Statistics 2

Statistics 1 WF-PS-STA1

elementary

K_W06

K_U06

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. 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.

2. 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.

3. Knowledge – The students know the concepts of multiple correlation and partial correlation. They are able to explain the coefficient of multiple and partial determination. They know a form of equation in multiple regression. They know the assumptions of the model. They understand differences between partial coefficients b in regression equation and beta weights. They are able to characterize methods of how to maximize a determination coefficient in multiple regression. They know what is collinearity among the predictors and the effect of catalysis.

Skills – The students are able to formulate a multiple regression equation, determine the values of partial coefficients in this equation and to interpret the obtained solution. They are able to calculate values of correlation and determination coefficient in multiple regression as well as of partial correlation and determination coefficient. They are able to interpret the obtained values correctly. They are able to compare various correlation coefficient. They are able to formulate or identify a research problem appropriate for multiple regression model. In a given multivariate research problem, the students are able to choose between models of analysis of variance and regression, and to justify their choice.

Competences – The students are able to explain a problem of predicting a value of one variable, based on a larger number of other variables. They are aware of the importance of the assumptions of the methods. They are able to respond critically to the results of the described 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 - 30 hours

Practical classes - 30 hours

Consultations - 5 hours

Students’ preparations for the lectures - 20 hours

Students’ preparations for the practical classes – 30 hours

Students’ preparation for the assessment test – 30 hours

Students’ preparation for the final exam – 35 hours

TOTAL – 180 hours [180 : 30 = 6]

ECTS points = 6