Statistical Inference

Study Course Description

Course Description Statuss:Approved

Course Description Version:5.00

Study Course Accepted:14.03.2024 11:43:10

Study Course Information
Course Code:		SL_106		LQF level:		Level 7
Credit Points:		4.00		ECTS:		6.00
Branch of Science:		Mathematics; Theory of Probability and Mathematical Statistics		Target Audience:		Life Science
Study Course Supervisor
Course Supervisor:		Jeļena Perevozčikova
Study Course Implementer
Structural Unit:		Statistics Unit
The Head of Structural Unit:
Contacts:		14 Baložu street, Riga, statistikarsu[pnkts]lv, +371 67060897
Study Course Planning
Full-Time - Semester No.1
Lectures (count)		12	Lecture Length (academic hours)		2	Total Contact Hours of Lectures		24
Classes (count)		12	Class Length (academic hours)		2	Total Contact Hours of Classes		24
Total Contact Hours								48
Part-Time - Semester No.1
Lectures (count)		12	Lecture Length (academic hours)		1	Total Contact Hours of Lectures		12
Classes (count)		12	Class Length (academic hours)		2	Total Contact Hours of Classes		24
Total Contact Hours								36
Study course description
Preliminary Knowledge:
1) Familiarity with probability theory. 2) Basic knowledge in R is required, as the software package R will be used for computation and case study applications.
Objective:
This course introduces students with the basics of mathematical statistics. It covers the classical methods of mathematical statistics. Students will learn how to distinguish between different data structures and how to apply descriptive statistical methods. They will learn how to estimate the central tendency, variance and other parameters of interest. For biostatistical applications when several samples have to be compared statistical testing procedures are of great importance. At the end of this course students will know how to apply such testing procedures, how to make power analysis to determine the necessary sample size in practical applications. Finally, it is important to analyse the association between different variables and perform more precise dependence analysis using regression analysis which will also be covered in this course.
Topic Layout (Full-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Basic concepts of mathematical statistics. Statistical population, random sample and its characteristics.			Lectures		1.00	auditorium
2	Simulated and built-in datasets in R. Different datasets including common biostatistical data and different statistical tasks to be discussed.			Classes		1.00	computer room
3	Descriptive statistics.			Lectures		1.00	auditorium
4	Histogram, empirical distribution function, boxplot, quantile-quantile plot and other descriptive statistics for different types of data and problems in R.			Classes		1.00	computer room
5	Parameter estimation. Maximum likelihood function.			Lectures		2.00	auditorium
6	Parameter estimation for different distributions in R.			Classes		2.00	computer room
7	Sampling distributions and confidence intervals.			Lectures		1.00	auditorium
8	Sampling distributions and confidence intervals in R.			Classes		1.00	computer room
9	Basics of hypothesis testing. T-test for the mean.			Lectures		1.00	auditorium
10	T-test statistic, critical and acceptance regions, p-value calculation for both one sided and two-sided hypothesis cases. Power simulations in R.			Classes		1.00	computer room
11	Statistical inference for different problems in one and two-sample cases: binomial test, two-sample variance test, paired and unpaired t-tests.			Lectures		1.00	auditorium
12	Different statistical tests for one and two-sample inference in program R.			Classes		1.00	computer room
13	Contingency tables and chi-squared tests.			Lectures		1.00	auditorium
14	Contingency tables and chi-squared tests in R.			Classes		1.00	computer room
15	Kolmogorov-Smirnov and other goodness-of-fit tests.			Lectures		1.00	auditorium
16	Goodness-of-fit tests in R for simple and composite hypothesis.			Classes		1.00	computer room
17	Association, dependence and correlation measures for both quantitative and qualitative data. Statistical tests for independence.			Lectures		1.00	auditorium
18	Correlation coefficients and independence tests in program R for different simulated and real datasets.			Classes		1.00	computer room
19	One-way ANOVA method.			Lectures		1.00	auditorium
20	ANOVA in R.			Classes		1.00	computer room
21	Simple linear regression.			Lectures		1.00	auditorium
22	Simple linear regression in R.			Classes		1.00	computer room
Topic Layout (Part-Time)
No.	Topic			Type of Implementation		Number	Venue
1	Basic concepts of mathematical statistics. Statistical population, random sample and its characteristics.			Lectures		1.00	auditorium
2	Simulated and built-in datasets in R. Different datasets including common biostatistical data and different statistical tasks to be discussed.			Classes		1.00	computer room
3	Descriptive statistics.			Lectures		1.00	auditorium
4	Histogram, empirical distribution function, boxplot, quantile-quantile plot and other descriptive statistics for different types of data and problems in R.			Classes		1.00	computer room
5	Parameter estimation. Maximum likelihood function.			Lectures		2.00	auditorium
6	Parameter estimation for different distributions in R.			Classes		2.00	computer room
7	Sampling distributions and confidence intervals.			Lectures		1.00	auditorium
8	Sampling distributions and confidence intervals in R.			Classes		1.00	computer room
9	Basics of hypothesis testing. T-test for the mean.			Lectures		1.00	auditorium
10	T-test statistic, critical and acceptance regions, p-value calculation for both one sided and two-sided hypothesis cases. Power simulations in R.			Classes		1.00	computer room
11	Statistical inference for different problems in one and two-sample cases: binomial test, two-sample variance test, paired and unpaired t-tests.			Lectures		1.00	computer room
12	Different statistical tests for one and two-sample inference in program R.			Classes		1.00	computer room
13	Contingency tables and chi-squared tests.			Lectures		1.00	auditorium
14	Contingency tables and chi-squared tests in R.			Classes		1.00	computer room
15	Kolmogorov-Smirnov and other goodness-of-fit tests.			Lectures		1.00	auditorium
16	Goodness-of-fit tests in R for simple and composite hypothesis.			Classes		1.00	computer room
17	Association, dependence and correlation measures for both quantitative and qualitative data. Statistical tests for independence.			Lectures		1.00	auditorium
18	Correlation coefficients and independence tests in program R for different simulated and real datasets.			Classes		1.00	computer room
19	One-way ANOVA method.			Lectures		1.00	auditorium
20	ANOVA in R.			Classes		1.00	computer room
21	Simple linear regression.			Lectures		1.00	auditorium
22	Simple linear regression in R.			Classes		1.00	computer room
Assessment
Unaided Work:
1) Review of the literature in preparation to each lecture according to course plan. 2) Practical tasks will be assigned. Students will receive prepared data file with defined tasks. Student will need to statistically process the data. In order to evaluate the quality of the study course as a whole, the student must fill out the study course evaluation questionnaire on the Student Portal.
Assessment Criteria:
Assessment on the 10-point scale according to the RSU Educational Order: • Practical tasks in R – 50%. • Final written exam – 50%.
Final Examination (Full-Time):		Exam (Written)
Final Examination (Part-Time):		Exam (Written)
Learning Outcomes
Knowledge:		• demonstrate extended knowledge of concepts and procedures in the collection, organisation, presentation and analysis of data; • describe fundamental techniques for statistical inference; • recognize and independently applied the main libraries and tools for statistical analysis in program R.
Skills:		Students will be able independently: • to input and prepare data for further statistical analysis in program R; • use specific significance tests including, z-test t-test (one and two sample), chi-squared test and different goodness-of-fit tests in program R; • find confidence intervals for parameter estimates in program R; • do correlation analysis, ANOVA and compute and interpret simple linear regression between two and more variables in program R.
Competencies:		Students will be competent: • to evaluate and choose the appropriate statistical methods and tools and construct a statistical model describing a problem based on different, also non-standard real-life situations; • to choose independently, perform, and interpret a statistical procedure that answers a given statistical problem; • to present a statistical analysis in a technical report; • to independently use a computational program for simulation and interpretation of statistical models, as well as for data analysis.
Bibliography
No.	Reference
Required Reading
1	Agresti, A., Franklin, C. A. Statistics: The Art and Science of Learning from Data (3rd ed.). Pearson Education, 2013.
Additional Reading
1	Bain, L. J., & Engelhardt, M. Introduction to probability and mathematical statistics. Cengage Learning, (2nd ed.), 2000.
2	Pagano, Marcello, and Kimberlee Gauvreau. Principles of biostatistics. Chapman and Hall/CRC, 2018.
3	Logan, Murray. Biostatistical design and analysis using R: a practical guide. John Wiley & Sons, 2011.
4	Casella, George, and Roger L. Berger. Statistical inference. Vol. 2. Pacific Grove, CA: Duxbury, 2002.