Contents
Introduction to Applied Statistics
Contents
Preface ................................................................................................................ IX
1 Graphical Data Display Methods ..............................................................1
Example 1.1: Bolt Strength ....................................................................... 2
1.1 Data Plot Display Methods ....................................................................... 2
1.1.1 The Dot Diagram ...................................................................................... 3
1.1.2 Scatter Plot ............................................................................................... 3
1.1.3 Box Plot ................................................................................................... 4
1.1.4 Histogram Plot ........................................................................................ 6
1.1.5 Normal Probability Plot ......................................................................... 8
1.2 Variation or Variability ............................................................................. 9
Example 1.2: Gas Mileage Ratings ......................................................... 10
1.3 Exercises ................................................................................................ 14
2 Basics of Statistics .................................................................................... 17
2.1 Data Collection – Population vs. Sample .............................................. 17
2.2 Introduction to Statistical Data Analysis ................................................ 20
2.3 Descriptive Statistics .............................................................................. 21
Example 2.1: Math Final Scores ............................................................ 22
Mean ....................................................................................................... 22
Variance and Standard Deviation ........................................................... 25
Median ................................................................................................... 27
Mode ...................................................................................................... 28
Minimum, Maximum and Range ........................................................... 29
Kurtosis .................................................................................................. 30
Skewness ................................................................................................ 31
Confidence Intervals for Unknown Mean and Unknown Standard Dev.33
2.4 Exercises ................................................................................................. 35
3 Probability Distributions and Normal Distribution ........................... 37
3.1 Random Variable Types .......................................................................... 38
3.2 Distribution Function .............................................................................. 39
3.3 Normal Distribution ................................................................................ 40
Normal Distribution (Curve) Properties ................................................. 41
Example 3.1 ............................................................................................ 41
3.4 Area Divisions Under the Normal Curve ............................................... 42
Chebyshev’s Rule ................................................................................... 44
Example 3.2: Helicopter Design ............................................................ 44
3.5 The Standard Normal Distribution .......................................................... 46
Example 3.3 ............................................................................................ 47
Example 3.4 ............................................................................................ 48
Example 3.5 ............................................................................................ 53
Example 3.6 ............................................................................................ 55
Example 3.7 ............................................................................................ 57
3.6 Exercises ................................................................................................. 58
4 Statistical Inference on Two Samples/Populations ............................... 61
4.1 The Two-Sample T-Test .......................................................................... 62
4.1.1 Unknown But Equal Variances ............................................................... 62
Example 4.1: Neighboring Coal Mines ................................................. 62
4.1.2 Variances are Unknown and not-Equal .................................................. 70
Example 4.2: Recycled Plastics ............................................................ 71
4.2 Paired T-Test ........................................................................................... 75
Example 4.3: Math Grades of Sixth Grade ............................................ 76
4.3 Single Mean Comparison to a Specified Value ...................................... 79
Example 4.4: High-Pressure Valve ......................................................... 80
4.4 Supplementary Material for Excel Commands ...................................... 82
Example 4.1: Neighboring Coal Mines .................................................. 82
Example 4.2: Recycled Plastics ............................................................. 83
Example 4.3: Math Grades of Sixth Grade ............................................. 84
Example 4.4: High-Pressure Valve........................................................... 85
4.5 Supplementary Material for Minitab Results .......................................... 86
Example 4.1: Neighboring Coal Mines ................................................... 86
Example 4.2: Recycled Plastics ............................................................. 90
Example 4.3: Math Grades of Sixth Grade ............................................. 90
Example 4.4: High-Pressure Valve........................................................... 92
4.6 Exercises ................................................................................................. 94
5 Simple Linear Regression (SLR) ........................................................... 97
Example 5.1 ............................................................................................ 99
5.1 Simple Linear Regression for Empirical Models ................................... 100
5.2 Residual and Fitted Values .................................................................... 103
5.3 Simple Linear Regression with Minitab ................................................. 112
5.4 Understanding Minitab Output .............................................................. 117
5.5 Simple Linear Regression with Excel .................................................... 118
5.6 Simple Linear Regression (SLR) using Matrix Notations ..................... 126
5.7 Parameter Estimation using Least Squares ............................................ 128
5.8 Matrix Notations .................................................................................... 130
5.9 Excel Workout ....................................................................................... 132
5.10 Exercises ................................................................................................ 135
6 Multiple Regression (MR) ...................................................................... 137
Example 6.1 .......................................................................................... 138
6.1 DOE Matrix/Table Generation with Minitab ....................................... 139
6.2 Drawing 3D Scatter Diagram in Minitab ............................................. 147
6.3 Multiple Linear Regression .................................................................. 152
6.4 Multiple Linear Regression with Minitab ............................................ 152
6.5 Multiple Regression with Minitab ....................................................... 159
6.5.1 Eliminating Insignificant Terms ............................................................ 163
6.5.2 P-value of F-Test ................................................................................... 164
6.5 Multiple Regression Analysis Continued .............................................. 164
6.6 Multiple Regression with Excel ........................................................... 169
6.7 Multiple Regression with Matrix Notations .......................................... 173
6.7.1 Matrix Notations .................................................................................... 173
6.8 Excel Workout ....................................................................................... 176
6.9 Exercises ................................................................................................ 179
7 Introduction to Designed Experiments .................................................. 181
7.1 Designed Experiments ........................................................................... 182
7.1.1 Experimental Design Space Resolution ................................................. 183
7.2 Objectives in Experiments ..................................................................... 186
7.3 Steps in Experimental Design ................................................................ 188
7.4 Orthogonality ......................................................................................... 188
7.5 Exercises ................................................................................................ 190
8 Full Factorial vs. Taguchi Design Experiments .................................... 191
8.1 OFAT Experiments ................................................................................ 192
8.2 Full Factorial Design ............................................................................. 192
8.3 L-8 Taguchi/Full Factorial Experiments by Mean Responses ............... 197
8.4 Taguchi Analysis using Signal to Noise Ratio (S/N) ............................. 205
8.5 Minitab Taguchi Analysis using Means Response Effects .................... 210
8.6 Exercises ................................................................................................ 231
9 Interactions in Taguchi Design Experiment .......................................... 233
Example 9.1 ........................................................................................... 234
9.1 Using Mean Responses and S/N Ratios in Taguchi Design .................. 236
9.2 Using Mean Responses and S/N Ratios in Taguchi Design w/ Minitab..240
9.3 Exercises ................................................................................................ 253
Appendix ........................................................................................................ 255
1 Excel Commands .................................................................................... 256
2 Z-Table for Cumulative Standard Normal Distribution Function............ 258
3 T-Table for -distribution .......................................................................... 260
4 Taguchi Array Selector ........................................................................... 261
References ....................................................................................................... 263
Index ................................................................................................................ 265