Foundations of Descriptive and Inferential Statistics

2013/02/11 by Henk van Elst
Computer Science · Decision Sciences · Mathematics · #Artificial intelligence #Bayesian Modeling and Causal Inference #Bayesian inference #Bayesian probability #Computer science #Data science #Decision-Making and Behavioral Economics #Descriptive statistics #Forecasting Techniques and Applications #Frequentist inference #Mathematics #Null hypothesis #Population #Raw data #Relevance (law) #Sociology #Statistical hypothesis testing #Statistical inference #Statistics #stat.AP #stat.OT

paper · pdf · doi:10.13140/rg.2.1.2112.3044

176 pages, 25 *.eps figures, LaTeX2e, hyperlinked references. Third thorough revision, further extended list of references, inclusion of relevant R commands

openalex publication_date 2013/02/11 · openalex created_date 2016/06/24 · arxiv created 2019/08/30 · arxiv updated 2019/09/02 · openalex updated_date 2026/08/05

Abstract

These lecture notes were written with the aim to provide an accessible though technically solid introduction to the logic of systematical analyses of statistical data to both undergraduate and postgraduate students, in particular in the Social Sciences, Economics, and the Financial Services. They may also serve as a general reference for the application of quantitative--empirical research methods. In an attempt to encourage the adoption of an interdisciplinary perspective on quantitative problems arising in practice, the notes cover the four broad topics (i) descriptive statistical processing of raw data, (ii) elementary probability theory, (iii) the operationalisation of one-dimensional latent statistical variables according to Likert's widely used scaling approach, and (iv) null hypothesis significance testing within the frequentist approach to probability theory concerning (a) distributional differences of variables between subgroups of a target population, and (b) statistical associations between two variables. The relevance of effect sizes for making inferences is emphasised. These lecture notes are fully hyperlinked, thus providing a direct route to original scientific papers as well as to interesting biographical information. They also list many commands for running statistical functions and data analysis routines in the software packages R, SPSS, EXCEL and OpenOffice. The immediate involvement in actual data analysis practices is strongly recommended.

Citations

• Methods of Measuring the Concentration of Wealth
• On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other
• On the stochasticity in relativistic cosmology
• THE LAW OF ANCESTRAL HEREDITY
• The cosmological billiard attractor
• X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling
• A power primer.
• Use of Ranks in One-Criterion Variance Analysis
• On the Theory of Scales of Measurement
• The Probable Error of a Mean
• Comparing measures of sample skewness and kurtosis
• The Proof and Measurement of Association between Two Things
• Coefficient Alpha and the Internal Structure of Tests
• Extensional versus intuitive reasoning: The conjunction fallacy in probability judgment.
• LIII. On lines and planes of closest fit to systems of points in space
• XV.—The Correlation between Relatives on the Supposition of Mendelian Inheritance.
• Measurement of Inequality of Incomes
• On the Theory of Correlation
• Regression Towards Mediocrity in Hereditary Stature.