ENGR 610Applied Statistics

Fall 2007 - Week 1

Marshall UniversityCITE

Jack Smith

http://mupfc.marshall.edu/~smith1106

Overview for Today Syllabus Introductions Chapters 1-3

Introduction to Statistics and Quality Improvement

Tables and Charts Describing and Summarizing Data

Homework assignment

Syllabus

Week 1 (Aug 23) Introduction - Descriptive Statistics 1-3

Week 2 (Aug 30) Discrete Probability Distributions 4

Week 3 (Sept 6) Continuous Probability Distributions 5

Week 4 (Sept 13) Estimation Procedures 8

Week 5 (Sept 20) Review, Exam 1 1-5, 8 

Week 7 (Sept 27) Hypothesis Testing 9

Week 7 (Oct 4) Hypothesis Testing 9

Week 8 (Oct 11) Design of Experiments 10

Week 9 (Oct 18) Design of Experiments 11

Week 10 (Oct 25) Review, Exam 2 9-11 

Syllabus, cont’d

Week 11 (Nov 1) Simple Linear Regression 12

Week 12 (Nov 8) Multiple Regression 13

Week 13 (Nov 15) More Regression 13

Fall Break (Nov 22) (no class)

Week 14 (Nov 29) Review, Exam 3  12-13

Week 15 (Dec 6) (Exam 3 due)  

Text -- Levine, Ramsey, Smidt, “Applied Statistics for Engineers and Scientists: Using Microsoft Excel and MINITAB” (Prentice-Hall, 2001) - with CD-ROM

Grading 25% - Homework and attendance 25% - Exam 1 25% - Exam 2 25% - Exam 3

Introductions Name Home town Undergraduate degree, major, where Major focus of study at MU Occupation, if working Background in statistics Hopes for this course

Introduction to Statistics (Ch 1)

What is Statistics? Variables Operational Definitions Sampling Software

What is Statistics? Descriptive Statistics

Methods that lead to the collection, tabulation, summarization and presentation of data

Inferential Statistics Methods that lead to conclusions, or estimates of

parameters, about a population (of size N) based on summary measures (statistics) on a sample (of size n) - in lieu of a census

Why Statistics? Describe numerical information Draw conclusions on a large population from

sample information only Derive and test models Understand and control variation Improve quality of processes Design experiments to extract maximum

information Predict or affect future behavior

Variables Categorical

Nominal Mutually exclusive Collectively exhaustive

Numerical Discrete or Continuous Scale

Ordered Interval - equally spaced Ratio - with absolute zero

Operational Definitions Objective, not subjective Specific tests, measurements Specific criteria Agreed to by all Consistent between individuals Stable over time

Sampling Advantages

Cost, time, accuracy, feasibility, scope Minimize destructive tests

Probability samples Simple random

With or without replacement Systematic random

Random start, but constant increment or rate

Non-probability samples Convenience, Judgment, Quota (representative)

Software Historical (mainframe, batch)

SAS, SPSS,… Specialized (workstations, stand-alone)

SAS, SPSS, MINITAB, S-PLUS (R*), BMDP,… Integrated (standard desktops)

DataDesk, JMP, SYSTAT, MINITAB Excel, add-ons (e.g., PHStat - from Prentice-Hall) MATLAB (Octave*)

*Open Source

Introduction to Quality Improvement Quality = fitness of use

Meeting user/customer needs, expectations, perceptions and experience

Quality of… Design - intentional differences, grades Conformance - meets/exceeds design Performance - long-term consistency

History of Quality Improvement

Middle Ages

> Industrial Revolution

> Information Age

Smith, Taylor, Ford, Shewhart, Deming

Read text!

Themes of Quality Improvement The primary focus is on process improvement

Shewhart-Deming cycle: Plan, Do, Study, Act Most of the variation in a process is systemic and not

due to the individual Teamwork is an integral part of a quality-management

organization Customer satisfaction - primary organizational goal Organizational transformation needs to occur to

implement quality management Fear must be removed from organizations Higher quality costs less, not more, but it requires an

investment in training

Tables and Charts (Ch 2) Process Flow Diagrams Cause-and-Effect Diagrams Time-Order Plots Numerical Data Concentration Diagrams Categorical Data Bivariate Categorical Data Graphical Excellence

Process Flow Diagrams

Cause-and-Effect Diagrams

Also known as an Ishikawa or a “fishbone” Diagram

Effect

Procedures or methods

People or personnel

Environment

Materials or supplies

Machinery or equipment

Time-Order Plots

Tables and Charts forNumerical Data

Stem-and-Leaf Displays Poor man’s histogram

Frequency Distribution “Binning” by range

Histogram Polygon

Concentration Diagrams

Data points overlaid on schematic or picture of object or process of interest

By location Displayed as individual symbols or

tallies

Tables and Charts forCategorical Data

Bar Chart Pie Chart

Almost always in percentages Pareto Diagram

Sorted (usually descending) Overlaid with cumulative line (polygon) plot Separate scales Usually in percentages

Examples

Tables and Charts forBivariate Categorical Data Contingency Table

Cross-classification Joint responses Percentages by row, column, total

Side-by-Side (Cluster) Bar Chart May prefer stacked bars with percentage data

A B C

1 5 3 2 102 2 3 4 93 0 2 3 5

7 8 9 24

Graphical Excellence Tufte, “The Visual Display of Quantitative

Information” Graphical excellence… gives the viewer the largest number

of ideas, in the shortest time, with the least ink - clearly, precisely, efficiently, and truthfully

Data-ink Ratio (data-ink)/(total ink used in graphic)

Chartjunk Non-data or redundant “ink”

Lie Factor (size of effect in graph)/(size of effect in data)

Describing and Summarizing Data - Descriptive Statistics (Ch 3)

Measures of… Central Tendency Variation Shape

Skewness Kurtosis

Box-and-Whisker Plots

Measures ofCentral Tendency Mean (arithmetic)

Average value: Median

Middle value - 50th percentile (2nd quartile) Mode

Most popular (peak) value(s) - can be multi-modal Midrange

(Max+Min)/2 Midhinge

(Q3+Q1)/2 - average of 1st and 3rd quartiles

1

NX i

i

N

Measures of Variation Range (max-min) Inter-Quartile Range (Q3-Q1) Variance

Sum of squares (SS) of the deviation from mean divided by the degrees of freedom (df) - see pp 113-5

df = N, for the whole population df = n-1, for a sample

2nd moment about the mean (dispersion)(1st moment about the mean is zero!)

Standard Deviation Square root of variance (same units as variable)

Sample (s2, s, n) vs Population (2, , N)

Quantiles Equipartitions of ranked array of observations

Percentiles - 100 Deciles - 10 Quartiles - 4 (25%, 50%, 75%) Median - 2

Pn = n(N+1)/100 -th ordered observation

Dn = n(N+1)/10

Qn = n(N+1)/4

Median = (N+1)/2 = Q2 = D5 = P50

Measures of Shape Symmetry

Skewness - extended tail in one direction 3rd moment about the mean

Kurtosis Flatness, peakedness

Leptokurtic - highly peaked, long tails Mesokurtic - “normal”, triangular, short tails Platykurtic - broad, even

4th moment about the mean

See p 118.

Box-and-Whisker Plots Graphical representation of five-number summary

Min, Max (full range) Q1, Q3 (middle 50%) Median (50th %-ile)

See pp 123-5

Shows symmetry (skewness) of distribution

Homework Ch 1

Appendix 1.2 Excel, Analysis ToolPak, PHStat add-in

Problems: 1.25 Ch 2

Appendix 2.1 Problems: 2.54, 2.55, 2.61

Ch 3 Appendix 3.1 Problems: 3.27, 3.31 (data on CD)

Next Week Probability and

Discrete Probability Distributions (Ch 4)