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					Univariate Statistics
   PSYC*6060

               Class 11

            Peter Hausdorf

          University of Guelph
                 Agenda
•   Final Exam Details
•   Howell Chapter 16
•   Group exercise
•   Thesis Examples
•   Cohen Article
              Final Exam
• 3 hours
• Questions
  – 10 multiple choice
  – 10 short answer
  – 3 multiple answer
• 50/50:conceptual/practical
         Howell Chapter 16
•   Design matrices
•   Integrating ANOVA and regression
•   ANOVA with unequal Ns
•   One way ANCOVA
•   Factorial ANCOVA
•   Alternative experimental designs
                 Design matrices
Allows us to look at ANOVA in a multiple
regression framework
   Y ij = m + t j + e ij             y = Xb + e

                                     m   A1   A2   A3
   Y 11= m + t 1   + e 11        1   1   1    0    0
   Y21 = m + t 1   + e 21        2   1   1    0    0
   Y12 = m + t 2   + e12    X=   3   1   0    1    0
   Y22 = m + t 2   + e22         4   1   0    1    0
   Y13 = m + t 3   + e13         5   1   0    0    1
   Y23 = m + t 3   + e23         6   1   0    0    1
          ANOVA – Unequal ns
            Non-Drinking    Drinking       Row Means

Michigan   13 15 14 16 12 18 20 22 19 21
                          23 17 18 22 20
                X11 = 14     X12 = 20       X1. = 18
Arizona    13 15 18 14 10 24 25 17 16 18
           12 16 17 51 10
           14
                X21 = 14     X22 = 20       X2. = 15.9
Column         X .1 = 14     X.2 = 20
Means
      ANOVA – Unequal ns
• Method I – each effect is adjusted for all
  other effects
• Method II – defines interaction first and
  then main effects
• Method III – assigns SS based on order
  in which you select the variables
          Linear Regression
Blood sugar




                 Sum of squares - regression
                 Sum of squares - error


              Skin fold (cm)
                   One Way ANCOVA
Weeks in Therapy                          Positive Thinking




                                              Psychotherapy




                       Depression Score
  Assumptions for ANCOVA
• Linear relationship between Y and
  covariate
• Homogeneity of regression
              Calculations
• Calculating SS Treat(adj)
  – Run regression with covariate only
  – Run regression with treatments only
  – SS Treat(adj) = SS regt,c – SS regc

• Calculating Adjusted means
  – Use regression equation and mean value
    of covariate and dummy codes for
    treatments
         Adjusted Means
• Use regression equation with mean
  value of covariate
           Factorial ANCOVA
• IV - 3X3 design with 1 covariate
  – Task
     • Pattern recognition
     • Cognitive
     • Driving Simulation
  – Smoking
     • Active
     • Delayed
     • Non
  – Distraction
• DV - Number of errors
                  Factorial ANCOVA
                              Pattern Recognition
    NS: Errors      9 8 12 10 ……..
         Distract 107 133 123 94 …….
    ……
                        Driving Simulation
    AS: Errors      3 2 0 0 ……
         Distract 130 83 91 92 ……

C     T1 T2 G1 G2 TG11 TG12 TG21 TG22 CTG11 CTG12 CTG21 CTG22

107    1   0 1    0       1        0       0       0     107         0         0         0   9

130 -1 -1 -1 -1       1        1       1       1       130     130       130       130   3
    Alternative Experimental
             Designs

• Matched Samples
• Difference Scores

				
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