Statistics (classes)

elementary

PS_W06

PS_U06

This two-semester course provides an introduction to descriptive and inferential statistics commonly used in psychology, and introduces hypothesis testing as a method of scientific investigation. The main purpose of the course is to learn basic statistical concepts and techniques. The program of the first semester covers the basic statistical concepts, which are necessary to build any statistical description of analyzed variables. The basic assumptions of statistical inference are also introduced. The material covered in the second semester includes methods of statistical data analysis, both univariate and multivariate, and explains the extent of their usefulness.

This two-semester course provides an introduction to descriptive and inferential statistics commonly used in psychology, and introduces hypothesis testing as a method of scientific investigation. The course includes lectures and practical classess. The main purpose of the course is to learn basic statistical concepts and techniques. The program of the first semester covers the basic statistical concepts, which are necessary to build any statistical description of analyzed variables. The basic assumptions of statistical inference are also introduced. Main topics include key statistical concepts, measures of central tendency and dispersion, and an introduction to probability and hypothesis testing. Concepts are introduced and discussed through lecture and discussion and then are applied through exercises in practical classes. Students who successfully complete this course will possess basic data analysis skills and should be able to demonstrate comprehension of basic statistical concepts and methods.

Second semester course is designed to provide students with an overview of the statistical methods typically used in psychological research. This course will build upon material from previous semester. Through this course, students will examine various statistical tests and their applications. Methods covered include, but are not limited to, t-tests, ANOVA, correlation, and regression. Distinguishing characteristics include identification of independent and dependent variables, types of variables used in each method, assumptions of each method and how to remedy unmet assumptions, as well as correct interpretation of results. Upon successful completion of the course students will be able to apply the methods of statistics and analytical reasoning to critically evaluate data, solve theoretical and practical problems, identify appropriate statistical procedures for specific problems or hypotheses, and effectively communicate findings. 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 in both semesters and only if they have successfully completed the practical classes. 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 and also in a written form towards the end of each semester.

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.

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.

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:

Practical classes - 32 hours

Consultations - 18 hours

Students’ preparations for the practical classes – 40 hours

Students’ preparation for the assessment test – 30 hours

TOTAL – 120 hours 120 : 30 = 4]

ECTS points = 4

Insufficient (2): A student gives incomplete or incorrect definitions of basic statistical terms (such as variance, standard error of statistic and the significance level), or does not know them at all. He or she is not able to specify (with understanding) the content of the main limit theorems. A student is not able to properly use the statistical methods, described in the classes, or uses them without any reflection, without considering their assumptions. He or she formulates incorrect or groundless conclusions and uses the statistical terminology inadequately. He or she provides explanations or justifications that have little or no connection with the analysed issue. Frequently, a student is not able to define the statistical problem correctly. A student does not pay attention to arithmetical errors and draws conclusions based on the incorrect values.

Sufficient (3): A student knows correct definitions of basic statistical terms and is able to specify the content of the main limit theorems. However, he or she is not able to discuss relations between various concepts and terms and is not able to synthesize information on a particular issue. A student only in a limited scope uses their knowledge to solve and explain statistical problems. A student is able to properly use only some of the statistical methods, described in the classes, but omits other or is not able to use them properly. He or she provides explanations that are incomplete or unclear. A student presents solutions to the statistical problems using terminology that is not always appropriate. A student leaves some of the arithmetical errors without any comment and uses them to draw incorrect conclusions.

Good (4): A student knows correct definitions of basic statistical terms and is able to specify the content of the main limit theorems. Moreover, he or she is able to discuss relations between various concepts and terms and is able to synthesize information on a particular issue, describing it in a coherent way. A student provides explanations that may lack some details, but they are consistent and of logical structure. A student is able to properly use the statistical methods, described in the classes, but he or she ignores some of their aspects or assumptions (crucial – at times). A student presents solutions to the statistical problems using correct terminology. A student notices the arithmetical errors that he or she has made and is able to adjust conclusions accordingly.

Very good (5): A student has an excellent knowledge of statistical issues, presented in the classes and is able to present them in a logical, coherent and comprehensive way, correctly using statistical terminology. A student is able to analyse a given statistical issue in a comprehensive way, including all available information and explaining the solution. He or she remains sensitive to inconsistencies or errors in how statistical issues are presented (during the discussion in the class or in the literature), he or she is able to capture and correct them. A student correctly uses the statistical methods, described in the classes and is able to discuss their limitations. A student happens to make small arithmetical errors, but they do not impact the quality of the conclusions he or she draws.

A final grade consists of:

A written assessment – 75% of the final grade. The scope of the assessment and examples of the questions or tasks are given to the students during the classes.

Students’ individual work and the quality of its presentation – 25% of the final grade.