Lecture 5: CI’s, Three Decisions
Generalization
Effect Size
Men with Stage 1 hypertension
on a 50 mmol/day Na diet will
have lower average blood
pressure than men on a 200
mmol/day Na diet.
How much lower, on
average, will the blood
pressure be with the 50
mmol/day diet?
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Estimated Effect Size
2
Confidence Interval
The difference in sample
means is an estimate of the
difference in population
means.
19.9 mmHg lower, on average.
1
∗
Difference
∗
1
Std ErrDif
3
t Distribution
4
Confidence Interval
19.9
df
80%
90% 95%
98%
99%
2.101 10.96
2=18
∗
=2.101
1
10
1
10
–19.9 2.101 4.90
–19.9 10.3→ 30.2, 9.6
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Lecture 5: CI’s, Three Decisions
Interpretation
Generalization
We are 95% confident that
the difference between the
population means is
between –30.2 mmHg and
–9.6 mmHg.
Men with Stage 1 hypertension
on a 50 mmol/day Na diet will
have an average blood pressure
from 9.6 to 30.2 mmHg lower
than men with Stage 1
hypertension on a 200 mmol/day
Na diet.
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Generalization
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3 Principles
Control
Replication
Randomization
Note that the generalization is
talking about men with Stage
1 hypertension in general not
the men who participated in
the experiment.
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3 Decisions
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Response
What is the response?
What are the treatments?
What is the experimental
material?
You have to decide what
response variable you will
use in your experiment.
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Lecture 5: CI’s, Three Decisions
Example
Treatments
Blood pressure after three
months on the diet.
Change in blood pressure.
You have to decide what
factor you will manipulate
to make treatments.
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Example
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Experimental Material
Manipulated factor – amount
of sodium in the diet.
Treatments
You have to decide what
experimental material will
be used in the experiment.
50 mmol/day
200 mmol/day
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Example
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Caution
Experimental material
consists of men with Stage
1 hypertension.
There is a difference
between experimental
material and experimental
units.
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Lecture 5: CI’s, Three Decisions
Difference
Example
Treatments are applied to
experimental units.
Experimental units can be
groups of experimental
material.
Response: Weight gain of hogs
(pounds).
Treatments: Normal feed,
Feed with additive (Paylean).
Experimental Material: hogs.
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20
Experimental units
Experimental units
There are 10 hogs is each of
20 pens.
Each pen is randomly assigned
one of the treatments, Normal
or Paylean.
Because the treatment, type of
feed, is applied to the pen, the
pen is the experimental units.
Response is really the average
weight gain of hogs in a pen.
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Alternative
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Caution
If pigs were fed
individually, then the
individual hog would be the
experimental unit.
Identifying what is the
experimental unit is very
important!
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