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Probability and Fundamentals of Inferential Statistics

Speakers: Prof. Dr. Rolf Steyer

Summer term 2016, Course, Language: English, Topic: Introduction to statistics for psychologists

This lecture is a first course in probability and inferential statistics. In the first part fundamental concepts of probability theory and their applications in empirical sciences are treated. The second part deals with the basic ideas of statistical inference.

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Date	Topic	Video	Material
2016-04-04	Why probability and inferential statistics? Random experiment and probability space Set of (all possible) outcomes Set of (all possible) events, σ-algebra Probability measure	Video (Stream) Video (Download; VLC Player)	Slides Probability and Conditional Expectation - Steyer, R., & Eid, M. (2013). Messen und Testen. Berlin: Springer. (Anhänge: Mathematische Grundbegriffe, Mengen und Mengenoperationen, Relationen und Relative, Abbildungen und Homomorphismen) Blackboard sketch 01 Blackboard sketch 02
2016-04-11	Rules of computation for probabilities Example: Joe and Ann, some events and their probabilities Conditional probability Multiplication rule	Video (Stream) Video (Download; VLC Player)	Slides (updated 2016-04-15) Blackboard sketches
2016-04-18	Theorem of Total Probability and Bayes Theorem Independence of events Independence of sets of events Conditional-probability measure First ideas about random variables Image and inverse image of a set under a mapping Events represented by a random variable	Video (Stream) Video (Download; VLC Player)	Slides Blackboard sketches
2016-04-25	Random variable Sigma-algebra generated by a random variable Sigma-algebra generated by a set system Borel sigma-algebra Real-valued random variable Numerical random variable Independence of two random variables	Video (Stream) Video (Download; VLC Player)	Blackboard sketches
2016-05-02	Independence of n random variables Joe-Ann example with self-selection Distribution of a random variable The distribution as a new probability measure Distribution function of a real-valued random variable Discrete random variable and its probability function Example: Indicator variable and its distribution Example: binomial distribution	Video (Stream) Video (Download; VLC Player)	Slides (updated 2016-05-12) Blackboard sketches
2016-05-09	Continuous random variable and its density Density of the normal distribution Expectation of a discrete random variable Expectation: General definition Expectation and mean squared error Transformation Theorem Variance and standard deviation Covariance and correlation Independence and covariance Rules of computation for expectations Expectation of a binomially distributed random variable	Video (Stream) Video (Download; VLC Player)	Slides (updated 2016-05-24) Blackboard sketches
2016-05-23	Implications of independence on covariance and correlation Rules of computation for expectations Example: Expectation of a binomially distributed random variable Rules of computation for variances Example: Variance of an indicator variable Example: Variance of a binomially distributed random variable Rules of computation for covariances Linear quasi-regression Conditional expectation value	Video (Stream) Video (Download; VLC Player)	Blackboard sketches
2016-05-30	Definition of a sample Estimator (a random variable) and estimate (its value) Expectation of a sample mean Expectation of a sample variance Variance of a sample mean Standard (deviation) error of a sample mean Unbiased estimator of the variance An estimator of the standard error of a sample mean	Video (Stream) Video (Download; VLC Player)	Slides Blackboard sketches
2016-06-06	Standard error of the sample mean: Example using the binomial distribution Summary of the most important concept concerning sample and estimator Examples for hypotheses in significance tests Test statistic in significance tests Basic idea of a significance test Example of a one-sided significance test Null hypothesis and alternative hypothesis Example of a two-sided significance test Area of rejection and area of non-rejection	Video (Stream) Video (Download; VLC Player)	Slides (updated 2016-06-14) Blackboard sketch 01 Blackboard sketch 02
2016-06-13	Error of type I and II in significance testing Error probabilities alpha and beta Power of a test How to decrease these error probabilities Illustrating alpha- and beta-error probabilities by a normally distributed test statistic Density of the normal distribution R-Programs related to the normal distribution	Video (Stream) Video (Download; VLC Player)	Slides Blackboard sketch
2016-06-20	Density of the chi-square distribution and R-programs Density of the t-distribution and R-programs Density of the F-distribution and R-programs	Video (Stream) Video (Download; VLC Player)	Blackboard sketches
2016-06-27	Confidence interval Central limit theorem	Video (Stream) Video (Download; VLC Player)	Slides Materials Blackboard sketch
2016-07-04		Video (Stream) Video (Download; VLC Player)	Blackboard sketches

Software

Tutorial SPSSinteraktiv (german)
To the tipps & tools-website with R (german)

Literature

Eid, M., Gollwitzer, M. & Schmitt, M. (2005). Statistik und Forschungsmethoden. Weinheim: Beltz.
Hays, W. L. (1994). Statistics. Fort Worth, TX: Harcourt Brace College Publishers.
Holling, H. & Gediga, G. (2013). Statistik: Wahrscheinlichkeitstheorie und Schätzverfahren. Göttingen: Hogrefe.
Müller, P. H. (Hrsg.) (1975). Lexikon der Stochastik. Berlin: Akademie-Verlag.
Sachs, L. & Hedderich, J. (2006). Angewandte Statistik. Methodensammlung mit R. Berlin: Springer.
Steyer, R. (2003). Wahrscheinlichkeit und Regression. Berlin: Springer.
Steyer. R. and Nagel, W. (2017). Probability and conditional expectation: Fundamentals for the empirical sciences. Chichester: Wiley.
Walz, G. (2004). Lexikon der Statistik. München: Elsevier.