1. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.1 Computer Intensive Techniques (Bootstrapping) Instructor: Ron S. Kenett Email: ron@kpa.co.ilron@kpa.co.il Course Website: www.kpa.co.il/biostatwww.kpa.co.il/biostat Course textbook: MODERN INDUSTRIAL STATISTICS, Kenett and Zacks, Duxbury Press, 1998

2. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.2 Course Syllabus Understanding Variability Variability in Several Dimensions Basic Models of Probability Sampling for Estimation of Population Quantities Parametric Statistical Inference Computer Intensive Techniques Multiple Linear Regression Statistical Process Control Design of Experiments

3. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.3Bootstrapping A computer intensive method, introduced in 1979 by Brad Efron from Stanford University in order to pool yourself out of the mess : T Take a Random Sampling With Replacement (RSWR) and compute statistic T T Resample M times and recompute statistic T Derive Empirical Bootstrap Distribution (EBD) TT E{EBD} and STD{EBD} and EBD percentiles estimate E{T} and STD{T} and Bootstrap Confidence Interval for population parameter

4. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.4 Bootstrap testing of the mean Hybrid1 2060 2127 1947 2140 1960 2134 2054 2094 2087 2267 2427 2174 2107 2267 2154 2167 2147 2214 2160 2180 2220 2167 2174 2280 2187 2180 2060 2054 2240 2140 Is this significantly different from 2150 ?

5. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.5 Boot1smp.exe

6. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.6 Hybrid1 2060 2127 1947 2140 1960 2134 2054 2094 2087 2267 2427 2174 2107 2267 2154 2167 2147 2214 2160 2180 2220 2167 2174 2280 2187 2180 2060 2054 2240 2140 Hybrid1 2060 2127 1947 2140 1960 2134 2054 2094 2087 2267 2427 2174 2107 2267 2154 2167 2147 2214 2160 2180 2220 2167 2174 2280 2187 2180 2060 2054 2240 2140 Hybrid1 2060 2127 1947 2140 1960 2134 2054 2094 2087 2267 2427 2174 2107 2267 2154 2167 2147 2214 2160 2180 2220 2167 2174 2280 2187 2180 2060 2054 2240 2140 Hybrid1 2060 2127 1947 2140 1960 2134 2054 2094 2087 2267 2427 2174 2107 2267 2154 2167 2147 2214 2160 2180 2220 2167 2174 2280 2187 2180 2060 2054 2240 2140 Hybrid1 2060 2127 1947 2140 1960 2134 2054 2094 2087 2267 2427 2174 2107 2267 2154 2167 2147 2214 2160 2180 2220 2167 2174 2280 2187 2180 2060 2054 2240 2140

7. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.7 X-bar Std 2135.0387.850 2149.84121.631 2141.19109.258 2149.0978.084 2134.00103.856 2122.1373.843 2119.6686.625 2113.59107.136 2138.97101.693 2163.0067.725 *Derive reference distribution by computing Empirical Bootstrap Distribution

8. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.8 2150 Empirical Bootstrap Distribution of mean 0.95 conf. BI = (2109.5, 2179.9) EBD of STD Empirical Bootstrap Distribution

9. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.9 Bootstrapping the ANOVA Hybrid1Hybrid2Hybrid3 206019071887 212719401834 194717001587 214019341814 196017071614 196016801680 213419401747 205417941660 209417071600 F= MSBetween/MSWithin = 49.274

10. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.10 F= 49.274 ANOVTEST.EXE EBD of F values

11. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.11 Draw samples from X and Y X: Stress or Load distributions Y: Strength distribution Estimate P( X>Y) Bootstrapping Stress Strength relationships

12. 1/2/2014 (c) 2000, Ron S. Kenett, Ph.D.12 X=.0352,.0397,.0677,.0233,.0873,.1156,.0286,.0200,.0797,.9972,.0245,.0251,.0469,.0838,.0796 Y= 1.7700,.9457, 1.8985, 2.6121, 1.0929,.0362, 1.0615, 2.3895,.0982,.7971,.8316, 3.2304,.4373, 2.5648,.6377 P( X>Y) = 0.04 with P.95 P.95 = 0.08 EBD of P(X>Y)