Computing a “Relative
Threshold”
• Use this result as input to the following slide for computing the value
of measuring an uncertain range.
• Example: You might invest in a new system if you get a productivity
improvement of over 10%. But your current range for this value is
5% to 20%. Compute the RT.
B
Relative Threshold
(RT)=B/A
Threshold: Below
this point is losing
money
“Worst Bound” of the 90%
CI; this is the undesirable
end of the range
A
“Best Bound” of the 90%
CI; this is the desirable
end of the range
The EOLF Chart
Expected Opportunity Loss Factor (EOLF)
1. Compute the
EOLF Curves for
Uniform Distributions
EOLF Curves for
Normal Distributions
Relative Threshold
(RT)*
•
•
0.5
2. Find the
0.4
RT on the
vertical axis
0.3
100
100
80
80
60
60
20
0.2
3. Look directly
to the right of the
RT value, until
you get to the
appropriate curve
(normal or
uniform,
depending on the
probability
distribution you
are using). This
is the EOLF
0.1
40
40
20
10
10
8
6
0
-0.2
2
1
0.8
0.6
0.4
0.2
-0.4
0.1 0.08
.01
0.06
-0.5
0.04
6
10
4
2
0.8 0.6 0.4
1
0.2
0.05
4.
1
-0.3
1
8
0.1
4
-0.1
10
Compute the
Expected Value of
Perfect
Information
(EVPI) =
EOLF/1000*units
in range*loss per
unit
Use the RT from the
previous slide to compute
the value of information.
Example: You invested in
the system in the example
on the previous slide. Let’s
say if the system does not
get a productivity
improvement greater than
10%, then you lost
$100,000 for each
percentage point you are
under the threshold. Use
this information and the RT
to compute the value of
reducing uncertainty about
the range of potential
productivity improvements.
Measuring to the threshold
1. Find the curve beneath the number of samples taken
Number Sampled
4. Find the
value on the
vertical axis
directly left of
the point
identified in
step 3; this
value is the
chance the
median of the
population is
below the
threshold
Chance the Median is Below the Threshold
50%
2
4
6
8
10
12 14 16
18
•
20
40%
•
30%
20%
10%
5%
2%
3. Follow the curve
1%
identified in step 1
until it intersects the
vertical dashed line
identified in step 2.
0.5%
0.2%
0.1%
0
1
2
3
4
5
6
7
8
9
10
Samples Below Threshold
2. Identify the dashed line marked by the number of
samples that fell below the threshold
Use this chart when using
small samples to determine
the probability that the
median of a population is
below a defined threshold
Example: You want to
determine how much time
your staff spends on one
activity. You sample 12 of
them and only two spend
less than 1 hour a week at
this activity. What is the
chance that the median time
all staff spend is more than
1 hour per week? Look up
12 on the top row, following
the curve until it intersects
the “2” line on the bottom
row, and look up the
number to the left. The
answer is just over 1%.
Population Percentage Estimate
2
4 # of Samples in subgroup
3. Repeat the process for the upper bound, using the
diagonal line above the sample size; follow the diagonal
line until it intersect the same vertical line as before;
follow it to the number on the vertical axis to the left
labeled “90% CI Upper Bound”
8%
90% CI Upper Bound
12%
16%
5
20%
10
30%
20
15
40%
50%
60%
70%
80%
Sample Size
40%
90% CI Lower Bound
•
2
4
6
8
10
2
4
6
8
20
2
4
6
8
30 2
4
6
8
40
30%
20%
10%
10
8%
15
1. Find
the total
sample
size; then
find the
diagonal
line that
starts on
the small
circle
beneath it
20
2. Follow the diagonal line until it
intersects the vertical line that
corresponds to the number of samples in
the subgroup; at that point lookup the
number on the vertical scale to the left
labeled “90% CI Lower Bound”
6%
4%
2%
0%
2
4
6
8
# of Samples in subgroup
•
Use this chart to
estimate the
percentage of a
population that falls
within a subgroup,
given a small sample
Example: you want to
measure how many
of your customers
have shopped at a
competitor in the last
week. You sample
20 and 10 of them
said they did shop at
a competitor. The
chart shows how to
compute the 90%
confidence interval
for the share of all
customers who
shopped there.
The “Enemy Tank” case
100
50
1. Subtract the smallest serial number
20
in the sample from the largest
10
5
2
A
1
Upper bound
0.5
0.2
0.1
0.05
Mean
0.02
0.01
0.005
Lower bound
0.002
0.001
0
2 4 6 8
10 2
4 6 8
20 2
4 6 8
302
4 6 8
40 2
4 6 8
50
Sample Size
3. Find the value for “A” on the vertical
2. Find the sample size on the
axis closest to the point on the curve
and add 1; multiply the result by the
answer in step 1. This is the 90% CI UB
for total serial numbered items
horizontal axis and follow it up
to the point where the vertical
line intersects the curve marked
“Upper Bound”
4. Repeat steps 2 and 3 for the Mean and Lower Bound
• This chart
shows how the
WWII
statisticians
estimated
German tank
production
based on serial
numbers of
captured tanks