1. SylabUZ
2. Faculty of Mathematics, Computer Science and Econometrics
3. winter term 2019/2020
4. Mathematics - First-cycle studies leading to Bachelor's degree
5. Practical Methods of Statistics

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Practical Methods of Statistics - course description

Aim of the course

Aim of the course is to familiarize students with different methods of statistical inference.

Prerequisites

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Mathematical analysis, probability theory and mathematical statistics.

Scope

Lecture
1. Statistical model. Sample space. The definition of random sample and statistics. Basic elements of estimation and hypothesis testing. (2 teaching hrs.)
2. Statistical inference concerning the mean and the variance of a normal distribution. (2)
3. Statistical inference concerning the probability of success in a binomial trials. (1)
4. Testing goodness of fit. (4)
5. Tests and confidence intervals for the difference in means of two normal populations (including a paired t-test). The F test to compare the variances of two samples from
normal populations. A test to compare the proportions (probabilities of success) in two groups. (4)
6. Analysis of variance. The 1-way classification and the 2-way classification. (4)
7. Rank methods. Rank tests for independence. The Spearman correlation coefficient and Kendall's coefficient. The Wilcoxon test. (5)
8. Analysis of nominal variables, (4)
9. Factor analysis. (4)

Laboratory
1. Statistical inference concerning the mean and the variance of a normal distribution. (2 teaching hrs.)
2. Point estimation, confidence intervals and tests for the probability of success in a binomial trials. (2)
3. Testing goodness of fit. (4)
4. Comparison the two populations ( including matched pair experiments). (4)
5. Analysis of variance. The 1-way classification. (2)

6. Test. (2)
7. Analysis of variance. The 2-way classification. (2)
8. Correlation between two variables. The Spearman correlation coefficient and Kendall's coefficient. (2)
9. The Wilcoxon test. (2)
10. Contingency table. Some measures of association: the Pearson coefficient, the Cramer coefficient and the Yula coefficient. Tests for independence. (4)
11. Factor analysis. (2)
12. Test. (2)

Teaching methods

Part of a lecture is presented on slides, and some in the traditional form (e.g. derivation of some results, proofs and examples). Laboratory - using the statistical package (e.g. Rproject) to analysis data.

Learning outcomes and methods of theirs verification

Outcome description	Outcome symbols	Methods of verification	The class form

Assignment conditions

1. Checking students prepare for class and their active participation in class.
2. Tests with the tasks of different difficulty.
3. Written exam with some questions, which verify knowledge of the theory and some questions, which verify skill to apply known methods of statistical inference.
The condition of taking part in the exam is a positive grade from laboratory (on receipt of at least 50% of the maximum sum of points from the written tests). To complete the course one has to obtain positive grade from exam. The course grade consists of a grade from laboratory (60%) and of a grade from exam (40%).

Recommended reading

1. P. J. Bickel, K.A. Doksum, Mathematical Statistics, Holden-Day, Inc. San Francisco, 1977.

2. J.L. Devore, Probability and Statistics for Engineering and the Sciences. Eighth Edition, Brooks/Cole, Cengage Learning Boston 2010. 

3. G.J. Kerns. Introduction to Probability and Statistics Using R. Kerns, G.J., 2010.

Further reading

1. T. Górecki, Podstawy statystyki z przykładami w R, Wydawnictwo BTC, Legionowo 2011.
2. M. Walesiak, E. Gatnar, Statystyczna analiza danych z wykorzystaniem programu R, Wydawnictwo Naukowe PWN, Warszawa 2009.
3. A. Zeliaś, Metody statystyczne, Polskie Wydawnictwo Ekonomiczne, Warszawa 2000.

Notes

Modified by dr Alina Szelecka (last modification: 03-07-2019 12:06)