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prob_stats_review

# prob_stats_review - Basic Probability and Statistics Review...

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1 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.

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Pat Hammett University of Michigan 2 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 3 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.

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