Veidlapa Nr. M-3 (8)
Study Course Description
Statistical Inference
Course Code
SL_106
Branch of Science
Mathematics; Theory of probability and mathematical statistics
ECTS
6.00
Target Audience
Life Science
LQF
Level 7
Study Type And Form
Full-Time; Part-Time
Study Course Implementer
Course Supervisor
Jeļena Perevozčikova
Structure Unit Manager
Andrejs Ivanovs
Structural Unit
Statistics Unit
Contacts
14 Baložu street, Riga, statistika@rsu.lv, +371 67060897
About Study Course
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.
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.
Learning Outcomes
Knowledge
1.• 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
1.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.
Competences
1.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.
Assessment
Individual work
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Individual 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.
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Examination
|
Title
|
% from total grade
|
Grade
|
|---|---|---|
|
1.
Examination |
-
|
-
|
|
Assessment on the 10-point scale according to the RSU Educational Order:
• Practical tasks in R – 50%.
• Final written exam – 50%.
|
||
Study Course Theme Plan
FULL-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Basic concepts of mathematical statistics. Statistical population, random sample and its characteristics.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Simulated and built-in datasets in R. Different datasets including common biostatistical data and different statistical tasks to be discussed.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Descriptive statistics.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Histogram, empirical distribution function, boxplot, quantile-quantile plot and other descriptive statistics for different types of data and problems in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Parameter estimation. Maximum likelihood function.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Parameter estimation. Maximum likelihood function.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Parameter estimation for different distributions in R.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Parameter estimation for different distributions in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Sampling distributions and confidence intervals.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Sampling distributions and confidence intervals in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Basics of hypothesis testing. T-test for the mean.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
T-test statistic, critical and acceptance regions, p-value calculation for both one sided and two-sided hypothesis cases. Power simulations in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Statistical inference for different problems in one and two-sample cases: binomial test, two-sample variance test, paired and unpaired t-tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Different statistical tests for one and two-sample inference in program R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Contingency tables and chi-squared tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Contingency tables and chi-squared tests in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Kolmogorov-Smirnov and other goodness-of-fit tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Goodness-of-fit tests in R for simple and composite hypothesis.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Association, dependence and correlation measures for both quantitative and qualitative data. Statistical tests for independence.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Correlation coefficients and independence tests in program R for different simulated and real datasets.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
One-way ANOVA method.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
ANOVA in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
2
|
Topics
|
Simple linear regression.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Simple linear regression in R.
|
Total ECTS (Creditpoints):
6.00
Contact hours:
48 Academic Hours
Final Examination:
Exam (Written)
PART-TIME
Part 1
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Basic concepts of mathematical statistics. Statistical population, random sample and its characteristics.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Simulated and built-in datasets in R. Different datasets including common biostatistical data and different statistical tasks to be discussed.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Descriptive statistics.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Histogram, empirical distribution function, boxplot, quantile-quantile plot and other descriptive statistics for different types of data and problems in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Parameter estimation. Maximum likelihood function.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Parameter estimation. Maximum likelihood function.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Parameter estimation for different distributions in R.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Parameter estimation for different distributions in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Sampling distributions and confidence intervals.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Sampling distributions and confidence intervals in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Basics of hypothesis testing. T-test for the mean.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
T-test statistic, critical and acceptance regions, p-value calculation for both one sided and two-sided hypothesis cases. Power simulations in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
1
|
Topics
|
Statistical inference for different problems in one and two-sample cases: binomial test, two-sample variance test, paired and unpaired t-tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Different statistical tests for one and two-sample inference in program R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Contingency tables and chi-squared tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Contingency tables and chi-squared tests in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Kolmogorov-Smirnov and other goodness-of-fit tests.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Goodness-of-fit tests in R for simple and composite hypothesis.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Association, dependence and correlation measures for both quantitative and qualitative data. Statistical tests for independence.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Correlation coefficients and independence tests in program R for different simulated and real datasets.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
One-way ANOVA method.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
ANOVA in R.
|
-
Lecture
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Auditorium
|
1
|
Topics
|
Simple linear regression.
|
-
Class/Seminar
|
Modality
|
Location
|
Contact hours
|
|---|---|---|
|
On site
|
Computer room
|
2
|
Topics
|
Simple linear regression in R.
|
Total ECTS (Creditpoints):
6.00
Contact hours:
36 Academic Hours
Final Examination:
Exam (Written)
Bibliography
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.