The course "Statistics III" aims to familiarize students with advanced statistical methodologies. First, an introduction to statistics is made with the repetition of basic concepts. Students are then introduced to common non-parametric statistical tests. These tests, unlike traditional parametric tests, do not rely on the assumption that the samples used come from a population that follows a normal distribution. It is a fact that this assumption is violated in many research and practical problems. In these cases non-parametric hypothesis tests can be applied regardless of data distribution and sample size.

The course continues with the presentation of two methods of multivariate statistical analysis, namely analysis of variance and covariance as well as cluster analysis.

1ⁿ – 2ⁿ Lecture: Introduction

• Review of basic statistical concepts
• The use of statistical controls in applied research
  • Null hypothesis
  • Significance level and size sample
  • Rejection area of the null hypothesis
• Criteria for choosing the appropriate statistical control
• Advantages- disadvantages of non-parametric controls

3ⁿ – 7ⁿ Lecture: Non-parametric statistical tests

• Goodness-of-fit tests
  • Kolmogorov-Smirnov test
  • χ²
  • Goodness-of-fit test /ul>
  • Testing the assumption of equality of medians
    • Formal test
    • One-sample Wilcoxon test
    • Wilcoxon test for two dependent samples
  • Testing the hypothesis that two independent samples come from the same population
    • Wilcoxon Sum Rank test
    • Wilcoxon-Mann-Whitney test
  • Testing the hypothesis that three or more random samples come from the same population
    • Kruskal-Wallis test
    • Equality of population variances test
  • Correlation analysis
    • Spearman's correlation coefficient
    • Kendall's correlation coefficient
  • Examples-applications

  8^h – 9^h Lecture: Analysis of Variance - Covariance

  • One-way analysis of variance
  • Two-way analysis of variance
  • Analysis of covariance (ANCOVA)
  • Examples-applications using appropriate software Estimation with interval

  10^h – 13^h Lecture: Cluster Analysis

  • Introduction
  • Distance (concept and measures of distance)
  • Practical problems
  • Hierarchical clustering
    • The algorithm
    li>
    • Choice of method
    • Example and comparison of methods
  • Selection criteria Number of Groups

  Examples-applications

Βασική βιβλιογραφία

• Ξεκαλάκη, Ε. 2002. Μη Παραμετρική Στατιστική, Αθήνα Εκδόσεις Μπένου.
• Καρλής, Δ. 2005. Πολυμεταβλητή Στατιστική Ανάλυση. Εκδόσεις Σταμούλη, Θεσσαλονίκη.
• Berenson L.Μ, Levine M.D., Szabat A.K. (2018). Βασικές Αρχές Στατιστικής για Επιχειρήσεις-Έννοιες και Εφαρμογές, Έκδοση: BROKEN HILL PUBLISHERS LTD

Συμπληρωματική βιβλιογραφία

• Siegel, S. and Castellan, N.J. Non-parametric Statistics for the Behavioral Sciences, McGraw- Hill

Hair, J.F., Black, W.C., Babin, B.J., Anderson, R.E.. 2010. Multivariate data analysis (7^th ed.) Pearson Academic.