Statistics

Learning Outcomes

The course’s material includes mathematical definitions, fundamental concepts, results and reasoning methodologies that pertain to basic Statistical analysis objects and models underlying the foundations and applications of computer science. Moreover the relevant connections of probability theory to several more specific branches of computer science are presented. The course directly supports most of the curriculum subjects and lessons: Note that during the lesson, specific examples of application are discussed in some of the above curricular subjects such as applications in telecommunication systems, cryptography, digital services (e-learning, e-health) using new technologies with the help of programs such as Matlab, SPSS and R.

Upon successfully completion of the course the students will be in position to:

• Know, describe and handle the basic knowledge of Statistical Analysis (indicatively: descriptive statistics, sampling and sampling distributions, estimation (principle of maximum likelihood)), Statistical inference, confidence intervals, confidence tests and assumptions, fit, linear regression, analysis of variance, logistic regression, statistical analysis with software, applications in computer science).
• ·         Select the appropriate mathematical concepts of statistical analysis and be able to model the particular problem of computer science that it is called upon to solve. In addition to develop mathematical thinking and being able to analyze and adapt acquired knowledge to applications of computer science.·
• To define the types of conclusions drawn by statistical inference, to be able to know what is the appropriate model for data analysis, and to evaluate the accuracy of the results of statistical methods.·
• Know the Matlab, SPSS and R programs and can interpret the results from them.

Course Contents

• Sample theory, samples, replacement, random samples and numbers.
• Sampling distributions and statistical interrelations.
• Frequency and relative frequency.
• Cluster sampling, stratified sampling, systematic sampling, statistical estimations unbiased estimations.
• Reliability and confidence intervals.
• Hypotheses testing and importance of statistics hypotheses, significance level, normal distribution testing.
• Interpretation of criterion t for dependent and independent samples.
• Adaptation test x2.
• Adaptation curve, regression and cross-correlation adaptation curve, regression, least square.
• Multiple regression, estimation fault, factors of cross-correlation.
• Correlation and independence.
• Interpretation of indicators of cross-correlation, Pearson, Spearman, Biserial, φ.
• Propagation analysis, interpretation of propagation analysis.
• Multiple-variables statistical analysis.

Recommended Readings

• M. Filippakis, Statistical Methods & Regression Analysis for New Technologies, Tsotras Publications, Athens 2017, 1rst Edition.
• T.Papaioannoy-S.Loukas, Introduction to Statistics, Stamoulis Publications, Athens (2002).
• Teaching Notes.