Basic Statistical Methods syllabus

Basic Statistical Methods

1. History of statistics
2. Various kinds of statistical problems and studies.
3. Collection and summarization and presentation of different types of univariate and bivariate data.
4. Descriptive statistics: measures of location,spread, skewness, kurtosis, various properties of these
5. measures and their utility.
6. Summarization and analysis of different types of bivariate data. Correlation, measures of
7. association, simple linear regression.
8. Summarization and analysis of different types of multivariate data. Multiple regression. Partial
9. and multiple correlation.
10. Tests of hypotheses: Different types of statistical hypotheses. Error probabilities, level of
11. significance and power of a test, non-central χ 2 . Tests for parameters of normal distributions
12. based on single and two populations. Large sample tests for parameters in Binomial and Poisson
13. distributions. Conditional tests.
14. Confidence intervals: criteria for goodness, pivotal quantities, relationship with tests of
15. hypothesis, illustrations.
16. Nonparametric Inference:
17. Formulation of the problem, order statistics and their distributions. Tests and confidence
18. intervals for population quantiles.
19. Sign test. Test for symmetry, signed rank test, Wilcoxon-Mann-Whitney test. Kruskal-Wallis
20. test. Estimation of location and scale parameters. Run test, Kolmogorov-Smirnov tests. Measures
21. of association: Kendall’s tau, Spearman’s rank correlation, Coefficient of concordance-tests of
22. independence.
23. Smoothing: Histogram, moving bin, and kernel type density estimation, curse of dimensionality.