Contrasts

Question 1

What is the procedure for determining contrast coefficients when the sample sizes are equal?

Answer 1

1. Divide the samples into 3 groups, corresponding with H0.
2. ck = 0 for all groups that do not participate.
3. ck = 1 for all groups that participate on one side of H0.
4. ck = -1 for all groups that participate on the other side of H0.

Question 2

what is the procedure for determining contrast coefficients when the samples sizes are not equal.

Answer 2

1. divide the samples into 3 groups, corresponding with H0.
2. ck = 0 for all groups that do not participate.
3. ck = [formula] for all group on one side of H0.
4. ck = - [formula] for all groups on the other side of H0.

Question 3

Which contrasts are used in this course?

Answer 3

1. a priori contrasts: planned contrasts, Helmert and trend analysis.
2. post hoc contrasts: Tukey and Scheffé

Question 4

What is the syntax for planned contrasts?

Answer 4

UNIANOVA BY group
/CONTRAST (group) = Special ( ck, -ck)
/METHOD = SSTYPE(3) 
/INTERCEPT= INCLUDE 
/CRITERIA = ALPHA (0.05)
/DESIGN = group

Question 5

Explain orthogonal contrasts.

Answer 5

all contrasts are uncorrelated.

• SSb represents dispersion of means
• contrast explains part of the dispersion of means.

contrasts are orthogonal when
ck1ck2 = 0 // (ck1ck2)/nk = 0

Question 6

What is the syntax for Helmert contrasts?

Answer 6

UNIANOVA BY group 
/CONTRAST (group) = HELMERT 
/METHOD = SSTYPE(3) 
/INTERCEPT = INCLUDE 
/CRITERIA = ALPHA (0.05) 
/DESIGN = group

Question 7

What is the syntax for Trend Analysis contrasts?

Answer 7

UNIANOVA BY group 
/CONTRAST (group) = Polynomial 
/METHOD = SSTYPE(3) 
/INTERCEPT = INCLUDE 
/CRITERIA = ALPHA (0.05)
/DESIGN = group

Question 8

What is the syntax for Tukey contrasts?

Answer 8

UNIANOVA BY group 
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE 
/POSTHOC = group(TUKEY) 
/CRITERIA = ALPHA (0.05) 
/DESIGN = group

Question 9

What is the test procedure for Scheffé?

Answer 9

1. hypotheses
2. critical value Fcv
3. Fcontrast > (K-1)xFcv
4. conclusion

Question 10

What is the syntax for Scheffé contrasts?

Answer 10

UNIANOVA BY group 
/CONTRAST = (group) Special (ck, -ck) 
/METHOD = SSTYPE(3) 
/INTERCEPT = INCLUDE 
/CRITERIA = ALPHA (0.05) 
/DESIGN = group