Statistics WF-ZPS-S

A knowledge of statistics (as well as a knowledge of methodology and logic) is a basic element in a knowledge system of a person who studies any empirical scientific discipline – psychology in particular. The lectures in statistics are designed to present the process of how theoretical methodological knowledge is linked to statistical description and inference. This linkage is presented in particular research situations, in which a researcher deals with a wide range of data that should be described, analysed and interpreted.
Psychology students should understand a position of statistics in empirical sciences. They should be aware that psychology refers mainly to statistics, based on a convenient assumption of an infinite number of elements in each analysed population. This “idealized” approach might not be correct in other cases. In case of a finite population a way of constructing estimators is different.
The students should master the tools of statistical description, estimation and of statistical inference, which are designed to adequately describe and analyse empirical data and to draw correct conclusions on empirically tested hypotheses. The lectures introduce knowledge that is necessary to understand research procedures, to plan an empirical research and to interpret the results of appropriate statistical methods.
The students should master a basic as well as an advance knowledge on how empirical research is planned and on how empirical data (experimental and correlational) is analysed. At the same time, the students should be aware of any factors that may distort a validity of any empirical data.
The program of the first semester covers the basic statistical concepts, which are necessary to built any statistical description of analysed variables. The basic assumptions of statistical inference are also introduced.
Moreover, statistics plays an important role in formulating empirical laws in social sciences. It is a separate discipline of knowledge in the sense that it has its own identity with a large repertoire of techniques derived from certain fundamental principles. These techniques, however, cannot be used without a proper reflection. Statistics is more a way of thinking or reasoning rather than a collection of useful recipes, which, when applied to the data, provide an answer to the questions. A user of statistical methods should have the necessary knowledge of the logical foundations of these methods, and of limitations associated with their use. They must also acquire the necessary practice to be able to choose the appropriate method for any given research problem and make the appropriate modifications, in case they are necessary. Noteworthy, the methodology of statistics depends on the inductive reasoning and is not fully codified or free of controversy. Different users may reach different conclusions, analysing the same data set. Existing data usually contain more information than can be disclosed by the available statistical tools. The extent to which a user manages to extract this information depends on their knowledge, but also on their skills and experience. Consequently, the statistics is actually an art of making choices. It is not easy to make such choices without a solid knowledge of the basics of selected statistical methods (single- or multi-dimensional), and of the criteria on how to select an appropriate method of analysis. It is also not easy to use these methods in a competent manner without the knowledge of their limitations and of legitimate (or not) interpretation of the results. Therefore, a psychologist should have a knowledge of the most commonly used statistical methods in psychology and the conditions for their use. They should also be able to choose the optimal method from the point of view of the research problem posed in the context of the data collected. The material covered in the second semester includes methods of statistical data analysis, both single- and multi-dimensional, and explains the extent of their usefulness.

Effects of teaching:
1. 4. Knowledge: The students are able to describe differences between estimation theory and statistical inference. They know concepts of: null hypothesis and alternative hypothesis, simple and composite. They are able to define errors in hypothesis testing. They can explain relations between errors, between errors and power of the test, and how errors are related to the sample size.
Skills: The students are able to construct a confidence interval for a population mean and variance. They are able to draw conclusions about the values of the population parameters considered. They are able to choose the correct test for a given null hypothesis (on a population mean), also accurately choosing between one-tailed and two-tailed tests.
Competences: In given examples of empirical problems, the students are able to make the correct decisions on a level of significance and a sample size.

2. Knowledge – The students know the logical-statistical basis for one-dimensional, one- and two-way analysis of variance and understand the meaning of their use. They can characterize these models: present null and alternative hypothesis, describe the necessary assumptions for the application of these methods as well as justify the need for their admission and indicate the consequences of their violation, is able to give a test statistics, the number of its degrees of freedom and its probability distribution. The students are familiar with the concept of a main effect. They can explain a concept of interaction. They know the multiple comparison tests and indicators of effect sizes used in the ANOVA models. They understand the concept of MANOVA model.
Skills – The students know how to properly use the analysis of variance models and is able to justify the decision to choose a particular analysis model to analyse the data. They interprets the values of statistics correctly. They are able to interpret and illustrate the effect of interaction correctly. They are able to identify the problem or formulate a research problem, appropriate for the application of these methods.
Competences – The students are able to explain the essence of the analysis of variance. They are aware of the importance of the assumptions of the methods. They are able to respond critically to the results of these methods and to their interpretation, pointing out the advantages and shortcomings of a particular analysis.

3. Knowledge – The students are able to explain a concept of covariance. They know correlation coefficient (Pearson's r) and the assumptions for its use. They are able to characterize a probability distribution of the coefficient and are able to give its degrees of freedom. They understand what determination coefficient (r-square) is. They know a form of equation in a simple linear regression and can explain what factors a and b are in this equation. They know the assumptions of the model and limitations of its use. They can explain what is residual in regression. They know the method of the least squares. They know a distinction between linear and nonlinear regression models.
Skills – The students are able to use Pearson's r correlation coefficient correctly and to accurately interpret the strength and direction of the relationship between variables. They are able to illustrate the probability distribution of the coefficient (graphically). They are able to interpret a value of determination coefficient (r-square) correctly. They are able to formulate a simple regression equation, determine the values of the coefficients and interpret the obtained solution. They can identify the problem or formulate a research problem appropriate for the application of the methods.
Competences – The students are able to explain the essence of the relationship between two variables. They are aware of the importance of the assumptions of the described methods. They are able to respond critically to the results of these methods and to their interpretation, pointing out the advantages and shortcomings of a particular analysis.

4. Knowledge – The students know chi-square probability distribution. They know applications of the chi-square test. They are able to give null and alternative hypothesis of the test, its assumptions. They know the form of the test statistics, its degrees of freedom and probability distribution. They know coefficients of contingency.
Skills – The students are able to illustrate (graphically) a chi-square probability distribution for different degrees of freedom. They are able to create a contingency table. They are able to use chi-square test properly. They are able to choose a contingency coefficient, appropriate for a given research problem, calculate its value and interpret it.
Competences – The students are able to explain the essence of a relationship between two categorical variables. They are aware of the importance of the assumptions of the described methods. They are able to respond critically to the results of these methods and to their interpretation, pointing out the advantages and shortcomings of a particular analysis.

ECTS:
Lectures - 48 hours
Consultations - 12 hours
Students’ preparations for the lectures - 90 hours
Students’ preparation for the final exam – 90 hours
TOTAL – 240 hours [240 : 30 = 8]
ECTS points = 8

Insufficient (2): A student knows less than 60,0% of basic statistical concepts, does not understand their meaning, and is not able to use them to describe empirical data.
Sufficient (3): A student correctly and with understanding uses at least 60,0% of statistical concepts and mastered the related skills and competences. A prerequisite, however, is to be able to define the most central statistical terms (such as variance, standard error of statistics and the significance level) and to specify the content of the main limit theorems.
Good (4): A student correctly and with understanding uses at least 80,0% of the knowledge, presented in the course of the semester, has skills and competences related to it. A student knows how a null hypothesis should be tested and is able to present this process for the statistical methods, introduced in the first semester (checking the assumptions, reconstructing the logic of how test statistic is constructed, constructing the probability distribution with correct degrees of freedom and providing a criterion for rejecting of the null hypothesis)
Very good (5): A student mastered a virtually whole scope of material, covered in the semester. He or she is able to correctly chose statistical methods, proper for solving certain research problems.

A final grade is based on a written exam, which students can take at the end of the year, after they have attended the lectures and only if they have successfully completed the practical classes: A positive grade (at least “sufficient”) in the practical classes in Statistics is a prerequisite to take the final, written exam. The final exam covers the content of the lectures, practical classes, and of the recommended literature. Examples of exam questions are given to the students on the ongoing basis during the practical classes.

The literature recommended here consists of comprehensive statistical textbooks that the Students may choose among.

Aczel, E. A., Statystyka w zarządzaniu. Warszawa 2000.

Aranowska, E., Metodologiczne problemy zastosowań modeli statystycznych w psychologii. Teoria i praktyka. Warszawa 1996.

Blalock, H. M., Statystyka dla socjologów. Warszawa 1977.

Ferguson, G. A., Takane, Y., Analiza statystyczna w psychologii i pedagogice. Warszawa 1997.

Francuz, P., Mackiewicz, R., Liczby nie wiedzą, skąd pochodzą. Przewodnik po metodologii i statystyce nie tylko dla psychologów. Lublin 2005.

King, B. M., Minium, E., W. Statystyka dla psychologów i pedagogów. Warszawa 2009.

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

• Description of WF-ZPS-S in USOSweb