Statistical Analysis and Processing of Experimental Data

Description: The course studies various methods for processing biomedical signals and data, including data representation techniques and statistical methods for analyzing experimental data. It examines the classification of multidimensional observations and pattern recognition tasks, providing a detailed overview of different recognition methods and their applications in automatic analysis of biomedical signals. Additionally, the course covers different classes of biomedical signals and their processing methods at various stages: preprocessing, digital filtering, pattern recognition, and syntactic classification of biosignals.

Amount of credits: 6

Course Workload:

Component: University component

Cycle: Profiling disciplines

Goal

• Developing skills in scientific processing of experimental data, analyzing them using statistical methods, assessing the reliability of the results, and applying them to practical problems.

Objective

• Teach methods of collecting, sorting, and grouping statistical data.
• Train students to calculate key statistical indicators describing experimental results (mean value, variance, standard deviation, etc.).
• Develop skills in presenting data using graphical and tabular methods.
• Enhance the ability to apply statistical methods for hypothesis testing.
• Teach techniques of correlation and regression analysis.
• Instruct on how to assess the accuracy, reliability, and error of experimental data.
• Develop skills in data processing using statistical software tools (Excel, SPSS, MATLAB, etc.).

Learning outcome: knowledge and understanding

• Knows the main theoretical concepts, methods, and principles of the discipline;
• Understands the key terms, methodology, and tools in the field of statistical analysis and experimental data processing;
• Recognizes their areas of application, advantages, and limitations;
• Is able to apply the acquired knowledge to solve specific practical tasks.

Learning outcome: applying knowledge and understanding

• Can apply the acquired knowledge and understanding in performing practical and laboratory tasks;
• Is able to apply statistical analysis methods to real data;
• Can adapt theoretical knowledge to practical situations and make decisions;
• Is capable of processing collected data and correctly interpreting the results of the analysis.

Learning outcome: formation of judgments

• Can form judgments based on collected data and analysis results;
• Is able to compare different perspectives and make scientifically grounded conclusions;
• Can critically evaluate evidence and arguments when making decisions;
• Is capable of choosing an appropriate position from the standpoint of ethics and professional responsibility.

Learning outcome: communicative abilities

• Can express ideas and analysis results clearly and understandably;
• Is able to engage in discussions in scientific and professional settings, providing well-founded arguments;
• Can work in a team and collaborate effectively with colleagues;
• Is capable of structuring and presenting complex information both orally and in written form.

Learning outcome: learning skills or learning abilities

• Can independently acquire new knowledge and skills;
• Develops the ability for self-learning through searching, analyzing, and selecting information sources;
• Learns to plan the learning process effectively and manage time;
• Engages in self-reflection, evaluating and improving professional development.

Teaching methods

Interactive lecture: guided discussion or conversation, moderation, presentation of slides or educational films, brainstorming, motivational speech.

Information and communication.

Search and research.

Solving learning tasks.

Assessment of the student's knowledge

Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.

The evaluating policy of learning outcomes by work type

Evaluation form

The student's final grade in the course is calculated on a 100 point grading scale, it includes:

• 40% of the examination result;
• 60% of current control result.

The final grade is calculated by the formula:

 

Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;

E is a digital equivalent of the exam grade.

Final alphabetical grade and its equivalent in points:

The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:

Topics of lectures

• Fundamentals of Statistical Analysis – The concept of statistics, its objectives, and its role in scientific research
• Types of Data and Data Collection Methods – Qualitative and quantitative data, methods of obtaining experimental data
• Systematization and Tabulation of Data – Grouping of data, presentation in the form of tables and charts
• Descriptive Statistics: Measures of Central Tendency – Concepts of mean, median, and mode, and their calculation
• Descriptive Statistics: Measures of Dispersion – Variance, standard deviation, coefficient of variation
• Graphical Representation of Data – Histogram, frequency polygon, box plot, and various types of charts
• Concept of Probability and Probability Distributions – Basic properties of probability, discrete and continuous distributions
• Normal Distribution and Its Properties – Gaussian curve, standard normal distribution, and its parameters
• Hypothesis Testing and Errors – Null and alternative hypotheses, Type I and Type II errors
• Confidence Intervals – Methods for calculating confidence intervals for parameters
• Correlation Analysis – Relationship between variables, correlation coefficient
• Fundamentals of Regression Analysis – Simple (single-factor) and multiple regression models
• Analysis of Variance (ANOVA) – A method for evaluating the significance of differences between group means
• Statistical Processing of Experimental Results – Steps of data analysis and interpretation:
• Presentation of Statistical Analysis Results – Formatting tables and charts, preparing a report and presentation

Key reading

• Aitgaliyeva A.S. Fundamentals of Statistics. – Almaty: Economics, 2020.
• Smagulova Zh.K. Statistical Analysis and Econometrics. – Astana: Foliant, 2021.
• Kaliyeva S.M. Methods of Experimental Data Processing. – Almaty: Kazakh University, 2019.
• Tileugabylova S.K. Statistical Calculations (in Excel and SPSS Environment). – Nur-Sultan: Foliant, 2021.
• Aikynbayev K. Fundamentals of Mathematical Statistics. – Almaty: Kazakh University, 2017.

Further reading

• 1. Montgomery, D.C., Runger, G.C. Applied Statistics and Probability for Engineers. – Wiley, 2022.
• 2. Walpole, R.E., Myers, R.H. Probability and Statistics for Engineers and Scientists. – Pearson, 2021.
• 3. Chatfield, C. The Analysis of Time Series: An Introduction. – CRC Press, 2020.
• 4.Devore, J. Probability and Statistics for Engineering and the Sciences. – Cengage, 2021.