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Statistics III

Objectives

This course unit aims to extend the knowledge acquired in Statistics II, as well as provide students with theoretical and practical knowledge concerning nonparametric statistical inference methodologies. The syllabus of the course comprises instruments nonparametric statistical inference as orders, statistics, order statistics, the estimators and sampling distributions, estimation nonparametric point and interval hypothesis tests and nonparametric. Are treated equally essential aspects of asymptotic distributions. The students should get to know the estimators and their properties, to construct confidence intervals and nonparametric testing of nonparametric hypotheses. For each non-parametric procedure, students should know clearly its applicability conditions.

General characterization

Code

100057

Credits

6.0

Responsible teacher

Tiago André Gonçalves Félix de Oliveira

Hours

Weekly - Available soon

Total - Available soon

Teaching language

Portuguese. If there are Erasmus students, classes will be taught in English

Prerequisites

Not apply.

Bibliography

Conover, W. (1999). Practical Nonparametric Statistics. John Wiley.; Lehmann, E. (1998). Nonparametrics. Statistical Methods Based on Ranks. Prentice Hall.; Siegel, S. & Castellan, N. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill.; Galvão de Mello, F. (1997). Probabilidades e Estatística II. Escolar Editora.; Murteira, B.; Silva Ribeiro, C.; Andrade e Silva,

Teaching method

Theoretical and practical classes and laboratory.

Evaluation method

1st Period – Assessment is continuous through three tests. Each test has a weight of 1/3 in the final grate. 
 
2nd Period – Exam (100%).

Subject matter

1.         INTRODUCTION
Statistical Inference. Nominal scale, ordinal scale, interval scale and ratio scale. Populations, samples, parameters, statistics, order statistic. Parametric methods, robust methods and nonparametric methods. Confidence intervals. Hypothesis testing. P-value.
 
2.         ANALYSIS OF A POPULATION
Confidence interval and the quantile test of a population 
 
3.         COMPARISON OF TWO POPULATIONS
Independent samples and paired samples
Sign test
Wilcoxon test
Mann-Whitney test
Confidence interval and Hodges-Lehmann estimate of the difference in location of two distributions
 
4.         COMPARISON OF MORE THAN TWO POPULATIONS
Test for variances
Independent or paired samples
Kruskal-Wallis test. Multiple comparisons
Cochran test
Friedman test
Chi-squared test for differences in probabilities
 
5.         RANDOMNESS AND INDEPENDENCE. MEASURES AND ASSOCIATION TESTS
Chi-squared test for independence. Carmér’s contingency coefficient. Pearson’s contingency coefficient
McNemar test
Spearman correlation coefficient and e de Kendall correlation coefficient
 
6.         GOODNESS-OF–FIT TESTS
Chi-squared test
Kolmogorov-Smirnov test
Lilliefors test. Shapiro-Wilk test.