Introduction to Statistical Thinking is targeted at
college students who are required to learn statistics, students with
little background in mathematics and often no motivation to learn more.
This book uses the basic structure of generic introduction to
statistics course.
Chapters cover:
Short introduction to statistics and probability
Data structures and variation
Provides numerical and graphical tools for presenting
and summarizing the distribution of data
Fundamentals of probability: Concept of a random
variable, Examples of special types of random variables, Normal random
variable, Sampling distribution and presents the Central Limit Theorem
and the Law of Large Numbers
Discussion of statistical inference. It provides an
overview of the topics that are presented in the subsequent chapter.
Basic tools of statistical inference, namely point
estimation, estimation with a confidence interval, and the testing of
statistical hypothesis
Discusses inference that involve the comparison of
two measurements
Analysis of two case studies
Large portions of this book are based on material from
the online book "Collaborative Statistics" by Barbara Illowsky
and Susan Dean.
The content of this book is licensed under
the conditions of the Creative Commons Attribution License
(CC-BY 3.0).
The objective of Multivariate Statistics with R is to
cover a basic core of multivariate material in such a way that the core
mathematical principles are covered, and to provide access to current
applications and developments.
The author notes that numerous multivariate statistics
books, but this book emphasises the applications (and
introduces contemporary applications) with a little more mathematical
detail than happens in many such "application/software" based books.
Chapters cover:
Multivariate data including graphical and dynamic
graphical methods (Chernoff's Faces, scatterplots, 3d scatterplots, and
other methods), animated exploration
Matrix manipulation: Vectors, Matrices, Crossproduct
matrix, Matrix inversion, Eigen values and eigen vectors, Singular
Value Decomposition, Extended Cauchy-Schwarz Inequality, and
Partitioning
Measures of distance: Mahalanobis Distance,
Definitions, Distance between points, Quantitative variables - Interval
scaled, Distance between variables, Quantitative variables: Ratio
Scaled, Dichotomous data, Qualitative variables, Different variables,
Properties of proximity matrices
Multidimensional scaling: Metric Scaling, Visualising
multivariate distance, Assessing the quality of fit
Multivariate normality: Exceptations and moments of
continuous random functions, Multivariate normality (including R
estimation), Transformations
Inference for the mean: Two sample Hotellin's T2
test, Constant Density Ellipses, Multivariate Analysis of Variance
Discriminant analysis: Fisher discrimination,
Accuracy of discrimination, Importance of variables in discrimination,
Canonical discriminant functions, Linear discrimation
Principal component analysis: Derivation of Principal
Components, Some properties of principal components, Ilustration of
Principal Components, Principal Components Regression, "Model"
criticism for principal components analysis, Sphericity, How many
components to retain, Intrepreting the principal components
Canonical Correlation: Canonical variates,
Interpretation, Computer example
Factor analysis: Role of factor analysis, The factor
analysis model, Principal component extraction, Maximum likelihood
solutions, Rotation, Factor scoring
The content in this book is licensed under a Gnu Free
Documentation Licence.
Little Book of R for Biomedical Statistics is a simple
introduction to biomedical statistics using the R statistics software.
This booklet tells you how to use the R software to
carry out some simple analyses that are common in biomedical
statistics. In particular, the focus is on cohort and case-control
studies that aim to test whether particular factors are associated with
disease, randomised trials, and meta-analysis.
This booklet assumes that the reader has some basic knowledge of
biomedical statistics, and the principal focus
of the booklet is not to explain biomedical statistics analyses, but
rather to explain how to carry out these analyses
using R.
The booklet examines:
Calculating Relative Risks for a Cohort Study
Calculating Odds Ratios for a Cohort or Case-Control
Study
Testing for an Association Between Disease and
Exposure, in a Cohort or Case-Control Study
Calculating the (Mantel-Haenszel) Odds Ratio when
there is a Stratifying Variable
Testing for an Association Between Exposure and
Disease in a Matched Case-Control Study
Dose-response analysis
Calculating the Sample Size Required for a Randomised
Control Trial
Calculating the Power of a Randomised Control Trial
Making a Forest Plot for a Meta-analysis of Several
Different Randomised Control Trials
The content in this book is licensed under a Creative
Commons Attribution 3.0 License.
