Statistics WF-FI-KGN-ST
1.
Introduction to statistics and its role in cognitive research
– what statistics is and why it is important in cognitive science.
2.
Measurement scales and types of data
– nominal, ordinal, interval, ratio.
3.
Basic concepts: population, sample, parameter, statistic
– differences and why they matter in research.
4.
Descriptive statistics
– mean, median, mode, variance, standard deviation.
5.
Statistical distributions and probability
– normal distribution, law of large numbers, fundamentals of probability theory.
6.
Hypotheses and statistical inference
– null and alternative hypotheses, Type I and Type II errors, p-value.
7.
Parametric tests – Student’s t-test
– one-sample, dependent-samples, and independent-samples tests.
8.
Non-parametric tests – Mann–Whitney U test, Wilcoxon test
– when to use them instead of parametric tests.
9.
Analysis of variance (ANOVA) and non-parametric tests for variance
– basics of ANOVA, comparing more than two groups.
10.
Correlations
– Pearson’s and Spearman’s correlation coefficients, examples in cognitive research.
11.
Linear regression
– basics of predicting one variable based on another.
12.
Chi-square test and modeling
– examining relationships in qualitative data.
13.
Bayesian statistics
– differences between classical and Bayesian approaches, examples in psychology and AI.
14.
Statistics and artificial intelligence
– how AI uses statistical methods.
15.
Data visualization and reporting
– how to present results: charts, tables, standards (APA, publications).
(in Polish) E-Learning
(in Polish) Grupa przedmiotów ogólnouczenianych
(in Polish) Opis nakładu pracy studenta w ECTS
Subject level
Learning outcome code/codes
Type of subject
Course coordinators
Learning outcomes
KOG1_W03
at an advanced level, terminology from the field of formal sciences (logic and mathematics) applied in cognitive science
recognizes, defines, and applies basic statistical concepts (e.g., mean, variance, standard deviation, normal distribution),
explains and interprets the meaning of statistical terms in the context of psychological and cognitive research,
uses mathematical and statistical symbols and notation in data analysis.
KOG1_W13
at an advanced level, the subject-matter and methodological specificity of cognitive science, as well as the basic research methods and heuristic strategies appropriate for the main branches of cognitive science
analyzes, compares, and evaluates the results of statistical calculations used in cognitive and psychological research,
selects and applies appropriate statistical tests for specific research problems,
interprets and presents the results of quantitative analyses in the form of tables and charts.
Assessment criteria
For a grade of 3.0 (satisfactory)
• The student knows all the basic concepts from the course (e.g., hypothesis, variable, normal distribution, correlation, t-test, Mann–Whitney U test, chi-square).
• Can generally describe the purpose and principle of basic statistical tests (e.g., “the t-test checks the difference between means”).
• Understands the meaning of the null and alternative hypotheses at a descriptive level.
• Can read a simple chart/statistic and explain in very general terms what it shows.
For a grade of 3.5 (satisfactory plus)
• The student can correctly choose a simple test for a research situation (e.g., when to use a t-test and when to use a Mann–Whitney U test).
• Can indicate the basic assumptions of the most commonly used tests (e.g., normality of distribution, equality of variances).
• Can distinguish between types of variables (quantitative, qualitative, ordinal).
• Is able to indicate the limitations of the results (“this test shows a relationship but does not prove causation”).
For a grade of 4.0 (good)
• The student can explain in detail the principle of parametric and non-parametric tests and indicate the differences between them.
• Can interpret test results (e.g., p-value, significance level, effect size).
• Can discuss analysis of variance and provide examples of its application.
• Understands and can explain correlation and regression as tools for studying relationships between variables.
For a grade of 4.5 (good plus)
• The student can link methods to research questions – for example, can propose which test would be appropriate for a given research example in cognitive science.
• Can interpret complex results (e.g., interactions in analysis of variance, chi-square test results in multi-way tables).
• Demonstrates the ability for critical evaluation – for example, indicates the risk of Type I and Type II errors, or problems with test power.
• Understands the basics of Bayesian probability and can explain how it differs from the classical approach.
For a grade of 5.0 (very good)
• The student demonstrates full proficiency in the course content: knows all tests discussed in class, their assumptions, interpretations, and limitations.
• Can independently interpret research results presented in a scientific article, indicating correctness or errors in the analysis.
• Can integrate knowledge – for example, combine classical statistics with the application of artificial intelligence algorithms for data analysis.
• Can critically assess the significance of results for theory in cognitive science, not only focusing on “raw statistics.”
• Expresses themselves precisely in scientific language, demonstrating methodological maturity.
The student is allowed two absences from lectures that do not require justification. The basis for passing the course is a test – achieving 60% gives a satisfactory grade. For activity and participation in class discussions, the instructor reserves the right to award additional points on the exam.
Bibliography
King, Bruce M., & Minium, Edward W. (2020). Statystyka dla psychologów i pedagogów. Warszawa: Wydawnictwo Naukowe PWN.
Szymańska, A. (2025). Mathematical Modeling in Psychology Using Artificial Intelligence. Warsaw: UKSW Press.
Additional information
Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system: