Using Real Data For Decision Analysis

8/14/2019 Using Real Data For Decision Analysis

1/15


2/15

Which class would you take?

Next semester, two professors will be teaching

Decision Theory.

VS.

Based on RateMyProfessor.com, the past gradesare posted over the five years.

mean = 1750.82mean = 1770.16 (out of 2000 points)

Which professor would you sign up for?

Dr. UragonnafailDr. Pieceofcake


3/15

Finding the Distribution

VS.

mean = 1750.82mean = 1770.16 (out of 2000 points)

Dr. Uragonnafail GPA distribution

X


4/15

Standardizing the axis

Dr. Pieceofcake GPA Distribution

0

1

2

3

4

5

6

1.5 1.591 1.682 1.773 1.864 1.955

Values in Thousands

Valuesx10^-2

Dr. Uragonnafail GPA distribuition

0

1

2

3

4

5

6

7

1.5 1.591 1.682 1.773 1.864 1.955

Values in Thousands

Va

lues

x

10^-3

Which professor would you sign up for now?

mean = 1750.82

var = 63.8635

mean = 1770.16

var = 7.139664

(out of 2000 points)


5/15

A matter of perspective

Which professor would you want if you

were a 4.0 students?

What if you were a slacker?

Remember: it is not just the centraltendency that is important, the dispersion

is also critical


6/15

There are a variety of probability models

that can be used to help make decisions

Binomial distribution

Poisson distribution

Normal distribution

Exponential distribution

Beta distribution etc, etc, etc

It is always important to use the correct

distribution to explain your data

BUT

More importantly, it is essential to always

consider the context by which you are

making the decision


7/15

Caveats in using real data to

make decisions

Fallacy of Averages

Assumptions of normality

Errors in estimations Impact of outliers

Residual Values


8/15

Fallacy of averages

0

0 .0 5

0 .1

0 .1 5

0 .2

0 .2 5

0 .3

0 .3 5

0 .4

0 .4 5

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

Duration of Drug Development

Freq

uencyofDevelopedDrugs

Mean / Average


9/15

Fallacy of Averages

0

0 .0 5

0 .1

0 .1 5

0 .2

0 .2 5

0 .3

0 .3 5

0 .4

0 .4 5

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0

Duration of Drug Developme nt

FrequencyofDeve

loped

Drugs

Mean Duration of Typical Process

Mean Duration of

Complex Processes

A simple case of fallacy of averages is the case of overall height of a specific

population. Men and Women have natural bimodal distributions, but combinedhave a normal distribution.


10/15

Assumptions of Normality

Normal distributions are not always bell

shapedRequirements for

normal distribution

symmetrical

68, 95, 99 rule

Not all distributions are normal, few are perfectly normally

distributed

Much of decision analysis is based on assumptions of the normal curve to make

calculations easier. It is important to understand the limitations of the normal

curve when basing your decisions off of it.


11/15

Errors in Estimations

Some linear-

regressions force

the line to the 0-0

point .

(meaning:x-intercept = 0

y-intercept = 0 )

When creating

regressions to the

data, have an

understanding of therange to which your

estimation is

reasonable.

Would it make sense to have a the regression line go be forced through the 0-0 pointin this case?


12/15

Impact of Outliers

Outliers can bias the regression estimation to

accommodate the extreme data point(s). What happens if you add Maudie Hopkins (19) and William Cantrell (86) [last civil

war widow] & Anna Nicole Smith (26) to J. Howard Marshal II (89)? Or, more

recently, Demi Moore (42) to Ashton Kutcher (27)?


13/15

Impact of Outliers

Outliers can also give a false sense of correlation between two variables. In a

correlation test, the strength of the relationship between the husbands age and the

wifes age would be incorrectly accentuated. This would reflect the incorrect

observation pertaining the compactness of the dataset.


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Residual value

Two datasets can give identical regression estimations. The graph on the

right has a larger residual value therefore there is a presence of greater

error. In other words, there is not as strong of a relationship of

predicting values of y from x.


15/15

Things to remember about real

data

It is messy! It is not always memoryless

i.e., the recent past really is a better indicator offuture performance

It can have many outliers that are: Important indications of new trends, or Oddities that should be eliminated

There is a major difference between

statistical significance and practicalsignificance Dont just look at the statistical results, look at

the data itself!

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Using Real Data For Decision Analysis