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E-grāmata: Native Statistics for Natural Sciences

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  • Formāts: 533 pages
  • Izdošanas datums: 01-Jul-2013
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-13: 9781628080858
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Native Statistics for Natural SciencesPalielināt
  • Formāts: 533 pages
  • Izdošanas datums: 01-Jul-2013
  • Izdevniecība: Nova Science Publishers Inc
  • ISBN-13: 9781628080858
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This is a book which presents several step-by-step complementary and chained statistical tools. These tools are applied to analyze structures and variability of natural systems helping to gradually understand and control their complexity. The book is organized into a series of chapters which are extensively illustrated by intuitive figures and simple numerical examples. Statistics represent a large field of applied mathematics aiming to extract and analyze information from sampled data issued from complex systems or populations. Extraction of reliable information on systems requires "e;a priori"e; of the application of strategic rules by which intrinsic variability and extrinsic limits are considered. Such strategic rules are given by sampling designs and experimental designs which are applied for open and close systems, respectively. Sampling designs presented in this book include simple random, systematic and stratified designs which are applied to estimate and control variability in open systems having different organizations or distributions. Moreover, sampling designs are appropriate tools for later biodiversity and spatiotemporal analysis of natural systems. Experimental designs include factorial, response surface and mixture designs which are specifically applied to control systems defined by different geometrical structures. Such geometrical structures have different dimensions defined by strategic values of experimental factors which could have potential effects on the studied system.
Preface xvii
Chapter 1 Global Classification Of Statistical Methods, Parameters And Aims
1(20)
A Introduction to Different Aims in Statistics
1(1)
B Introduction to Statistical Methodology
2(2)
C Basic Questions Linked to Basic Statistical Information
4(2)
D Descriptive Variables and Basic Statistical Information
6(1)
E Background on Succession and Complementarity of Statistical Methods Presented in the Book
6(11)
E.1 Descriptive Parameters and Inference Methodology
9(2)
E.2 Classification and Identification of Populations from Comparison Tests
11(1)
E.3 Link Analyses and Predictive Methods of Variability
12(1)
E.4 Preparative Methods of Reliable Information
13(1)
E.4.1 Sampling Designs
14(1)
E.4.2 Experimental Designs
14(1)
E.5 Dsitribution Pattern Detection and Biodiversity Analysis
15(2)
F Statistics for Biology: From and Beyond the Current Book
17(4)
Chapter 2 Introduction To Statistical Inference And Population Induction
21(8)
A Statistical Inference: Goals, Types, Ways
21(1)
B Parametric Estimation
22(1)
B. 1 Estimation by Punctual Parameters
23(2)
B.2 Estimation by Confidence Interval
24(1)
C Nonparametric Statistics
25(1)
D Estimator Properties
26(2)
D.1 Non-Biased Estimator
26(1)
D.2 Convergent Estimator
27(1)
D.3 Exhaustive Estimator
28(1)
E Interest of Graphical Population Analysis
28(1)
Chapter 3 Punctual Estimation Of Population Characteristics Using Numerical And Graphical Parameters From Sample
29(40)
A Occurrence Parameters
29(1)
B Position Parameters
30(12)
B.1 Central Trend Parameters
31(1)
B.1.1 The Mode
31(1)
B.1.2 The Median
31(1)
B.1.3 The Arithmetic Mean
31(1)
B.2 Numerical Application on Central Trend Parameters
32(1)
B.3 Interpretation of Central Trend Parameters
33(1)
B.4 Numerical Application on Interpretation of Central Trend Parameters
34(1)
B.5 Graphical Determination of the Median
34(1)
B.6 Intermediate Position Parameters
35(2)
B.7 Numerical Application
37(1)
B.8 Extreme Position Parameters
37(2)
B.9 Numerical Application
39(1)
B.10 Other Position Parameters
40(1)
B.10.1 Range Midpoints
40(1)
B.10.2 Geometric Mean
40(1)
B.10.3 Harmonic Mean
41(1)
B.10.4 Quadratic Mean
42(1)
C Dispersion Parameters
42(13)
C.1 Role of Dispersion Parameters
42(1)
C.2 Sample Range
43(1)
C.3 Inter-Quartile Range
43(1)
C.4 Dispersion
44(3)
C.5 Variance
47(1)
C.6 Standard Deviation
48(1)
C.7 Numerical Application
49(1)
C.7.1 Example 1
49(1)
C.7.2 Example 2
50(2)
C.8 Variation Source of Standard Deviation
52(1)
C.8.1 Variation of Standard Deviation Linked to Sampling
52(1)
C.8.2 Variation of Standard Deviation Linked to Population Content
52(3)
D Precision and Scale Parameters
55(3)
D.1 Coefficient of Variation
55(1)
D.2 Reduced Values
56(1)
D.3 Centered and Reduced Values
57(1)
E Shape Parameters
58(8)
E.1 Gamma Type (γ) Shape Parameters
58(1)
E.1.1 The Skewness
58(2)
E.1.2 The Kurtosis
60(1)
E.2 Beta-Type Shape Parameters
61(1)
E.3 Quantele-Based Shape Parameters
62(1)
E.3.1 Symmetry Measures
62(1)
E.3.2 Kurtosis Measures
62(1)
E.4 Numerical Application
62(1)
E.4.1 Example 1
62(4)
E.4.2 Example 2
66(1)
F Synthesis about the Moments of Random Variable
66(3)
Chapter 4 Estimation Of Population Parameters By Confidence Intervals
69(14)
A General Interest of Confidence Interval
69(1)
B Principle of Calculation of Confidence Interval
69(2)
C Confidence Interval Linked to Normal Distribution
71(7)
C.1 Confidence Interval of a Normally Distributed Variable X
71(2)
C.2 Confidence Interval of Population Mean
73(1)
C.3 Confidence Interval of Mean Difference D
74(1)
C.4 Confidence Interval of a Proportion Π in an Infinite Size Population
75(1)
C.5 Confidence Interval of a Proportion Π in a Finite-Size Population
76(1)
C.6 Confidence Interval of a Difference between Two Proportions πA, πB in Two Populations
77(1)
C.7 Numerical Application
77(1)
D Confidence Intervals Based on Chi-2 Distribution
78(2)
D.1 Confidence Interval of Population Variance σ2
78(2)
E Confidence Intervals Based on Fisher Distribution
80(3)
E.1 Confidence Interval of a Correlation Coefficient
80(1)
E.2 Confidence Interval of a Proportion π
80(3)
Chapter 5 Graphical Representations Of Statistical Variables
83(18)
A Introduction
83(1)
B Graphical Representations of a Continuous Variable
83(10)
B.1 Histogram
83(4)
B.1.1 Calculation of Number of Classes
87(1)
B.1.2 Calculation of the Width of Classes
87(1)
B.1.3 Limits of Classes' Calculation
88(1)
B.1.4 Frequencies of Classes
88(1)
B.1.5 Histogram Plotting
88(1)
B.1.6 Histogram Smoothing
89(1)
B.2 Tukey Box Plot
90(2)
B.3 Numerical Application
92(1)
C Graphical Representation of a Quantitative Discrete or Qualitative Ordinal Variable
93(3)
C.1 Bar Chart
93(1)
C.1.1 Application Example on Discrete Variable
94(2)
C.1.2 Application Example on Ordinal Variable
96(1)
D Graphical Representations of Qualitative Variables
96(5)
D.1 Pie Chart
96(1)
D.2 Stacked Columns Chart
96(2)
D.3 Numerical Application
98(3)
Chapter 6 Different Probability Laws Describing Variability Of Statistical Populations
101(58)
A Normal Distribution
103(17)
A.1 Natural Origins of Normal Distribution
103(1)
A.2 Probabilistic Origins of Normal Distribution
103(1)
A.3 General Characteristics of Normal Distribution
104(2)
A.4 Standardized Normal Distribution
106(4)
A.5 Statistical Characteristics of Normal Distributions
110(1)
A.6 Confidence Interval of Normal Distribution
111(3)
A.7 Reading of Z-Table
114(1)
A.8 Cumulative Distribution Function
115(2)
A.9 The P-Value Concept
117(2)
A.10 Links between Normal Distribution and Other Statistical Distributions
119(1)
B Student Distribution
120(5)
B.1 Statistical Origin and Meaning
120(1)
B.2 Statistical Characteristics of T-Distribution
120(4)
B.3 Links between Student and Other Probability Distributions
124(1)
C Chi-2 Distribution
125(4)
C.1 Statistical Origin and Application Fields
125(1)
C.2 Statistical Characteristics of Chi-2 Distribution
126(2)
C.3 Links between Chi-2 and Other Probability Distributions
128(1)
D Fisher-Snedecor Distribution
129(2)
D.1 Statistical Origin and Application Fields
129(1)
D.2 Statistical Characteristics
129(1)
D.3 Links between Fisher-Snedecor and Other Probability Distributions
130(1)
D.3.1 F-F Link
130(1)
D.3.2 t-F link
131(1)
D.3.3 Χ2-F link
131(1)
E Binomial Distribution
131(12)
E.1 Objective and Definitions
131(1)
E.2 Origin and Study Field
132(2)
E.3 Probability Distribution of Binomial Law
134
E.4 Practical Way to Calculate Binomial Coefficient
37(103)
E.5 Moments of Binomial Distribution
140(1)
E.5.1 Expected Frequency of Considered Modality
140(1)
E.5.2 Variance of Occurrence Frequency
141(1)
E.5.3 Skewness
141(1)
E.5.4 Numerical Application
141(2)
F Negative Binomial or Pascal Distribution
143(5)
F.1 Statistical Origins and Application Fields
143(1)
F.2 Statistical Characteristics
144(3)
F.3 Numerical Application
147(1)
G Hypergeometric Distribution
148(4)
G.1 Application Field and Objective
148(3)
G.2 Characteristic Parameters of Hypergeometric Distribution
151(1)
H Poisson Distribution
152(7)
H.1 Statistical Origins and Application Fields
152(2)
H.2 Statistical Characteristics of Poisson Distribution
154(5)
Chapter 7 Parametric Hypothesis Tests To Statistical Comparisons Between Two Values
159(48)
A Parametric versus Nonparametric Statistics
159(1)
B Decomposition of Data Distribution into Central and Peripheral Parts
159(3)
C Background on Different Comparison Tests
162(2)
D Methodology of Comparison Test
164(5)
D.1 Definition of the Comparison Aim
165(1)
D.2 Exclusive Hypotheses Specification
165(1)
D.3 Checking or Recalling of Test Condition(S)
165(1)
D.4 Standardized Value Calculation
166(1)
D.5 Comparison of Calculated and Cutoff Standardized Statistics
166(1)
D.6 One and Two-Tailed Comparison Tests Conclusions
166(3)
E Hypothesis Tests for Comparisons between Two Means
169(21)
E.1 Comparison of a Sample Mean to a Population Mean
169(1)
E.1.1 The Case of Great Sample
169(2)
E.1.2 The Case of Small Sample
171(1)
E.1.3 Numerical Application
171(4)
E.2 Comparison between Two Means of Two Independent Samples
175(1)
E.2.1 The Case of Great Samples
175(1)
E.2.2 The Case of Small Samples
176(3)
E.2.3 Probabilistic Origin of Student T-Test for Comparison between Two Means
179(1)
E.2.4 Numerical Application
180(1)
E.3 Comparison between Two Means of Two Paired Samples
181(1)
E.3.1 Principle of the Hypothesis Test
181(2)
E.3.2 Characteristics of the Random Difference Variable
183(1)
E.3.3 The Case of Great Size Paired Samples
183(1)
E.3.4 The Case of Small Size Paired Samples
184(1)
E.3.5 Probabilistic Origin of Student T-Test for Comparison between Two Means
185(1)
E.3.6 Numerical Application
185(1)
E.4 Comparison between Two Means of Two Samples with Unequal Population Variances
186(1)
E.4.1 Aspin-Welch Test
186(2)
E.4.2 Numerical Application
188(2)
F Comparison between Proportions
190(4)
F.1 Comparison between a Sample Proportion (p) and a Population Proportion (π)
190(1)
F.2 Comparison between Proportion pa and pB of Two Independent Samples
191(1)
F.2.1 Calculation of z Statistic
191(1)
F.2.2 Application Conditions
192(1)
F.2.3 Numerical Application
192(2)
G Comparison between Variances
194(9)
G.1 Comparison between Variances of Two Independent Samples
194(1)
G.1.1 Variance Ratio Test
194(1)
G.1.2 Numerical Application
195(1)
G.2 Comparison between Two Variances of Paired Samples
196(1)
G.2.1 Student Test
196(1)
G.2.2 Numerical Application
197(1)
G.3 Student Test of Variances' Ratio between Paired Samples
198(1)
G.3.1 Principle
198(1)
G.3.2 Numerical Application
199(2)
G.4 Comparison between Several Variances by Bartlett Test
201(1)
G.4.1 Aim, Interests and Characteristics
201(1)
G.4.2 Principle and Calculations
201(1)
G.4.3 Numerical Application
202(1)
H Hypothesis Tests Concerning Symmetry and Kurtosis
203(4)
H.1 Testing Symmetry
203(2)
H.2 Testing Kurtosis
205(1)
H.3 Numerical Application
206(1)
Chapter 8 Parametric Comparison Between Several Means: Analysis Of Variance
207(22)
A Introduction
207(1)
B Principle of Anova
208(3)
C Illustration of the Principle of Anova-1
211(1)
D Methodological Steps of Fisher-Snedecor Test
211(6)
D.1 Aim
211(1)
D.2 Hypotheses
211(1)
D.3 Application Conditions
212(1)
D.4 Fisher F-Ratio Calculation
212(1)
D.4.1 Between-Sample Variance Calculation
212(2)
D.4.2 Within-Sample Variance Calculation
214(1)
D.4.3 Calculation of Fisher-Snedecor F-Ratio and Anova Test Conclusion
215(2)
E Numerical Application
217(3)
F Geometrical Principle of ANOVA
220(3)
G Algebraic basis of ANOVA
223(4)
G.1 Classification of ANOVA-1 Models
223(1)
G.2 General Equations of ANOVA-1 Models
224(2)
G.3 Intrinsic Variance of Random Factor
226(1)
H Link between F and T Statistics
227(2)
Chapter 9 Nonparametric Comparison Tests Applied To Two Samples
229(60)
A Introduction
229(2)
B Nonparametric Comparison Tests Applied to Ordinal and Continuous Variables
231(24)
B.1 Comparison between General Levels of Two Independent Samples by Mann-Whitney Ranks Test
231(1)
B.1.1 Objective and Characteristics of Test
231(1)
B.1.2 Principle
231(3)
B.1.3 Numerical Application
234(1)
B.1.4 Normal Approximation of the Mann-Whitney Statistic
234(2)
B.1.5 Improved Normal Approximation
236(2)
B.1.6 Numerical Application
238(1)
B.1.7 Mann-Whitney Test with Tied Ranks
239(1)
B.2 Comparison between Locations of Two Paired Samples by the Wilcoxon Signed Ranks Test
240(1)
B.2.1 Objective and Characteristics
240(1)
B.2.2 Principle of the Test
240(2)
B.2.3 Numerical Application
242(3)
B.2.4 Normal Approximation of the Wilcoxon Signed Ranks Test
245(1)
B.2.5 Numerical Application
245(2)
B.2.6 Wilcoxon Signed Ranks Test with Tied Values
247(1)
B.2.7 Wilcoxon Signed Ranks Test by Considering Null Differences
247(1)
B.3 Comparison between General Levels of Several Independent Samples by the Kruskal-Wallis Test
248(1)
B.3.1 Objective and Characteristics
248(1)
B.3.2 Principle and Methodology
248(2)
B.3.3 Numerical Applications
250(2)
B.3.4 Kruskal-Wallis Test in the Case of Tied Ranks
252(1)
B.4 Comparison between the Shapes of Two Distributions BY Kolmogorov-Smirnov Test
253(1)
B.4.1 Aim and Interest
253(1)
B.4.2 Principle and Calculation
253(1)
B.4 Numerical Application
254(1)
C Nonparametric Tests for Qualitative Nominal Variables
255(32)
C.1 Comparison between Two Proportions by the Chi-2 Test
255(1)
C.1.1 Objective and Characteristics
255(1)
C.1.2 Principle of the Chi-2 test
256(1)
C.1.3 Numerical Application
257(2)
C.1.4 Calculation of the Chi-2 Test from Contingency Table
259(5)
C.1.5 Numerical Application
264(2)
C.1.6 Generalization of the Chi-2 Formula Beyond Two Modalities and Two Samples
266(2)
C.1.7 Explicit Presentation of the Degree of Freedom of a (q x g) Contingency Table
268(1)
C.2 Comparison between More Than Two Proportions by Chi-2 Test
269(1)
C.2.1 Hypotheses, Statistic Calculation and Application Conditions
269(1)
C.2.2 Numerical Application
270(3)
C.3 Comparison between Two Proportions in Two Independent Samples by Fisher Exact Test
273(1)
C.3.1 Objective and General Characteristics of the Test
273(1)
C.3.2 Principle of Fisher Exact Test
273(3)
C.3.3 Other Way to Calculate Tables' Probabilities in Fisher Exact Test
276(1)
C.3.4 Numerical Application
277(3)
C.4 Testing Randomness of a Qualitative Modality
280(1)
C.4.1 Objective and Characteristics
281(1)
C.4.2 Principle of Run Test
281(2)
C.4.3 Numerical Application
283(1)
C.4.4 Normal Approximation of Run Test
284(2)
C.4.5 Numerical Application
286(1)
C.4.6 Run Test for One-Tailed Distribution
286(1)
C.4.6.1 Run Test for Contagious or Clustered Distribution
287(1)
C4.6.2 Numerical Application
287(1)
C4.6.3 Run Test for Uniform or Regular Distribution
287(1)
C4.6.4 Numerical Application
288(1)
Chapter 10 Link Analysis Between Two Or More Variables
289(26)
A Link Analysis between two Qualitative Variables by the Chi-2 Test
289(9)
A.1 Objective, Principle and Field Application
289(1)
A.2 Calculation of Chi-2 Statistic
290(1)
A.3 Basic Information from Contingency Table
291(2)
A.4 Independence Frequencies Calculation and Application Condition of Chi-2 Test
293(1)
A.5 Calculation of the Effect
294(1)
A.6 Chi-2 Calculation and Conclusion
294(2)
A.7 Numerical Application
296(2)
B Link Analysis between Two Continuous Quantitative Variables by Simple Linear Regression
298(7)
B.1 Objective and Field Application
298(1)
B.2 General Principle of Simple Linear Model
298(2)
B.3 Calculation of Regression Line Parameters
300(1)
B.3.1 Slope
300(1)
B.3.2 Intercept
300(1)
B.3.3 Correlation Coefficient
300(1)
B.3.4 Determination Coefficient
301(1)
B.4 Validation of Simple Linear Model
302(1)
B.4.1 Validation of Predicted Part
303(1)
B.4.2 Validation of Residual Part
304(1)
B.4.3 Whole Significance Test of Linear Model
305(1)
C Other Statistical Tests About Simple Linear Model
305(3)
C.1 Comparison of Intercept to 0
305(1)
C.2 Comparison of Calculated Slope to a Reference Value
306(1)
C.3 Comparison between Two Calculated Slopes
307(1)
D Numerical Application
308(2)
E Data Linearization by Appropriate Transformation
310(1)
F Trend Detection between Two Variables by Means of Non Parametric Test
311(4)
F.1 Interest of Spearman Correlation Coefficient
311(1)
F.2 Spearman Correlation Calculation
312(1)
F.3 Correction of Spearman Correlation for Tied Data
312(2)
F.4 Numerical Application
314(1)
Chapter 11 Sampling Designs
315(54)
A Introduction
315(2)
B General Aim and Methodology of Sampling Designs
317(1)
C Population Analysis Based on System Decomposition
318(5)
C.1 Analysis of Homogeneity Level in Population
319(2)
C.2 Different Types of Components and Sampling Units for System Analysis
321(2)
D Introduction to Different Sampling Designs in Relation to Different Population Types
323(2)
D.1 Links between Individual Behaviors, Population Distribution and Sampling Design
323(2)
E Simple Random Sampling: Aim, Principle, Properties, Parameters
325(8)
E.1 Aim
325(1)
E.2 Principle and Methodology
325(3)
E.3 Properties and Interests
328(1)
E.4 Numeric Evaluations of Reliability of Random Sampling
328(1)
E.4.1 Sample Randomness Test
328(1)
E.4.2 Calculation of Minimal Sample Size in Relation to Sample Cost and Desired Population Precision
329(4)
E.4.2.1 Calculation of Minimal Sample Size in Large Population with Stable Coefficient of Variation
333(1)
E.4.2.2 Calculation of Minimal Sample Size in the Case of a Small Population
333(1)
E.4.2.3 Calculation of Minimal Sample Size in Population with Not Stable Coefficient of Variation
334(2)
E.4.3 Graphical Determination of Minimal Sample Size
334(2)
F Stratified Sampling
336(18)
F.1 General Principles
336(2)
F.2 Properties
338(3)
F.3 Determination of the Number of Strata by Analysis of Variance (ANOVA)
341(4)
F.4 Sample Size Calculation
345(5)
F.5 Estimation of Strata and Population Parameters
350(1)
F.5.1 Means of Population and Strata
350(1)
F.5.2 Variances of Population and Strata
351(1)
F.5.3 Standard Error of Population Mean
352(2)
G Systematic or Regular Sampling
354(15)
G.1 Aim and General Methodological Principles
354(2)
G.2 Diversity of Systematic Sampling Designs
356(1)
G.2.1 Transect-Based Sampling
356(4)
G.2.2 Mapping-Based Sampling
360(1)
G.3 Determination of Systematic Design Parameters
361(1)
G.3.1 Calculation of Sampling Step
361(2)
G.3.2 Graphical Determination of Minimal Sample Area
363(2)
G.3.3 Determination of the Number of Sampling Units
365(2)
G.4 Properties of Systematic Sampling
367(2)
Chapter 12 Spatial Pattern Analysis
369(16)
A General Aim and Approaches
369(1)
B Spatial Pattern Fitting Based on Probability Distribution Functions
369(7)
B.1 Random Pattern fitting
369(3)
B.2 Clumped Pattern Fitting
372(2)
B.3 Regular Pattern Fitting
374(2)
C Identification of Spatial Distribution Patterns Using Different Calculated Indices
376(4)
C.1 Index of Dispersion
376(3)
C.2 Green Index
379(1)
C.3 Index of Aggregation of Negative Binomial Law
379(1)
D Pattern Analysis Based on Taylor's Power Law
380(5)
Chapter 13 Biodiversity Quantification Methods
385(8)
A Introduction
385(1)
B Richness Indices
385(2)
C Evenness Indices
387(4)
C.1 Shannon Diversity Index
388(2)
C.2 Simpson Diversity Index
390(1)
D Similarity Analysis between Two Samples of Species Abundances
391(1)
E Beyond Biodiversity Indices
392(1)
Chapter 14 Experimental Designs
393(56)
A Introduction
393(3)
B Definition and Interest of Experimental Design
396(1)
C Different Components of Experimental Design
397(7)
C.1 Factors and Responses
397(5)
C.2 Mathematical Modeling of Responses
402(2)
D Classification of Experimental Designs
404(4)
D.1 Classification of Experimental Designs According to Factor Types
404(2)
D.2 Classification of Experimental Designs According to Study Aims
406(1)
D.3 Classification of Experimental Designs According to Characteristics of Analyzed System
407(1)
D.3.1 D-optimal Designs
407(1)
D.3.2 A-optimal Designs
408(1)
D.3.3 G-optimal Designs
408(1)
E Factorial Designs
408(15)
E.1 Full Factorial Designs
408(2)
E.1.1 Determination and Signification of Constant Coefficient a0
410(1)
E.1.2 Determination and Signification of First Factor Coefficient a1
411(1)
E.1.3 Determination and Signification of Second Factor Coefficient a2
412(1)
E.1.4 Determination and Signification of Interaction Coefficient a12
413(3)
E.1.5 Calculation of FDPI Coefficients: Numeric Application on 22 Design
416(1)
E.1.6 Transformation of FDPI Coefficients from Standardized to Experimental Forms
416(2)
E.2 Fractional Factorial Designs
418(2)
E.2.1 Definition of Alias
420(1)
E.2.2 Basic Hypotheses to Build Fractional Factorial Design
420(1)
E.2.3 Application of Alias Theory and Equivalence Relationship
421(2)
E.2.4 Construction of a Fractional Design from a Full Factorial Design
423(1)
F Response Surface Designs
423(20)
F.1 Composite Design
424(1)
F.1.1 Geometric Presentation
424(1)
F.1.2 Construction of Composite Design
424(3)
F.1.3 Numerical Application
427(2)
F.2 Box-Behnken Design
429(1)
F.2.1 Geometric Presentation
429(1)
F.2.2 Construction and General Characteristics of Box-Behnken Designs
429(3)
F.2.3 Numerical Application
432(4)
F.3 Doehlert Design
436(1)
F.3.1 Geometric Presentation
436(2)
F.3.2 Construction and General Characteristics of Doehlert Design
438(3)
F.3.3 Numerical Application
441(2)
G Simplex Mixture Designs
443(6)
G.1 General Characteristics
443(1)
G.2 Geometric Presentation
444(1)
G.3 Construction of Scheffe's Simplex Design
445(3)
G.4 Numerical Application
448(1)
APPENDICES
449(48)
Appendix 1 Tables of One- and Two-Tailed Critical Values (Z) of Normal Distribution
451(2)
Appendix 2 Table of critical values of Student T-distribution
453(2)
Appendix 3 Tables of critical values of F distribution
455(4)
Appendix 4 Table of Critical Values of Chi-2 Distribution
459(1)
Appendix 5 Table of Critical Values of Wilcoxon
460(1)
T Distribution
460(1)
Appendix 6 Table of Critical Values of Mann-Whitney Statistic
461(20)
Appendix 7 Table of Critical Values of Kruskal-Wallis Statistic
481(3)
Appendix 8 Table of Critical Values for Run Test
484(10)
Appendix 9 Table of Kolmogorov-Smirnov Statistics
494(2)
Appendix 10 Table of Random Numbers
496(1)
References 497(12)
Index 509
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