Mathematical and probability statistics
Four year Bachelor of Education Science
Major: Mathematical Statistics
Mi nor: Physics
Experience: 5 years
It covers: probability and statistics
Statistics: Descriptive Statistics, Data Analysis (Graphic Representations, Measures of Central Tendency, Dispersion, Position, Regression and Correlation); Probability (Combinatorics, Random Variables, Probability Distributions for Discrete and Continuous Random Variables; Inferential Statistics (Sampling and Sampling Distributions, Central Limit Theorem, Confidence Intervals, Hypothesis Testing, Inference Concerning Correlation and Regression); Analysis of Variance (Categorical Data Analysis; Chi-square; Contingency Tables; Homogeneity tests; Decision Theory); Process and Quality Control (Control Charts)
Basic Review: Box plots, histograms, bar charts, pie charts, counting principles; descriptive statistics, mean, median, mode, five-number summary, standard deviation, range, IQR, Probability distributions.
Estimation Theory: Estimates by method of moments, their properties; Maximum likelihood estimates & their properties, Fisher information, Rao-Cramer inequality, efficient estimates; Bayes estimates, prior and posterior distributions, conjugate priors; Sufficient and jointly sufficient statistics, Neyman-Fisher factorization criterion, Rao-Blackwell theorem; Estimates for parameters of normal distribution, their properties; Chi-square, Fisher and Student distributions; Sampling distributions; Confidence intervals (For sampling distribution and for parameters of normal distribution).
Hypotheses Testing: Testing simple hypotheses, Bayes decision rules, types of error, most powerful tests, likelihood ratio tests, randomized tests; Composite hypotheses, power function, monotone likelihood ratio and uniformly most powerful tests; t-tests and F-tests; Goodness-of-fit tests, chi-square tests, tests of independence and homogeneity, Kolmogorov-Smirnov test, Effect Sizes; Two independent samples, paired sample t-tests; Test for equality of variance.
Regression and Classification: Simple linear regression, least-squares fit, statistical inference in simple linear regression, confidence intervals, prediction intervals; Classification problem, boosting algorithm; Multiple linear regression; Correlation; Normal probability plots and other assumption checking techniques; Effect Sizes; Logistic regression; Correlation and regression techniques for quantitative and qualitative data analysis; nominal scales, interactions; other related multivariate methods.
ANOVA: Basic One-Way, repeated measures, mixed model, factorial, randomized block ANOVA, ANCOVA; Effect Sizes; Preplanned comparisons; Post-hoc analysis/comparisons: Bonferroni, Tukey, LSD, Dunnett's.
Non-parametric Statistics: Kruskal Wallis; Sign Test; Wilcoxin Signed-Rank; Wilcoxin Rank Sum Test.