Class 1 Stat 604 Fall 1997

Introduction

The three pre-term stat courses

Stat 603 - 11 classes

Stat 604 - 6 classes. An accelerated 603

Stat 608 - 6 intense classes. Waiver exam preparation. Equivalent to Stat 621

My assumptions about this class (you!)

Objectives of Stat604

Review intro stat ideas

Change emphasis toward interpretation and practical application

Learn the software

Get ready for Stat 621

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 overviews

603/4

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

Stat 621

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. Value added - the idea of precision.

What to get out of the course

Using software in internship - the pain is worth it

Perform statistical analysis - hands on

No stats background - not math based

Big project, THE learning experience

PRACTICAL APPLIED MODERN STATISTICS

Success in the course

Critical evaluation of an analysis

Mastery of stat package

Confidence to perform analysis/use tools

Presentation and communication of results

Todays material.

• Key concept: Summarizing data
• Key tool: the Empirical rule
• Key graphics: Histogram, boxplot and normal quantile

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 , estimated

Median = order the data, the one in the middle. No standard notation.

Variance = average squared distance from the mean. True , estimated

S.D. = . True , estimated s

IQR = 75 pctile - 25 pctile. No standard notation.

Shapes of distributions/histograms.

Symmetric bell shaped; mean median

Right skew; mean greater than median

Left skew; mean smaller than median

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

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, ( and ) 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.

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.