STAT 652

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STAT 652
Lecture 18
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Writing ANOVA Models as Regression Models
i1,t
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Multiple Regression
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Equations
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Test For equal Means
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Test
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The Analysis of Covariance
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Example
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Tests

• Test for ß(3)0 is equivalent to (i) test of
  equal slope, (ii) test of parallelism, (iii)
  test for no interaction between the treatment and
  the covariate.
• If we fail to reject ß(3)0 then test for ß(1)0
  is equivalent to (i) test for identical lines,
  (ii) test for no treatment effect.
• If we fail to reject both of the hypotheses and
  test ß(2)0 is equivalent to (i) No covariate
  effect, (ii) The lines are constant.

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Model for ANCOVA
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Test for No Interactions
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Possible Decisions
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Test For equal Intercepts
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The Test
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Possible Decision
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ANCOVA Data

• An experiment on the use of Drug treatment of
  leprosy Bacilli carried out in Philippines.
• On each patient 6 sites where leprosy bacilli
  congregate were selected.
• The score X represents the abundance of leprosy
  bacilli before the experiment.
• Score Y represents the abundance of the bacilli
  after a course of Medication.
• The treatments are drug A and D and Drug F is an
  inert drug or a control.

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Test for equal slope, no interaction
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Test for equal intercepts, identical lines
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Test for significant covariate or constant line