Stat 601, Fall 2000, Class 1

Introduction




Objectives of Stat601

*
Review intro stat ideas
*
Change emphasis toward interpretation and practical application
*
Learn the software
*
Enjoy it

Quick review of the syllabus

*
Course material
*
Grading/assessment
*
TA's and office hours??
*
Evaluations
*
Computing

The role of questions in class

*
Good questions
*
Insights
*
Clarifications
*
Tie backs/big picture
*
Bad questions
*
Missed last class
*
Flex muscles

Metaphor; the spoken language, not the grammar.

Course overview

*
Material
*
Classes 1-4. Understanding/measuring variability. Why it is important. Factor in variability/uncertainty to the decision making process
*
Who cares? The Basel Accord
*
Risky investments need higher reserves
*
Need to measure risk. e.g. J.P.Morgan
*
Risk == volatility of returns
*
Volatility == variability
*
Classes 5-10. Regression/statistical modeling/forecasting/explaining variability
*
Models
*
Stock market
*
Market share
*
Real estate prices
*
What's different? Our model explicitly incorporate variability; don't just get to model the process, get to say how good the model is. Meta-information: statements about the quality oif information. Value added - the idea of precision.
*
What to get out of the course
*
Perform statistical analysis - hands on
*
No stats background - not math based
*
Project, THE learning experience
*
PRACTICAL APPLIED MODERN STATISTICS
*
Success in the course
*
Learn the right questions to ask
*
Critical evaluation of another's analysis
*
Mastery of stat package
*
Confidence to perform analysis/use tools
*
Presentation and communication of results
*
Guarantee: you will be faced with more data, not less. This course is about evaluating, summarizing and leveraging information
*
Popular quote ``if you can't measure it you can't manage it''

Today's material

Basic statistical graphics and summaries

Graphics

Box plot Identification of outliers
Histogram Shape of data, skewness. Outliers
Normal quantile plot Diagnostic for normality

Summary measures

  CENTER SPREAD
Sensitive to outliers Mean Variance/SD
Robust Median IQR

Definitions and notation

*
Mean = average. True $\mu$, estimated $\overline{x}$
*
Median = order the data, the one in the middle. Not standard.
*
Variance = average squared distance from the mean. True $\sigma^2$, estimated s2
*
S.D. = $\sqrt{{\rm Variance}}$. True $\sigma$, estimated s
*
IQR = 75 pctile - 25 pctile. Not standard.

Shapes of distributions/histograms

*
Symmetric bell shaped; mean $\sim$ median
*
Right skew; mean greater than median
*
Left skew; mean smaller than median

*
Symmetric bell shaped - good news.
*
Skewness - watch out!

The empirical rule

If data bell shaped and symmetric then say approximately normal.

Key: the mean and standard deviation summarize the data efficiently in these circumstances.

The EMPIRICAL RULE rule applies when data is approximately normal.

Rule of thumb for normal data - it ties together the mean and standard deviation, ($\mu$ and $\sigma$) into a rule that establishes where most of the data should lie. If the data is outside this range then it's an ``atypical'' observation; in J.P. Morgan's terminology an adverse market move.

Special one: $1.645 \times \sigma$ gives a 10% chance of falling out of the range. That is 5% on each side (tail), one in 20 times we see the lower event, about 1 trading day a month.

Review

*
Summary measures
*
Robust vs. Sensitive
*
Empirical rule for mound shaped and symmetric data
*
Ties together mean and s.d. to help define an ``unusual event''
*
Disparate data may be approx normal, ie GMAT and GM
*
But not ALL data is normal, ie Eisner's compensation.



2000-09-08