 Study

# Computing

## Statistical Data Analysis

• Class 45
• Practice 12
• Independent work 93
Total 150

### Course title

Statistical Data Analysis

Elective

183454

5

5

### Course objectives

Presentation of statistical data; population and sample; sampling methods; population parameters.
Objective of multivariate statistical analysis; Data, objects, variables and scales (Stevens's classification); Classification of multivariate techniques; Summarizing, describing and graphical representation of multivariate data.
Measures of central tendency (mean, median, mode); measures of dispersion (standard deviation, variance, quantile, and IQR); Statistical inferences; correlation coefficient; linear correlation.
Hypothesis testing; type of errors; parametric hypothesis testing; sampling distributions; Tests for means (one and two sample tests - matched pairs and independent); t-test.
Tests for variances (one and two sample tests); Chi-square test; F-test.
Difference of means; variance of two normal populations; comparing of two population proportions; Tests for population proportions (one and two sample tests); U-test.
Interpretation of the tests results; Sample size; Interpretation of p-value; Example of applications: statistical quality control and control charts.
Midterm exam.
Advantage, disadvantage and use of nonparametric statistical procedures; Nonparametric tests for single sample; Nonparametric tests for two independent and two related samples; Nonparametric tests for three and more independent and related samples.
Data manipulation prior to multivariate analysis (missing data, outlier detection, transformations of data, standardization, normality, linearity, homoscedascity, homoegenity); Data appropriate for multivariate analysis: data, correlation, variance-covariance, sum-of-squares and cross-products matices, residuals; distances (statistical and Mahalanobis); Sample geometry and Random sampling.
Analysis of variance (ANOVA/MANOVA) and design of experiment.
Simple linear regression; Multiple linear regression.
Applied correlation and regression analysis, interpretation and relation to ANOVA.
Bayesian versus Frequentist inference.
Final exam.

(.), Željko Pauše: Uvod u matematičku statistiku, Školska knjiga, 1992,
(.), Mirta Benšić, Nenad Šuvak: Primijenjena statistika, Sveučilište J. J. Štrosmajera, 2013,
(.), 1) David M. Diez, Crhisopher D. Barr, Mine CerinkayaRundel: OpenIntro Statistics, OpenIntro, 2015.,
(.), 2) L. Fahrmeir, T. Kneib, S. Lang, B. Marx: Regression: Models, Methods and Applications, Springer, 2013.,
(.), 3) G. James, Daniela Witten,Tre vor Hastie, Robert Tibshirani: An Introduction to Statistical Learning with Applications in R, Springer, 2013.,

#### Minimal learning outcomes

• Define main notions in the statistical data analysis
• Explain mathematical backgrounds of main statistical procedures
• Apply procedure of data preparation and visualization
• Apply statistical test on real data
• Analyze the relation between statistical variables by applying regression analysis and correltion analyis
• Justify the adequacy of statistical inference for given data
• Interpret the results of statistical data analysis and explain their practical meaning