# PMC by dffhrtcv3

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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
• 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
– Run regression with covariate only
– Run regression with treatments only
– SS Treat(adj) = SS regt,c – SS regc

– Use regression equation and mean value
of covariate and dummy codes for
treatments
• Use regression equation with mean
value of covariate
Factorial ANCOVA
• IV - 3X3 design with 1 covariate
• 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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