Use of Statistical Control

1
Analysis of Covariance

• Use of Statistical Control

2
Exercise 11.1

• Participants are randomly assigned to two
  conditions, one in which they consume a soft
  drink that contains caffeine and one in which
  they consume a similar soft drink but without
  caffeine. A half hour later they take a driving
  simulator test and receive a performance score
  (0-10). Two weeks before the study, the driving
  ability of each participant was assessed (scored
  0-5). Relevant data are provided in the table

(a) Does amount of caffeine affect driving
performance? (? .05) (b) Does amount of
caffeine affect driving performance if variance
due to existing skill is first removed from the
dependent variable? (? .05)
3
One-Factor ANOVA on Performance Scores
4
How ANCOVA Works

• A regression analysis is performed in which
  performance is predicted from driving skill
• Performance scores are predicted based on driving
  skill using the regression equation generated in
  the analysis
• These predicted scores are subtracted from the
  actual performance scores to produce a residual
• This results in removal a variance in performance
  scores that is due to driving skill
• what is left over, the residual scores, contain
  reduced within cells variability
• An ANOVA is then performed on the residuals
• subtract one degree of freedom from the error
  degrees of freedom before computing the MSE.

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Regression Equation forPredicting Performance
from Driving Skill
A
A
P
A
P
A caffeine absent B caffeine present
P
6
Predicted and Residual Values
One-factor ANOVA is performed on these scores
7
One-Factor Analysis of Covarianceon Performance
Scores
8
Exercise 11.2

• Several teaching methods are assessed for their
  influence on math scores. Thirty-two students
  are randomly assigned to four teaching method
  conditions. Also available for students were
  data on the number of hours they studied in the
  past on their academic work.

(a) Does teaching method affect math scores if
variance due to time spent studying is first
removed from the dependent variable? (?
.05) (b) If warranted, determine which pairs of
population means differ. (? .05)
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Regression Line
10
ANCOVA on Achievement Scores
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Post Hoc Analysis

• Perform a Tukey procedure on residual achievement
  scores
• This will indicate which pair(s) of population
  means differ
• Use MSE and df from the analysis of covariance
• (The use of an a priori test would be
  straightforward. Simply conduct the test on
  residual achievement scores.)

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Tukeys HSD post hoc test
Preliminary Calculations
Hypothesis Tests
Reject H0. Achievement is higher with Method 3
than with Method 2.