# Courses: Course information

Professionelle Videokamera im Studio des Multimediazentrums der Universität Jena
Foto: Jan-Peter Kasper/FSU
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
1. Why probability and inferential statistics?
2. Random experiment and probability space
3. Set of (all possible) outcomes
4. Set of (all possible) events, σ-algebra
5. Probability measure
Video (Stream)

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
1. Rules of computation for probabilities
2. Example: Joe and Ann, some events and their probabilities
3. Conditional probability
4. Multiplication rule
Video (Stream)

Slides
(updated 2016-04-15)

Blackboard sketches
2016-04-18
1. Theorem of Total Probability and Bayes Theorem
2. Independence of events
3. Independence of sets of events
4. Conditional-probability measure
5. First ideas about random variables
6. Image and inverse image of a set under a mapping
7. Events represented by a random variable
Video (Stream)

Slides

Blackboard sketches
2016-04-25
1. Random variable
2. Sigma-algebra generated by a random variable
3. Sigma-algebra generated by a set system
4. Borel sigma-algebra
5. Real-valued random variable
6. Numerical random variable
7. Independence of two random variables
Video (Stream)

Blackboard sketches
2016-05-02
1. Independence of n random variables
2. Joe-Ann example with self-selection
3. Distribution of a random variable
4. The distribution as a new probability measure
5. Distribution function of a real-valued random variable
6. Discrete random variable and its probability function
7. Example: Indicator variable and its distribution
8. Example: binomial distribution
Video (Stream)

Slides
(updated 2016-05-12)

Blackboard sketches
2016-05-09
1. Continuous random variable and its density
2. Density of the normal distribution
3. Expectation of a discrete random variable
4. Expectation: General definition
5. Expectation and mean squared error
6. Transformation Theorem
7. Variance and standard deviation
8. Covariance and correlation
9. Independence and covariance
10. Rules of computation for expectations
11. Expectation of a binomially distributed random variable
Video (Stream)

Slides
(updated 2016-05-24)

Blackboard sketches
2016-05-23
1. Implications of independence on covariance and correlation
2. Rules of computation for expectations
3. Example: Expectation of a binomially distributed random variable
4. Rules of computation for variances
5. Example: Variance of an indicator variable
6. Example: Variance of a binomially distributed random variable
7. Rules of computation for covariances
8. Linear quasi-regression
9. Conditional expectation value
Video (Stream)

Blackboard sketches
2016-05-30
1. Definition of a sample
2. Estimator (a random variable) and estimate (its value)
3. Expectation of a sample mean
4. Expectation of a sample variance
5. Variance of a sample mean
6. Standard (deviation) error of a sample mean
7. Unbiased estimator of the variance
8. An estimator of the standard error of a sample mean
Video (Stream)

Slides

Blackboard sketches
2016-06-06
1. Standard error of the sample mean: Example using the binomial distribution
2. Summary of the most important concept concerning sample and estimator
3. Examples for hypotheses in significance tests
4. Test statistic in significance tests
5. Basic idea of a significance test
6. Example of a one-sided significance test
7. Null hypothesis and alternative hypothesis
8. Example of a two-sided significance test
9. Area of rejection and area of non-rejection
Video (Stream)

Slides
(updated 2016-06-14)

Blackboard sketch 01
Blackboard sketch 02
2016-06-13
1. Error of type I and II in significance testing
2. Error probabilities alpha and beta
3. Power of a test
4. How to decrease these error probabilities
5. Illustrating alpha- and beta-error probabilities by a normally distributed test statistic
6. Density of the normal distribution
7. R-Programs related to the normal distribution
Video (Stream)

Slides

Blackboard sketch
2016-06-20
1. Density of the chi-square distribution and R-programs
2. Density of the t-distribution and R-programs
3. Density of the F-distribution and R-programs
Video (Stream)

Blackboard sketches
2016-06-27
1. Confidence interval
2. Central limit theorem
Video (Stream)

Slides
Materials

Blackboard sketch
2016-07-04 Video (Stream)

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.
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