DEMOCRITUS UNIVERISTY OF THRACE Dept. of Physical Education and Sport Sciences Doctoral Program of Study COURSE OUTLINE 1. COURSE TITLE: Advanced Statistics 2. COURSE COORDINATOR/ LECTURER: Mavrommatis George, Professor tel/fax: 2531039645 e-mail: gmavroma@phyed.duth.gr 3. ADDITIONAL LECTURERS: 4. TEACHING STRATEGY: Lectures 5. SEMESTER: Spring semester 6. TYPE OF COURSE: Compulsory 7. DIRECTION OF STUDY: Doctorate program 8. ECTS: 10 9. AIM OF THE COURSE The aim of the courses is the introduction in the initial principles of Statistic and the familiarization of students with basic principles of applied Statistics, the analysis of variance, the regression, the factorials analysis and the classifications, mostly in the Physical Education. Furthermore the aim of the courses is to developing the student s potential to apply the above analysing data and getting statistical results. 10. LEARNING OUTCOMES After the completion of the course the students will be able to: 1. To recognize and understand the basic principles of applied statistics, the test theory and the analysis of variance, the regressions, the factors analysis, the discriminant and cluster analysis 2. To recognize the data models of above contents 3. To know the application of statistical analysis for respects data model 4. To getting results for the analysis and to can interpret them Detailed Outline of Learning Outcomes Learning Outcomes Educational Activities Assessment Criteria To recognize and understand the basic principles of applied statistics, the test theory and the analysis of variance, the regressions, the factors analysis, the discriminant and cluster analysis lectures exams Student workload (hours/semester) 100 To recognize the data models of above contents Lectures exams 80 1
To know the application of statistical analysis for respects data model To getting results for the analysis and to can interpret them Lectures Lectures exams 60 exams 60 TOTAL 300 11. COURSE CONTENTS Initial principles of Statistic, variance, standard deviations, normal distribution, confidence interval, t-test for independent and dependent samples, analysis of variance for independent and dependent samples, non parametric test of Mann- Witney and Wilcoxon, test of Kruskal-Wallis, non parametric test of Spearman, Chi- Square goodness of fit and Chi-Square Test for independence, simple and multivariate regression analysis, nonlinear simple regression, logistic regression and description of canonical regression model, basic linear algebra, principal component analysis, factor analysis, discriminant analysis and cluster analysis. 12. TEACHING APPROACH Lectures, conversations, 13. TIME SCHEDULE OF LECTURES Lecture Lecturer Topic 1 Mavrommatis G. Introduction in the basic principles of Statistic, hypothesis test, significant level, errors type I and II, reject area and t- test for independent samples 2 Mavrommatis G. One-Way Analysis of Variances for independent samples, two-way Analysis of Variances for independent samples 3 Mavrommatis G. Analysis of variances for repeated measures. 4 Mavrommatis G. Simple and multivariate regression analysis 5 Mavrommatis G. Nonlinear simple regression, logistic regression and description of canonical regression model 6 Mavrommatis G. Non parametric test of Mann-Witney and Wilcoxon, test of Kruskal-Wallis, non parametric test of Spearman, Chi-Square goodness of fit and Chi-Square Test for Independence 7 Mavrommatis G. Basic principles of linear algebra 8. Mavrommatis G. Principal component analysis 9 Mavrommatis G. Principal component analysis 10 Mavrommatis G. 11 Mavrommatis G. Factor analysis Discriminant analysis 2
12 Mavrommatis G. Classification analysis Final Assessment 14. EVALUATION OF STUDENTS LEARNING Assessment Criteria Percentage of Final Grade Presences (10%) Written exams at the end of semester (90%) 16. REQUIRED TEXT OR READINGS/OTHER MATERIAL 1. Γούργουλης Β., Μαυρομάτης Γ «Βασικές έννοιες εφαρμοσμένης Στατιστικής στη Φυσική Αγωγή», Salto,2002 2. Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης δεδομένων», University Studio Press, 1999 3. Καρλής Δ. «Πολυμεταβλητή Στατιστική Ανάλυση», Αθ. Σταμούλη, 4. Παπαδημητρίου Γ., «Η Ανάλυση Δεδομένων», Γιώργος Δάρδανος, 2007 5. Γναρδέλης Χ., «Αναλυση δεδομένων με το SPSS 14 for Windows», 6. Ferguson G., Takane Y. Statistical Analysis in Psychology and Educational, Mac Graw-Hill,1989 7. Sharma S., Applied Multivatiate Techniques, Wiley, 1996 8. Tabachnick B. and Fidell L., Using Multivariate Statistics, Pearson, 17. ACADEMIC INTEGRITY Students in this course will complete all course work and related activities in compliance with the Law N. 2121/1993in effect for Intellectual Rights. Plagiarism of any kind will not be tolerated under any circumstances being a serious disciplinary offence with significant ratifications and it results in an immediate F grade for this course. In addition all such cases will be immediately directed to the Directing Committee. Any words or ideas that are not yours should be accompanied by full and complete citations. 3
18. DETAILED COURSE CONTENT Lecture 1 Basic principles of Statistic, the concept of variance, standard deviation, standardize transformation, normal distribution and sampling distribution, central limit theorem, error type I and II, significance level, rejection area. Introduction in the basic principles of Statistic, t-test for independent and dependent samples Lecture 2 One-Way Analysis of variances for independent and dependent samples Variance, Standard deviation, normal distribution, confidence interval, significance level 1. Γούργουλης Β., Μαυρομάτης Γ «Βασικές έννοιες εφαρμοσμένης Στατιστικής στη Φυσική Αγωγή», Salto,2002 2. Ferguson G., Takane Y. Statistical Analysis in Psychology and Educational, Mac Graw-Hill,1989 Description of one way data model for independent sample, sum of squares within and between groups, mean sum of squares, F-values, post hoc tests, dependent samples, data model with one dependent factor, sum of squares within subjects, the meaning of interaction as standard error Sum of squares within and between groups, mean sum of squares, F- values, post hoc tests, sum of squares within subjects 1. Γούργουλης Β., Μαυρομάτης Γ «Βασικές έννοιες εφαρμοσμένης Στατιστικής στη Φυσική Αγωγή», Salto,2002 2. Γναρδέλης Χ., «Αναλυση δεδομένων με το SPSS 14 for Windows», 3. Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης 4. Ferguson G., Takane Y. Statistical Analysis in Psychology and Educational, Mac Graw-Hill,1989 Lecture 3 Two-Way analysis of variances for independent and dependent samples, analysis of variance for mixed models Description for data model of analysis of variance for two independent factors, examples, main effects, interaction, mixed models, examples relatives to analysis of variances with two factors of which one is dependent, clarification of the concepts sum of squares of subjects within rows, interaction rows by columns and interaction subjects by columns Main effects, interaction, simple main effect, mixed models 4
within rows. 1. Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης 2.Γναρδέλης Χ., «Αναλυση δεδομένων με το SPSS 14 for Windows», 3.Ferguson G., Takane Y. Statistical Analysis in Psychology and Educational, Mac Graw-Hill,1989 Lecture 4 Non parametric tests of Mann- Witney, Wilcoxon, Spearman, Kendal, and Kruskal-Wallis, Chi square tests Non parametric tests, rank values, mean of rank value, tables of frequencies, contingency tables, non parametric tests for two or three independent samples and two dependent samples, non parametric coefficient of correlation, chi square test of goodness fit and independences. Mean of rank value, contingency tables, chi square test of goodness fit and independencies 1. Γούργουλης Β., Μαυρομάτης Γ «Βασικές έννοιες εφαρμοσμένης Στατιστικής στη Φυσική Αγωγή», Salto,2002 2. Γναρδέλης Χ., «Αναλυση δεδομένων με το SPSS 14 for Windows», Lecture 5 Simple and multiple regression Points cloud, regression line, method of least squares, regression coefficients, standard error of estimate, coefficient of determination, Beta coefficients, partial correlation coefficient, linearity test of model, the use of categorical variables Method of least squares, standard error of estimate, coefficient of determination, Beta coefficients, partial correlation coefficient 1. Γούργουλης Β., Μαυρομάτης Γ «Βασικές έννοιες εφαρμοσμένης Στατιστικής στη Φυσική Αγωγή», Salto,2002 2. Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης 3. Καρλής Δ. «Πολυμεταβλητή Στατιστική Ανάλυση», Αθ. Σταμούλη, 4. Γναρδέλης Χ., «Αναλυση δεδομένων με το SPSS 14 for Windows», Lecture 6 5
Non linear simple regression, logistic regression, element of canonical regression Non linear simple regression of second or third degree, standard error of estimate, coefficient of determination, confidence intervals of non linear models, partial coefficient of determination, model of logistic regression, coefficients of logistic regression, logit(p), antilog of coefficients in logistic regression, log-likelihood function, tests in coefficients of logistic model, canonical regression model, canonical factors, variables loading. Partial coefficient of determination, likelihood ratio statistic, canonical factors 1.Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης 2.Καρλής Δ. «Πολυμεταβλητή Στατιστική Ανάλυση», Αθ. Σταμούλη, 3.Γναρδέλης Χ., «Αναλυση δεδομένων με το SPSS 14 for Windows», Lecture 7 Introduction to linear algebra, scalar product, matrices, eigenvalues and eigenvectors, diagonalization Vectors, scalar product, matrices, types of tables, matrix inverse, matrix operations, eigenvalues and eigenvectors, verticality of eigenvectors, transition of one space to on ether, diagolazation of one Symmetric Matrix. Lecture 8 Εigenvalues, eigenvectors, scalar product, scalar matrix, diagonalization 1. Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης 2. Καρλής Δ. «Πολυμεταβλητή Στατιστική Ανάλυση», Αθ. Σταμούλη, 3. Παπαδημητρίου Γ., «Η Ανάλυση Δεδομένων», Γιώργος Δάρδανος, 2007 4. Sharma S., Applied Multivatiate Techniques, Wiley, 1996 5. Tabachnick B. and Fidell L., Using Multivariate Statistics, Pearson, Principal Components Analysis (PCA) Data model of principal components analysis, factor axes, homogenization and centralization of data,, unit vectors, determination of factor axes, diagonalization of correlation matrix, trace of a square matrix, eigenvalues and eigenvectors of factor axes, coordinates of values on factor axes, inertia and cumulative inertia, projection of subjects on factor axes, absolute and relative contribution of subjects, coordinates of variables, equation of Diagonalization of correlation matrix, eigenvalues and eigenvectors of factor axes, inertia, equation of transition, 6
transition, absolute and relative contribution of variables, number of factor axes absolute and relative contribution of variables 1.Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης 2.Καρλής Δ. «Πολυμεταβλητή Στατιστική Ανάλυση», Αθ. Σταμούλη, 3.Παπαδημητρίου Γ., «Η Ανάλυση Δεδομένων», Γιώργος Δάρδανος, 2007 4.Sharma S., Applied Multivatiate Techniques, Wiley, 1996 5.Tabachnick B. and Fidell L., Using Multivariate Statistics, Pearson, Lecture 9 Data model of principal components analysis, factor axes, homogenization and centralization of data, unit vectors, determination of factor axes, diagonalization of correlation matrix, trace of a square matrix, eigenvalues and eigenvectors of factor axes, coordinates of values on factor axes, inertia and cumulative inertia, projection of subjects on factor axes, absolute and relative contribution of subjects, coordinates of variables, equation of transition, absolute and relative contribution of variables, number of factor axes Principal Components Analysis (PCA) Lecture 10 Diagonalization of correlation matrix, eigenvalues and eigenvectors of factor axes, inertia, equation of transition, absolute and relative contribution of variables 1.Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης 2.Καρλής Δ. «Πολυμεταβλητή Στατιστική Ανάλυση», Αθ. Σταμούλη, 3.Παπαδημητρίου Γ., «Η Ανάλυση Δεδομένων», Γιώργος Δάρδανος, 2007 4.Sharma S., Applied Multivatiate Techniques, Wiley, 1996 5.Tabachnick B. and Fidell L., Using Multivariate Statistics, Pearson, Factor analysis (FA) Data model of factor analysis, differences among FA and PCA, orthogonal model, assumptions, loadings, communality, latent factor, unique factor, structural loadings, specificity, application levels of factor analysis, Bartlett s test of sphericity, partial correlation coefficient, the two estimation techniques of factor analysis the PCA and maximum likelihood analysis, axes rotation, factor scores, Factor, communality, partial correlation coefficient, axes rotation 7
example 1.Καρλής Δ. «Πολυμεταβλητή Στατιστική Ανάλυση», Αθ. Σταμούλη, 2.Γναρδέλης Χ., «Αναλυση δεδομένων με το SPSS 14 for Windows», 3.Sharma S., Applied Multivatiate Techniques, Wiley, 1996 4.Tabachnick B. and Fidell L., Using Multivariate Statistics, Pearson, Lecture 11 Discriminant Analysis Lecture 12 Data model of discriminant analysis, test of Discriminant factor significance between predefined groups, Wilk s analysis, Wilk s lamda, discriminant factor analysis, factor lamda, discriminante axes, projection of subjects on Mahalanobis discriminant axe, discriminant coefficients, linear distance functions of discrimination, linear combination variance, covariance coordinates, the best discriminate linear combination, eigenvalues and eigenvectors, quality of discriminant analysis, additional element, Mahalanobis distance, example 1.Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης 2.Καρλής Δ. «Πολυμεταβλητή Στατιστική Ανάλυση», Αθ. Σταμούλη, 3.Παπαδημητρίου Γ., «Η Ανάλυση Δεδομένων», Γιώργος Δάρδανος, 2007 4. Sharma S., Applied Multivatiate Techniques, Wiley, 1996 5.Tabachnick B. and Fidell L., Using Multivariate Statistics, Pearson, Cluster Analysis The meaning of the distance of two cases, the union of two classes, minimization of within classes variance, hierarchical and nonhierarchical clustering, distance between subjects, clustering process, Ward criterion, lost minimization of between classes variances, the union of a new class with another, table of between classes lost variances, dendrogram nodes, the best partition criterion, value test interpretation of classes Cluster, Ward method, dendrogram nodes, partition, clustering value test 1. Μαυρομάτης Γ., «Στατιστικά μοντέλα και μέθοδοι ανάλυσης 2. Καρλής Δ. «Πολυμεταβλητή Στατιστική Ανάλυση», Αθ. Σταμούλη, 3. Παπαδημητρίου Γ., «Η Ανάλυση Δεδομένων», Γιώργος Δάρδανος, 2007 4. Sharma S., Applied Multivatiate Techniques, Wiley, 1996 5. Tabachnick B. and Fidell L., Using Multivariate Statistics, Pearson, 8