Statistical techniques for data analysis
Preface ...................................................................................................................... v
CHAPTER 1. What Are Data? ................................................................................. 1
Definition of Data ................................................................................................ 1
Kinds of Data ....................................................................................................... 2
Natural Data .................................................................................................... 2
Experimental Data........................................................................................... 3
Counting Data and Enumeration ................................................................ 3
Discrete Data .............................................................................................. 4
Continuous Data ......................................................................................... 4
Variability ............................................................................................................ 4
Populations and Samples...................................................................................... 5
Importance of Reliability ..................................................................................... 5
Metrology............................................................................................................. 6
Computer Assisted Statistical Analyses ............................................................... 7
Exercises .............................................................................................................. 8
References............................................................................................................ 8
CHAPTER 2. Obtaining Meaningful Data ............................................................. 10
Data Production Must Be Planned ..................................................................... 10
The Experimental Method.................................................................................. 11
What Data Are Needed.................................................................................. 12
Amount of Data............................................................................................. 13
Quality Considerations .................................................................................. 13
Data Quality Indicators ...................................................................................... 13
Data Quality Objectives ..................................................................................... 15
Systematic Measurement ................................................................................... 15
Quality Assurance .............................................................................................. 15
Importance of Peer Review................................................................................ 16
Exercises ............................................................................................................ 17
References.......................................................................................................... 17
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CHAPTER 3. General Principles............................................................................ 19
Introduction........................................................................................................ 19
Kinds of Statistics .............................................................................................. 20
Decisions............................................................................................................ 21
Error and Uncertainty......................................................................................... 22
Kinds of Data ..................................................................................................... 22
Accuracy, Precision, and Bias............................................................................ 22
Statistical Control............................................................................................... 25
Data Descriptors............................................................................................ 25
Distributions....................................................................................................... 27
Tests for Normality ............................................................................................ 30
Basic Requirements for Statistical Analysis Validity......................................... 36
MINITAB .......................................................................................................... 39
Introduction to MINITAB............................................................................. 39
MINITAB Example ...................................................................................... 42
Exercises ............................................................................................................ 44
References.......................................................................................................... 45
CHAPTER 4. Statistical Calculations..................................................................... 47
Introduction........................................................................................................ 47
The Mean, Variance, and Standard Deviation.................................................... 48
Degrees of Freedom........................................................................................... 52
Using Duplicate Measurements to Estimate a Standard Deviation .................... 52
Using the Range to Estimate the Standard Deviation ........................................ 54
Pooled Statistical Estimates ............................................................................... 55
Simple Analysis of Variance.............................................................................. 56
Log Normal Statistics......................................................................................... 64
Minimum Reporting Statistics ........................................................................... 65
Computations ..................................................................................................... 66
One Last Thing to Remember ............................................................................ 68
Exercises ............................................................................................................ 68
References.......................................................................................................... 71
CHAPTER 5. Data Analysis Techniques................................................................ 72
Introduction........................................................................................................ 72
One Sample Topics ............................................................................................ 73
Means ............................................................................................................ 73
Confidence Intervals for One Sample....................................................... 73
Does a Mean Differ Significantly from a Measured or Specified Value .. 77
MINITAB Example....................................................................................... 78
Standard Deviations ...................................................................................... 80
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Confidence Intervals for One Sample....................................................... 80
Does a Standard Deviation Differ Significantly from a
Measured or Specified Value.................................................................... 81
MINITAB Example....................................................................................... 82
Statistical Tolerance Intervals ....................................................................... 82
Combining Confidence Intervals and Tolerance Intervals ............................ 85
Two Sample Topics ........................................................................................... 87
Means ............................................................................................................ 87
Do Two Means Differ Significantly ......................................................... 87
MINITAB Example....................................................................................... 90
Standard Deviations ...................................................................................... 91
Do Two Standard Deviations Differ Significantly ................................... 91
MINITAB Example....................................................................................... 93
Propagation of Error in a Derived or Calculated Value ..................................... 94
Exercises ............................................................................................................ 96
References.......................................................................................................... 99
CHAPTER 6. Managing Sets of Data .............................................................. 100
Introduction...................................................................................................... 100
Outliers............................................................................................................. 100
The Rule of the Huge Error......................................................................... 101
The Dixon Test............................................................................................ 102
The Grubbs Test .......................................................................................... 104
Youden Test for Outlying Laboratories ...................................................... 105
Cochran Test for Extreme Values of Variance............................................ 107
MINITAB Example..................................................................................... 108
Combining Data Sets........................................................................................ 109
Statistics of Interlaboratory Collaborative Testing........................................... 112
Validation of a Method of Test ................................................................... 112
Proficiency Testing...................................................................................... 113
Testing to Determine Consensus Values of Materials................................. 114
Random Numbers ............................................................................................ 114
MINITAB Example..................................................................................... 115
Exercises .......................................................................................................... 118
References........................................................................................................ 120
CHAPTER 7. Presenting Data .............................................................................. 122
Tables............................................................................................................... 122
Charts ............................................................................................................... 123
Pie Charts .................................................................................................... 123
Bar Charts.................................................................................................... 123
Graphs .............................................................................................................. 126
Linear Graphs.............................................................................................. 126
Nonlinear Graphs ........................................................................................ 127
Nomographs ................................................................................................ 128
MINITAB Example..................................................................................... 128
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Extreme Value Data ......................................................................................... 220
Statistics of Control Charts .............................................................................. 221
Property Control Charts............................................................................... 221
Precision Control Charts ............................................................................. 223
Systematic Trends in Control Charts........................................................... 224
Simulation and Macros .................................................................................... 224
MINITAB Example................................................................................ 225
Exercises .......................................................................................................... 226
References........................................................................................................ 229
CHAPTER 10. Conclusion ................................................................................... 231