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