prob_stats_review - Basic Probability and Statistics Review...

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Basic Probability and Statistics Review
Six Sigma Black Belt Primer
Pat Hammett, Ph.D.
January 2003
Instructor Comments:
This document contains a review of basic probability and statistics. It also
includes a practice test at the end of the document. Note: answers to the
practice test questions are included in an appendix.

Pat Hammett University of Michigan
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Table of Contents
1. VARIABLES- QUALITATIVE AND QUANTITATIVE ..................... 3
1.1 Qualitative Data (Categorical Variables or Attributes) ........................... 3
1.2 Quantitative Data ............................................................................................... 4
2. DESCRIPTIVE STATISTICS ................................................ 6
2.1 Sample Data versus Population Data .................................................................... 6
2.2 Parameters and Statistics ..................................................................................... 6
2.3 Location Statistics (measures of central tendency) ....................................... 7
2.4 Dispersion Statistics (measures of variability) ............................................... 8
3. FREQUENCY DISTRIBUTIONS ........................................... 10
3.1 Frequency Measures .............................................................................................. 10
3.2 Histogram ................................................................................................................. 11
3.3 Discrete Histogram ............................................................................................... 12
3.4 Continuous Data Histogram ................................................................................. 13
4. PROBABILITY AND ERROR ................................................ 15
4.1 Probability Properties ........................................................................................... 15
4.2 Type I and II Errors ............................................................................................ 17
4.3 p-values and statistical significance ................................................................. 19
5. NORMAL DISTRIBUTION ................................................. 20
5.1 Properties of the Normal Distribution ............................................................ 20
5.2 Estimating Probabilities Using Normal Distribution ..................................... 21
5.3 Calculating Parts Per Million Defects Given Normal Distribution ............. 22
6. LINEAR REGRESSION ANALYSIS ........................................ 26
6.1 General Regression equation ............................................................................... 26
6.2 Simple linear regression ...................................................................................... 26
6.3 Correlation .............................................................................................................. 28
6.4 Using Scatter Plots to Show Linear Relationships ....................................... 29
6.5 Multiple linear regression ................................................................................... 30
Appendices:
A – Practice Test
B – Normal Distribution Tables
C – Useful Excel Functions

Pat Hammett University of Michigan
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1. VARIABLES- QUALITATIVE AND QUANTITATIVE
A variable is any measured characteristic or attribute that differs for
different subjects. For example, if the length of 30 desks were measured, then
length would be a variable.
Key Learning Skills –
• Understand the difference between a qualitative (categorical) variable
and a quantitative variable.
• Understand the types of qualitative (categorical) variables: Nominal,
Ordinal, and Binary.
• Understand the difference between a discrete and a continuous
quantitative variable.
Terms and Definitions:
1.1 Qualitative Data (Categorical Variables or Attributes)
Qualitative data involves assigning non-numerical items into groups or
categories. Qualitative data also are referred to as categorical data. The
qualitative characteristic or classification group of an item is an attribute .
Some examples of qualitative data are:
• The pizza was delivered on time.
• Categorical Variable: Delivery Result
• Attribute: On Time, Not On Time
• The survey responses include disagree, neutral, or agree.
• Categorical Variable: Survey Response
• Attribute: Disagree, Neutral, Agree
• This car comes in black, white, red, blue, or yellow.
• Categorical Variable: Color
• Attribute: Black, White, Red, Blue, or Yellow.
Categorical variables are typically assigned attributes using a nominal,
ordinal, or binary scale.