Transcript Three way ANOVA.pptx

If there was One way then and Two way, then you knew
that there had to be………
Three way Mixed Model
 In a Human Factors experiment, there were two Job types, Dimensional
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stimulus (two or three dimensions), and five Analysts who performed
ratings.
Job type and dimension may be considered fixed (repeatable) factors.
Analyst may be considered random (different in another run of the
experiment).
Primary interest is consistency (or differences) between stimulus types,
two or three dimensional.
Data from Hicks 1982, Fundamental Concepts in Design of
Experiments (good reference).
Data structure (partial…)
Layout of Design
Linear Model notation
Di  Dimension
J j  Job
Ak  Analyst
Yijkl  Rating
Linear Model
Yijkl    Di  J j  Ak  DJ ij 
DAik  JAjk  DJAijk   (ijk )l
ANOVA Summary
Detailed ANOVA with Mean Squares
What are “correct” F-tests? Table first…
Candidate terms for coefficients
For each term in the model:
Subscripts : Di , DJ ij , DAik , DJAijk ,  (ijk )l
Then candidates for variance components:
2
2
Candidates : D , DJ ,  DA
,  DJA
,  2
EMS using Restricted Model (Cornfeld-Tukey)
Correct F-tests for Fixed Effects
Residuals by Predicted
Normality Plot of Residuals
Shapiro-Wilk Test of Normality
Goodness-of-Fit Test
Shapiro-Wilk W Test
W
0.984424
Prob<W
0.8463
Note: Ho = The data is from the Normal distribution. Small p-values
reject Ho.
Conclusions
The differences among levels of the fixed effects are
not greater than that which would be expected by
chance over this population of Analysts.
If one were to consider Analysts fixed, then one would
test all terms against Experimental Error (which has
lower variation), but any conclusions would only apply
to these Analysts.
All factors fixed analysis
Dimension and Analyst
LS Means HSD
Job and Analyst
LS Means HSD