Lecture 7: Models, Conditions, Analysis
Models
Models
Two independent samples
Two independent samples
Y is the observed value.
 is the grand population mean.
 is the effect of treatment i.
 is the random error.
Y is the observed value.
 is the population mean for
the treatment i.
 is the random error.
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Models
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Conditions
“true” value
Observed value = “true”
value + residual error
 Constant.
 Pieces add.
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Conditions
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Conditions
Residual (random) error
The conditions on the
random error are exactly the
same as we saw in Stat 401.
Add to zero.
Same standard deviation ( ).
Independent.
Normally distributed.
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Lecture 7: Models, Conditions, Analysis
Analysis
Informal Analysis
Informal.
Formal.
Check Conditions
(secondary).
Estimate the “true” values
(parameters) using the data
from the experiment.
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Estimates
Estimates
Use the overall sample
mean (
) to estimate the
overall population mean
( ).
Use the treatment sample
mean ( ) to estimate the
treatment population mean
( ).
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Estimates
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Visualizing the Model
Use the difference
( ̂
) to estimate
the effect of treatment i
).
(
+
Overall
Mean
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+
+
Treatment
Residual
+ Error
Effect
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Lecture 7: Models, Conditions, Analysis
Informal Analysis
Sodium in diet experiment
Analysis
 Compute estimates of the
“true” values (parameters)
from the experimental data.
 Informal.
 Formal.
 Check Conditions.
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Informal Analysis
Informal Analysis
∑

 50 mmol Na/day
153.05 mmHg
The average blood pressure
for all 20 men in the
experiment.

143.10 mmHg
 200 mmol Na/day

163.00 mmHg
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Informal Analysis
+9.95
 Effect of 50 mmol Na/day

9.95 mmHg
–9.95
 Effect of 200 mmol Na/day

9.95 mmHg
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Lecture 7: Models, Conditions, Analysis
Formal Analysis
Partitioning Variability
The Analysis of Variance –
ANOVA
Quantify the total amount
of variability and split it
among the sources.
Total Variability
Variability due to
treatments effects.
+
Variability due to
chance (random) error.
Measurement
Experimental Material
Planned Systematic
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Total Variability
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Total Variability
∑
How much variability is
there for the entire set of
experimental data?
Compute a sample variance.
4140.95
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Partitioning Variability
Partitioning Variability
Sum of Squares
C Total
Degrees of Freedom
C Total
Sum of Squares
Treatments
+
Degrees of Freedom
Treatments
Sum of Squares
Error
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+
Degrees of Freedom
Error
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