Statistical Design of Experiments
Statistical Design of Experiments
Statistical Design of Experiments
Statistical Design of Experiments
Analysis of Variance
Analysis of Variance
ANOVA
ANOVA
Let’s consider the simplest model:
Let’s consider the simplest model:
One Factor -
One Factor -
A
A
(one-way Anova)
(one-way Anova)
SS
SS
Total
Total
= SS
= SS
A
A
+ SS
+ SS
E
E
SS
SS
Total
Total
= sum of squared
= sum of squared
deviations of each observation
deviations of each observation
from the overall mean
from the overall mean
y
y
y
y
i
i
= between group variation,
= between group variation,
controlled Variation
controlled Variationuncontrolled Variation
SS
SS
E
E
= sum of squared deviations
= sum of squared deviations
of each observation from its
of each observation from its
factor level mean
factor level mean
y
y
A
A
y
y
i
i
i
i
= within group variation,
= within group variation,
uncontrolled Variation
SS
SS
A
A
= sum of squared deviations
= sum of squared deviations
of each Factor A level mean from
of each Factor A level mean from
the overall mean
the overall mean
y
y
y
y
A
A
i
i
 |
 |
 |