# Statistics 2

**Teacher**: dr. Miljenko Huzak, professor

**Semester**: second

**ECTS**: 6

Required course

To train students for *planning statistical experiments or observations, analysis of data *and* statistical inference* about population based on sample by use of standard statistical models and methods for:

- Comparison and testing laws of distribution,
- Regression analysis,
- Model selection,
- Interval and point estimation of model parameters and hypothesis testing,
- Valuation of model fit,
- Dimension reduction,
- Classification/discrimination of data,
- Analysis of survival based on censored data.

After the completion of this course, students are expected to know how:

- To apply and perform Mann-Whitney-Wilcoxon’s test
- To apply and perform Kolmogorov-Smirnov test and its version, Lillefors test
- To calculate and interpret Spearman correlation coefficient, multiple correlation coefficient and partial correlation coefficient
- To calculate multiple confidence intervals and to estimate p-value of multiple tests
- To plan experiment or observation by analysing standard errors and power functions
- To set up a multivariate model, to fit it, validate and select one
- To set up a (multiple) logistic regression model, to fit it, validate and select one
- To apply computer-intensive methods (Monte Carlo, bootstrap, cross-validation) for point and interval estimation of parameters, for estimation of test statistics sample distribution, model validation and testing of hypothesis by permutation methods
- To estimate and apply survival function by Kaplan-Meier estimate
- To set up, estimate and interpret risks by use of Cox hazard model

**Nonparametric methods for law comparison.**Rank tests (Mann-Whitney-Wilcoxon statistics, Spearman’s coefficient of correlation), Kolmogorov-Smirnov tests, Tests of normality (Lilliefors test), ROC curve.**Multivariate data**. Normal distribution, Multiple confidence intervals and multiple testing, Multiple correlation, Partial correlation, Linear regression models (Kronecker product, Gauss-Markov properties, model selection), MANOVA and MANCOVA models, Allocation and discrimination, Principal component analysis (the best linear prediction).**Log-linear models.**Parameter estimation, Prediction, Wald test, Model selection.**Computer intensive methods.**Monte Carlo methods, Bootstraping, Cross-validation, Permutation tests.**Survival analysis.**Kaplan-Meier estimator, Cox proportional-hazards model.