then a quadratic, then a cubic.

In output, if the quadratic is a negative, it will be an inverted U and if pos, will just be a U

(fit terms in x, x^2, x^3 etc.)

Question 4

helmert contrasts

Answer 4

compare each level to the mean of the subsequent levels

A vs mean(B,C,D,E), B vs mean(C,D,E), C vs mean(D,E)

Question 5

difference contrasts or ‘reverse Helmert’

Answer 5

compare each level to the mean of the previous levels)

eg B vs A, C vs mean(A,B), D vs mean(A,B,C), E vs mean(A,B,C,D)

Question 6

repeated contrasts

Answer 6

compare adjacent levels

Question 7

If you had a treatment had 4 levels and you wanted to compare all levels to the third level, what would you type?

Answer 7

contrasts(treatment)

Question 8

How do you know if contrasts are orthogonal?

Answer 8

They are if they are uncorrelated and the

Sum of products is zero

Question 9

which treatments are orthogonal and which arent?

Answer 9

Helmert and difference contrasts are orthogonal
Polynomial contrasts are orthogonal

Treatment and simple are not

Question 10

why do orthogonal contrasts make your life easier?

Answer 10

estimate of effect of contrast 1 is independent of effect of contrast 2