Statistics in Psychology 1 2404-P-1-SP-sj

Table of topics.
1. Introduction - what is statistics, basic concepts of statistics.
Parameter and statistics, sample and population; What is a parameter and what is a (descriptive) statistic? What symbols correspond to the parameter and statistics?

2. type of variables: measurement scales according to S. Stevens, properties, examples, division of variables into quantitative/qualitative and mathematical (continuous/discrete). Relative and absolute zero, examples. Stanley Stevens' five big questions. Does a given variable correspond to only one measurement scale? Is every variable with two categories unambiguously nominal? Discretization and extrapolation - is it possible to change the nature of the variable or measurement? Can a variable be continuous, but in measurement be as nominal?

3. distribution of the value of a variable - what is it? Distribution in the sample and in the population (nomenclature: empirical and theoretical). Why do theoretical and empirical distributions differ? Why do the results in the sample differ from those in the population? What is the density of a distribution? Standardization of the distribution and its consequences.

4. Descriptive statistics for one sample and for two - measures of central tendency, dispersion, skewness and kurtosis and their properties. How to calculate measures of central tendency and measures of dispersion? Formula for standard deviation; relationship between standard deviation and variance. Description of the distribution on the basis of descriptive statistics and diagnostics for normality. Classical and positional measures. Quantiles, quartiles and percentiles. Contingency table - obtained and expected counts (what is expected, when expected). The chi-square statistic and what it means. Correlation coefficients for two quantitative and qualitative variables - their characteristics.

Z-score (z-score) - what is it? How it is calculated and interpreted.

Mean - the average in the sample and the average in the population. Confidence interval for the mean, interpretation and calculation (the final formula, which includes the arithmetic mean, quantile and standard error, sum of squares), standard error - what does the standard error say? Relationship of standard error and sample size.

5. Graphs - construction, what does it represent, advantages and disadvantages. Bar graph - what is shown by the width of the bar and what is shown by the height. Can the height of the bars change in a bar graph? Histogram - what is indicated by the width of the bar, and what is the height. Can the shape of a histogram, such as the height of rectangles, change - what does it depend on? Boxplot - what is the source of inspiration for this graph? QQplot - what does it represent, what can it be used for. Diagnosis of normality of distribution based on graphical tools. Pie chart.

6. Normal distribution - what is it, what is the notation, what are its properties, what does it mean that the distribution is parameterized? Range of typical values of a variable. Rule of three sigma. Z-scores (z-scores) - calculation and interpretation.
DIAGNOSTICS OF NORMALITY - what are the tools? Dependence on sample size.

7. Probability - classical (i.e., frequency) and Bayesian definition of the concept of probability. Two properties of density.

8. sampling distribution - what is it? Central limit theorem - how does it work? Is n = 30 sufficient, and if so, when?

9. theory of estimators - what does it mean that the estimator is unconstrained, minimum variance and consistent? Confidence interval for the mean - calculation and interpretation.

10. Correlation analysis (different coefficients) - Null hypothesis; alternative hypothesis; test assumptions, effect sizes. Recording of results according to APA editorial style. Reading information from the recording of statistics.

10. correlation analysis (various coefficients) - Null hypothesis; alternative hypothesis; test assumptions, effect sizes. Notation of results according to APA editorial style. Reading information from the recording of statistics.

11. classical statistical tests - null hypothesis, alternative hypothesis, test bias, parametric and non-parametric tests. The general mechanism of statistical tests, i.e. what happens to the data during statistical hypothesis verification. How can the null hypothesis be wrong? What is a test statistic? What are its properties. Where does the distribution of the test statistic come from, what does it mean? What does the side of the test mean? Difference between parametric and non-parametric tests; give examples; dependence of the shape of the distribution on the number of degrees of freedom.

p-value(p-value). What is p-value, what does p-value indicate, what is the relationship between test statistic and p-value? What allows you to calculate p-value? Does a statistically significant result mean that the research hypothesis or null hypothesis is confirmed? P-value - what are its properties. Interpretation of p-value according to the American Statistical Association. What are the relationships between p-value and the fact that the test is one- or two-sided? Phenomena associated with p-value.

Effect size (effect size). What is it? What is it used for? Selected effect sizes and threshold systems (benchmarks) according to J.Cohen and used in social psychology.

12. chi-square test - The null hypothesis of the chi-square test; What does the test statistic of this test mean; What does the shape of the distribution of the test statistic of this test depend on; the notation of the chi-square test; the expected abundance, and the abundance obtained, what does a large value of the test statistic indicate? What is the notation of the results? The notation of results according to the APA editorial style. Reading information from the recording of statistics.

13-14. Student's t-test - version for one sample and independent groups. Nomenclature (factor, levels, dependent variable). Null hypothesis and alternative hypothesis; how does the difference between means relate to the test statistic? What does the sign of the Student's t-test statistic depend on? What does it mean when the value of the t-statistic is in the interval [-1,1], and what - when it is outside it. The d-Cohen effect size, what is it, what values does it take? Cohen's and Lovakov's and Agadullina's thresholds for the d-Cohen effect size. Notation of results according to APA editorial style. Reading information from the recording of statistics.

Levene's test - null hypothesis, is there an effect size, how do we deal with the absence of an effect size? Rule of thumb regarding standard deviations. Notation of results according to APA editorial style.

15. the power of a statistical test - the relationship between the power of a test, the error of the 1st and 2nd type and the effect size.
DISCUSSIONS IN STATISTICS - winner's curse and statistical overpowered studies. Dependence of p-values on sample size. Replication crisis - what it means, causes and examples. Five commandments of correct p-value interpretation. Why p-value does not say that the result was obtained randomly (or: is the work of chance)?