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Table of Contents
by Jürgen Pilz, Rob Verdooren, Dieter Rasch
Applied Statistics
Cover
Preface
References
1 The R‐Package, Sampling Procedures, and Random Variables
1.1 Introduction
1.2 The Statistical Software Package R
1.3 Sampling Procedures and Random Variables
References
2 Point Estimation
2.1 Introduction
2.2 Estimating Location Parameters
2.3 Estimating Scale Parameters
2.4 Estimating Higher Moments
2.5 Contingency Tables
References
3 Testing Hypotheses – One‐ and Two‐Sample Problems
3.1 Introduction
3.2 The One‐Sample Problem
3.3 The Two‐Sample Problem
References
4 Confidence Estimations – One‐ and Two‐Sample Problems
4.1 Introduction
4.2 The One‐Sample Case
4.3 The Two‐Sample Case
References
5 Analysis of Variance (ANOVA) – Fixed Effects Models
5.1 Introduction
5.2 Planning the Size of an Experiment
5.3 One‐Way Analysis of Variance
5.4 Two‐Way Analysis of Variance
5.5 Three‐Way Classification
References
6 Analysis of Variance – Models with Random Effects
6.1 Introduction
6.2 One‐Way Classification
6.3 Two‐Way Classification
6.4 Three‐Way Classification
References
7 Analysis of Variance – Mixed Models
7.1 Introduction
7.2 Two‐Way Classification
7.3 Three‐Way Layout
References
8 Regression Analysis
8.1 Introduction
8.2 Regression with Non‐Random Regressors – Model I of Regression
8.3 Models with Random Regressors
References
9 Analysis of Covariance (ANCOVA)
9.1 Introduction
9.2 Completely Randomised Design with Covariate
9.3 Randomised Complete Block Design with Covariate
9.4 Concluding Remarks
References
10 Multiple Decision Problems
10.1 Introduction
10.2 Selection Procedures
10.3 The Subset Selection Procedure for Expectations
10.4 Optimal Combination of the Indifference Zone and the Subset Selection Procedure
10.5 Selection of the Normal Distribution with the Smallest Variance
10.6 Multiple Comparisons
References
11 Generalised Linear Models
11.1 Introduction
11.2 Exponential Families of Distributions
11.3 Generalised Linear Models – An Overview
11.4 Analysis – Fitting a GLM – The Linear Case
11.5 Binary Logistic Regression
11.6 Poisson Regression
11.7 The Gamma Regression
11.8 GLM for Gamma Regression
11.9 GLM for the Multinomial Distribution
References
12 Spatial Statistics
12.1 Introduction
12.2 Geostatistics
12.3 Special Problems and Outlook
References
Appendix A: List of Problems
Appendix B: Symbolism
Appendix C: Abbreviations
Appendix D: Probability and Density Functions
Index
End User License Agreement
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Title Page
Table of Contents
Cover
Preface
References
1 The R‐Package, Sampling Procedures, and Random Variables
1.1 Introduction
1.2 The Statistical Software Package R
1.3 Sampling Procedures and Random Variables
References
2 Point Estimation
2.1 Introduction
2.2 Estimating Location Parameters
2.3 Estimating Scale Parameters
2.4 Estimating Higher Moments
2.5 Contingency Tables
References
3 Testing Hypotheses – One‐ and Two‐Sample Problems
3.1 Introduction
3.2 The One‐Sample Problem
3.3 The Two‐Sample Problem
References
4 Confidence Estimations – One‐ and Two‐Sample Problems
4.1 Introduction
4.2 The One‐Sample Case
4.3 The Two‐Sample Case
References
5 Analysis of Variance (ANOVA) – Fixed Effects Models
5.1 Introduction
5.2 Planning the Size of an Experiment
5.3 One‐Way Analysis of Variance
5.4 Two‐Way Analysis of Variance
5.5 Three‐Way Classification
References
6 Analysis of Variance – Models with Random Effects
6.1 Introduction
6.2 One‐Way Classification
6.3 Two‐Way Classification
6.4 Three‐Way Classification
References
7 Analysis of Variance – Mixed Models
7.1 Introduction
7.2 Two‐Way Classification
7.3 Three‐Way Layout
References
8 Regression Analysis
8.1 Introduction
8.2 Regression with Non‐Random Regressors – Model I of Regression
8.3 Models with Random Regressors
References
9 Analysis of Covariance (ANCOVA)
9.1 Introduction
9.2 Completely Randomised Design with Covariate
9.3 Randomised Complete Block Design with Covariate
9.4 Concluding Remarks
References
10 Multiple Decision Problems
10.1 Introduction
10.2 Selection Procedures
10.3 The Subset Selection Procedure for Expectations
10.4 Optimal Combination of the Indifference Zone and the Subset Selection Procedure
10.5 Selection of the Normal Distribution with the Smallest Variance
10.6 Multiple Comparisons
References
11 Generalised Linear Models
11.1 Introduction
11.2 Exponential Families of Distributions
11.3 Generalised Linear Models – An Overview
11.4 Analysis – Fitting a GLM – The Linear Case
11.5 Binary Logistic Regression
11.6 Poisson Regression
11.7 The Gamma Regression
11.8 GLM for Gamma Regression
11.9 GLM for the Multinomial Distribution
References
12 Spatial Statistics
12.1 Introduction
12.2 Geostatistics
12.3 Special Problems and Outlook
References
Appendix A: List of Problems
Appendix B: Symbolism
Appendix C: Abbreviations
Appendix D: Probability and Density Functions
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Number
of inhabitants in 23 municipalities of Vienna.
Chapter 2
Table 2.1 Number of noxious weed seeds.
Table 2.2 Some results of the first 20 steps in the iteration of the Heifer exam...
Table 2.3 A two‐by‐two contingency table – model I.
Table 2.4 A two‐by‐two contingency table – model II.
Table 2.5 A two‐by‐two contingency table – for calculating association measures.
Table 2.6 Mother tongue and marital status of the mother of 50 children.
Table 2.7 Hair and eye colour of 2000 German persons.
Chapter 3
Table 3.1
P‐
quantiles
Z
(
P
) of the standard normal distribution.
Table 3.2 Situations and decisions in hypotheses testing.
Table 3.3 Values of the power function
for
n
= 9, 16, 25,
σ
= 1 and specia...
Table 3.4 The litter weights of mice (in grams) and the differences between the ...
Table 3.6 (
γ
1
,
γ
2
)‐values and the corresponding coefficients used in th...
Chapter 4
Table 4.1 Values of
.
Table 4.2 Confidence table of two kinds of smokers.
Chapter 5
Table 5.1 Observations
y
ij
of an experiment with
a
levels of a factor
A
.
Table 5.2 Theoretical ANOVA table: one‐way classification, model I.
Table 5.3 Empirical ANOVA table: one‐way classification, model I.
Table 5.4 Performances (milk fat in kg)
y
ij
of the daughters of three sires.
Table 5.5 ANOVA table for testing the hypothesisH0 : a1 = a2 = a3 = 0...
Table 5.6 Results of testing pig fattening – fattening days (from 40 kg to 110 k...
Table 5.7 Empirical ANOVA table of a two‐way cross‐classification with equal sub...
Table 5.9 ANOVA Table of Example 5.9.
Table 5.8 Observations (loss in per cent of dry mass, during storage of 300 days...
Table 5.10 Analysis of variance table of a two‐way cross‐classification with equ...
Table 5.11 Observations of the carotene storage experiment of Example 5.12.
Table 5.12 ANOVA table for the carotene storage experiment of Example 5.12.
Table 5.13 Theoretical ANOVA table of the two‐way nested classification for mode...
Table 5.14 Observations of the example.
Table 5.15 ANOVA table of a three‐way cross‐classification with equal subclass n...
Table 5.16 Three‐way classification with factors kind of storage, packaging mate...
Table 5.17 ANOVA Table for data of Table 5.16.
Table 5.18 Water temperature (
T
), water salinity (
S
), and density of shrimp popu...
Table 5.19 ANOVA table of a three‐way nested classification for model I.
Table 5.20 Observations of a three‐way nested classification.
Table 5.21 Observations of a mixed classification type (A≻B) × C with
a
= ...
Table 5.22 ANOVA table for a balanced three‐way mixed classification(B ≺ A)x C...
Table 5.23 ANOVA table and expectations of the MS for model I of a balanced thre...
Table 5.24 Observations of a mixed classification type (A×B)≻C with
a
= 2,...
Chapter 6
Table 6.1 Expected mean squares of the one‐way ANOVA model II.
Table 6.2 Milk fat performances
y
ij
of daughters of ten sires.
Table 6.3 ANOVA table of model II with
E(
MS
)
of the example of Problem 6.1.
Table 6.4 ANOVA table of model II of the unbalanced one‐way classification with ...
Table 6.5 Deviations of the specification
y
of three at random chosen products fr...
Table 6.6 The column
E
(
MS
) of the two‐way nested classification for model II.
Table 6.7 Data of the example for Problem 6.9.
Table 6.8 The column
E
(
MS
) as supplement for model II to the analysis of variance...
Table 6.9 (Kuehl 1994) Observations of products produced by operator
A
i
on machin...
Table 6.10 Test statistics for testing hypotheses and distributions of these tes...
Table 6.11 Expectations of the
MS
of a three‐way nested classification for model ...
Table 6.12 Observations
y
ijkl
of a three‐way nested classification model II.
Table 6.13 ANOVA table with df and expected mean squares
E
(
MS
) of model (6.29).
Table 6.14 Data in a three‐way mixed classification((
B
≺
A
)x
C
)
Table 6.15 ANOVA table with df and expected mean squares
E(MS)
of model (6.30).
Table 6.16 Data in a three‐way mixed classification
C
≺ (
AxB
) m...
Chapter 7
Table 7.1 Expectations of the
MS
in Table 5.10 for a Mixed model (Levels of
A
fix...
Table 7.2 Yield per plot
y
in kilograms of a variety trial.
Table 7.3 Yield per plot
y
in kilograms of a variety‐location, two‐way classifica...
Table 7.4 Yields of 6 varieties tested on 12 randomly chosen farms.
Table 7.5
E(
MS
)
for balanced nested mixed models.
Table 7.6 Data of an experiment to determine the content uniformity of film‐coat...
Table 7.7 Data from Example 7.5 with a random factor
A
of batches and a fixed fac...
Table 7.8 ANOVA table – three‐way ANOVA – cross‐classification, balanced case.
Table 7.9 Expected mean squares for the three‐way cross‐classification – balance...
Table 7.10 ANOVA table of the three‐way nested classification – unbalanced case.
Table 7.11 Expected mean squares for the balanced case of model III.
Table 7.12 Expected mean squares for balanced case of model IV.
Table 7.13 Expected mean squares for model V.
Table 7.14 Expected mean squares for model VI.
Table 7.15 Expected mean squares for model VII.
Table 7.16 Expected mean squares for model VIII.
Table 7.17 ANOVA table for the balanced three‐way analysis of variance – mixed c...
Table 7.18 Expected mean squares for model III.
Table 7.19 Expected mean squares for model IV.
Table 7.20 Expected mean squares for the balanced model V.
Table 7.21 Expected mean squares for model VI.
Table 7.22 ANOVA table for the three‐way balanced analysis of variance – mixed c...
Table 7.23 Expected mean squares for balanced model III.
Table 7.24 Expected mean squares for balanced model IV.
Table 7.25 Expected mean squares for the balanced model V.
Table 7.26 Expected mean squares for model VI.
Table 7.27 Expected mean squares for the balanced model VII.
Table 7.28 Expected mean squares for model VIII.
Chapter 8
Table 8.1 The height of hemp plants (
y
in centimetres) during growth (
x
age in w...
Table 8.2 Shoe sizes (
x
in centimetres
)
and body heights (
y
in centimetres) from...
Table 8.3 Average withers heights of 112 cows in the first 60 months of life.
Table 8.4 Carotene content (in mg/100 g dry matter)
y
of grass in dependency of t...
Table 8.5 Lower and upper bounds of the realised 95%‐confidence band for
β
0
...
Table 8.6 Time in minutes (
x
) and change of rotation in degrees (
y
) from experim...
Table 8.7 Leaf surfaces of oil palms
y
insquare metres and age
x
in years
Table 8.8 Relative frequencies of 10 000 simulated samples for the correct accep...
Table 8.9 Leaf surface
y
i
in
m
2
of oil palms on a trial area in dependency of age...
Table 8.10
D
‐ and
G
‐optimal designs for polynomial regression for x ∈ [
a, b
] and
Table 8.11 Locally optimal designs for the exponential regression.
Table 8.12 Locally optimal designs for the logistic regression.
Table 8.13 Locally optimal designs for the Bertalanffy regression.
Table 8.14 Locally optimal designs for the Gompertz regression.
Table 8.15 Optimal size of sub‐samples (
k
) and optimal nominal type‐II‐risk (
β
...
Table 8.16 Optimal size of subsamples (
k
) and optimal nominal type‐II‐risk (
β
...
Chapter 9
Table 9.1 Nested ANOVA table for the test of the null hypothesis
H
β
0
:
β
Table 9.2 Nested ANOVA table for the test HA0: ‘all
a
i
are equal’.
Table 9.3 Strength of a monofilament fibre produced by three different machines
M
Table 9.4 Data of a randomised double‐blind study.
Table 9.5 Data of a randomised complete block design with four blocks (factor B)...
Chapter 10
Table 10.1 Sample means of Example 10.1.
Table 10.2 Values of
n
Gu
used in the simulation experiment.
Table 10.3 Values of average
found in the subset selection.
Table 10.4 Optimal values of
P
B
used in the simulation experiment.
Table 10.5 Average total size of the simulation experiment (upper entry) and the...
Table 10.6 Relative frequencies of correct selection calculated from 100 000 run...
Table 10.7 Simulated observations of Example 5.7.
Table 10.8 Differences
between means of Example 5.7.
Table 10.9 Minimal sample sizes for several multiple decision problems.
Chapter 11
Table 11.1 Link function, random and systematic components of some GLMs.
Table 11.2 Observations (loss during storage in percent of dry mass during stora...
Table 11.3 Analysis of variance table of Problem 11.4.
Table 11.4 Values of
N
ijk
(
n
ijk
) of the block experiment.
Table 11.5 Number
n
of wasps per group and number
k
of these
n
wasps finding eggs...
Table 11.6 Number of soldiers dying from kicks by army mules.
Table 11.7 Values of
k
ijk
(
n
ijk
) on plots
k
= 1, …,
m
ij
in block
i
and genotype
j
...
Table 11.8 Values
k
ij
and
m
ij
found in three strains.
Table 11.9 Clotting time of blood in seconds (
y
) for normal plasma diluted to ni...
Chapter 12
Table 12.1 Gauss–Krüger code numbers.
List of Illustrations
Chapter 3
Figure 3.1 The power functions of the t‐test testing the null hypothesis
H
0
:
μ
...
Figure 3.2 Graphical representation of the two risks
α
and
β
and the...
Figure 3.3 Result of the example.
Figure 3.4 Graph of the triangular sequential two‐sample test of Problem 3.14.
Chapter 8
Figure 8.1 Scatter‐plot for the association between age and height of hemp pla...
Figure 8.2 Scatter‐plot for the observations of Example 8.2.
Figure 8.3 Scatter‐plot of the data in Example 8.3.
Figure 8.4 Scatter‐plot and estimated regression line of the carotene example ...
Figure 8.5 Estimated regression lines of the carotene example (sack
, glass
Figure 8.6 Scatter‐plot and estimated regression line of the carotene example ...
Figure 8.7 Scatter‐plot of the observations from Table 8.3 and the fitted func...
Figure 8.8 Scatter‐plot of the data and the fitted exponential function in the...
Figure 8.9 Fitted regression function of the example in Problem 8.28.
Figure 8.10 Fitted regression function of the example in Problem 8.32.
Figure 8.11 Graph of the triangle of the test of Example 8.7.
Chapter 9
Figure 9.1Figure 9.1 Scatter‐plot of the example in Problem 9.1 with M1 as 1, ...
Figure 9.2 Scatter‐plot with regression lines of the example in Problem 9.2.
Chapter 10
Figure 10.1 Relationship between the total experimental size
N
and
.
Chapter 11
Figure 11.1 Data fitted with the
lm-function
.
Figure 11.2 Data fitted with
glm-functions
.
Chapter 12
Figure 12.1 Exploratory spatial data analysis of dataset s100.
Figure 12.2 Exponential semi‐variogram model underlying the dataset s100.
Figure 12.3 Empirical directional variograms for dataset s100.
Figure 12.4 Variogram cloud and omnidirectional variogram of elevation data.
Figure 12.5 Empirical semi‐variogram (circles) and the fitted theoretical semi...
Figure 12.6 Predicted values and standard errors for s100.
Figure 12.7 Association between standard deviations and data locations.
Figure 12.8 Determining a 95% confidence interval for Box–Cox parameter.
Figure 12.9 Empirical and fitted semi‐variogram model for Meuse zinc data.
Figure 12.10 OK‐predicted values of zinc data (on a log‐scale).
Figure 12.11 OK variances of predicted zinc values.
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