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Lecture 2 Delivered
Transcript of Lecture 2 Delivered
Data: n. (pl.) more than one realization of measured characteristic(s) of an element/unit
Probability: n. the numeric value representing the chance, likelihood, or possibility that a particular event will occur.
"The logic of science." -- E. T. Jaynes
Statistical inference: n. the theory, methods, and practice of forming judgments about the parameters of a population and the reliability of statistical relationships, typically on the basis of random sampling.
Evidence-based management: the combination of research and relevant data in making managerial decisions.
Binomial Distribution (np)
Poisson Distribution (lambda)
Normal Distribution (mu,sigma)
Uniform Distribution (a,b)
Exponential Distribution (lambda)
Expense ratios are higher for intermediate government bond funds.
With 95% confidence, the difference in average expense ratios is 0.012 to 0.163 higher for intermediate government funds.
Relevance of evidence
Bayes Rule and the role of belief.
Probabilistic statements occupy the role -- in science -- of stating uncertainty in a common language.
Bayesian decision-making is the essence of evidence-based management.
Decision criteria and transparency
Careful attention to process renders clarity in the decision-making process.
Problem definition and careful attention to sequence and logical structure permit disagreement in an explicable framework, e.g. we cannot dispute the facts but we may well dispute their relevance.
Is the treatment worth the expense?
Little evidence to suggest that car seats are effective for two to six year olds.
Pertinent evidence, examples, and facts.
The reason that the evidence supports the claim.
A statement of opinion to be supported.
Stephen Toulmin's Model of Argumentation
Backing: Evidence supporting the application of a warrant.
Rebuttals: mitigating factors in the disqualification of warrants.
Qualifiers: Limits on the strength or applicability of a warrants.
The most significant cause of death among American children.
Use data to investigate the efficacy of child safety seats.
Claim: Car safety seats do not improve outcomes for children aged 2 through 6
The evidence from a sample implies truth in a population.
The evidence contains signs, clues, symptoms, or components of the claim.
The evidence is linked to authoritative source interpretations.
Evidence is connected by analogy, event, or precedent.
The evidence is caused by or as a result of the claim.
The evidence is indicative of a broader, relevant principle.
Just the facts on the size of the problem and the "cures"
The data on all reported crashes with fatalities.
Experimental evidence does not show the advantage of car seats either.
Robert W. Walker, Ph. D.
Associate Professor of Quantitative Methods
A random sample of 184 bond funds.
Fund Number: Identification number unique to each fund.
Type: Intermediate government / short term corporate
Assets: In millions of dollars
Fees: Sales charges (yes or no)
Expense ratio: Ratio of expenses to net assets
Return 2009: Twelve-month return in 2009
3-year return: Annualized returns 2007-2009
5-year return: Annualized returns 2005-2009
Risk: Risk-of-loss classification for the mutual fund.
Data can be acquired from http://www.willamette.edu/~rwalker/GSM5103/data/BEARXSP500.xlsx
The elements of a sound argument are statements of logic replete with bounding conditions.
This is also true of the statements of statistics.
And of science -- when probability enters.
Union and intersection/joint probability
Conditional probability and independence
P(Type=IG and Fees=Yes)=34/184
What do we know?
These programs cost money per participant.
They recover money in unpaid benefits now and over time.
The failure rate is low.
Generally, the benefits ($860 on average) are less than cost.
What are the goals? What quantities are we minimizing/maximizing?
How do we translate the quantities that we can measure and assumptions about those that we can't into decisions?
In USA Today (March 18, 2012)
Drug testing welfare applicants nets little.
Net effect is minimal if not costly. Must assume saved benefits.
No drug test, wo welfare: Program protects taxpayer dollars.
Even if costly, funds are only disbursed to those with negative tests.
How do we account for those not taking the test?
Some drop from fear and some from not needing TANF but this matters for accounting
For state employees, if performance metrics can't establish reasonable suspicion, then there may be better uses of resources.
An Extended Example using Juries [Resources > Probability > Juries.xlsx
Problem setup: A murder
Three pieces of evidence:
Blood type: P(E1|NG)=0.45
Bayes rule gives us: P(G|E1,E2,E3)
It all depends on the Prior.....
Two outcomes: + and -
Two statuses: User and non-user
Claim: Car seats do not improve crash outcomes for 2-6 year olds.
Evidence: No difference in the death outcome from broad observational data.
Warrant: Fatal crashes are just like others and the death outcome is just like injuries in relation to car seats.
Probability is :
(1) a priori (known),
(2) empirical (data), or
What do we learn
Because what we are learning from data is almost always a
. How likely is a variable to take on particular values?