Statistics in Psychology 2 2404-P-2-SP-sj

1. The Student’s t-test for repeated measurements — terminology (factor, dependent variable). Assumptions of the test, i.e. what data may be used.
The test statistic and its form. How the value of the test statistic is calculated. What is the distribution of the test statistic? Cohen’s d effect size for a two-group design.

2. Analysis of variance (ANOVA).
• Basic concepts of ANOVA: factor (independent variable) and dependent variable; factor levels and experimental groups.
• Assumptions of ANOVA: discussion of the conditions for the applicability of ANOVA (normality of distributions within groups, homogeneity of variances, independence of observations).
• The F-test in analysis of variance: the concept of comparing between-group and within-group variability; the construction of the F-test statistic – sums of squares, the distribution of the F-test statistic (Snedecor’s F-distribution) and the interpretation of its value obtained in the analysis.
• Degrees of freedom: interpretation of the number of degrees of freedom in the numerator and denominator of the F-test and their relationship to the number of groups and observations.
• Effect size (η² – eta squared): method of calculation and interpretation; Cohen’s interpretation thresholds (small, medium, large effect).
• Post-hoc tests: the significance of post-hoc tests in analysis of variance; pairwise comparisons; interpretation and reporting of effect sizes for post-hoc tests.
- Introduction to two-way analysis of variance: the concept of factor interaction; the principle behind the construction of the F-test statistic

3. Simple and multiple linear regression.
The relationship between correlation and regression analysis. The difference between them. Assumptions of the regression model – which variables can we use? What relationship should link them?
Simple (univariate) regression analysis. Terminology – regression; dependent variable and independent variable; predictor; explained variable, explanatory variable; linear combination; regression residuals; notation for predicted values. What does prediction involve? How is this done using the regression formula? Interpretation of regression coefficients, standardised and unstandardised. Regression analysis as a statistical model – model assumptions, regression coefficients (interpretation). Reporting regression results in accordance with APA guidelines. Diagnosis of the regression model – What should follow a normal distribution? The dependent variable, the independent variable, or something else? Adjusted R-squared, explained variance, tests of statistical significance for regression coefficients.

4. Exploratory factor analysis
Terminology. What are observable variables, and what are latent variables? Factor extraction methods. Correlation matrix and spherical matrix. Testing assumptions: Bartlett’s test. KMO measure. Determinant of the correlation matrix – what number can the determinant of the matrix be? What does the ‘E’ in the notation below the correlation matrix table mean? Eigenvalues of the correlation matrix – what number can an eigenvalue be? Scatter plot – structure (what is on the horizontal axis and what is on the vertical axis). What does a scatter plot look like, and what should it not look like? Criteria for determining the number of factors (based on the percentage of explained variance, the Catell criterion/scatter plot and the Kaiser criterion). Factor rotation – what is the purpose of rotation and what types are there? Factor loadings and cross-loadings – their interpretation and the selection of questionnaire items for the final version.

6. Power analysis – what is it and what is it used for? Type I and Type II errors, effect size and sample size – the relationships between them. The dependence of test power on effect size and sample size. The ‘winner’s curse’ and ‘overpowered studies’, and their implications for scientific literature.

9. Normality tests available in SPSS: the Kolmogorov–Smirnov test and the Shapiro–Wilk test.
• classification of normality tests;
• the null hypothesis and the alternative hypothesis
• construction and interpretation of test statistics for the K-S and S-W tests,
• limitations of normality tests: the influence of sample size on the results of these tests.