Contrasts Flashcards

1
Q

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

A
  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.
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2
Q

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

A
  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.
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3
Q

Which contrasts are used in this course?

A
  1. a priori contrasts: planned contrasts, Helmert and trend analysis.
  2. post hoc contrasts: Tukey and Scheffé
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4
Q

What is the syntax for planned contrasts?

A
UNIANOVA BY group
/CONTRAST (group) = Special ( ck, -ck)
/METHOD = SSTYPE(3) 
/INTERCEPT= INCLUDE 
/CRITERIA = ALPHA (0.05)
/DESIGN = group
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5
Q

Explain orthogonal contrasts.

A

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

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6
Q

What is the syntax for Helmert contrasts?

A
UNIANOVA BY group 
/CONTRAST (group) = HELMERT 
/METHOD = SSTYPE(3) 
/INTERCEPT = INCLUDE 
/CRITERIA = ALPHA (0.05) 
/DESIGN = group
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7
Q

What is the syntax for Trend Analysis contrasts?

A
UNIANOVA BY group 
/CONTRAST (group) = Polynomial 
/METHOD = SSTYPE(3) 
/INTERCEPT = INCLUDE 
/CRITERIA = ALPHA (0.05)
/DESIGN = group
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8
Q

What is the syntax for Tukey contrasts?

A
UNIANOVA BY group 
/METHOD = SSTYPE(3)
/INTERCEPT = INCLUDE 
/POSTHOC = group(TUKEY) 
/CRITERIA = ALPHA (0.05) 
/DESIGN = group
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9
Q

What is the test procedure for Scheffé?

A
  1. hypotheses
  2. critical value Fcv
  3. Fcontrast > (K-1)xFcv
  4. conclusion
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10
Q

What is the syntax for Scheffé contrasts?

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