# Non-Parametric Statistics

**Human Resources Management and Organisational Behaviour**

5 ECTS; 2º Ano, 2º Semestre, 30,0 T + 30,0 PL + 15,0 OT

**Lecturer**

- Luis Miguel Lindinho da Cunha Mendes Grilo

**Prerequisites**

Not applicable.

**Objectives**

It is intended that students achieve in the curricular unit of non-parametric statistics the learning outcomes:

a) identify, when faced with data incompatible with parametric analysis, which statistical tests are appropriate for one sample;

b) acquire knowledge about different statistical tests to compare populations on the basis of independent or paired samples;

c) acquire knowledge about measures of non-parametric association.

**Program**

1. Introduction

1.1. Introduction to SPSS statistical software

1.2. Hypothesis testing

1.2.1. Null hypothesis and alternative hypothesis

1.2.2. Error type I and error type II

1.2.3. Test statistic and rejection region

1.2.4. P-value

1.3. Tests of parametric hypotheses versus tests of non-parametric hypotheses

2. Tests involving a sample

2.1. The Runs test of randomness

2.2. The binomial test

2.3. Adjustment tests

2.3.1. The Kolmogorov-Smirnov adjustment test

2.3.2. The Lilliefors Normality Test

2.3.3. The chi-square test

2.3.4. Reference to other adjustment tests

3. Non-parametric tests for two populations

3.1. Tests involving two independent samples

3.1.1. The chi-square homogeneity / independence test.

3.1.2. The Fisher's exact test for 2X2 tables

3.1.3. The Wilcoxon-Mann-Whitney test

3.1.4. The Kolmogorov-Smirnov test for two populations

3.2. Tests involving two paired samples

3.2.1. The McNemar test

3.2.2. The test of the signals

3.2.3. The Wilcoxon test

4. Nonparametric tests for more than two populations

4.1. Tests involving k independent samples

4.1.1. The chi-square test for k samples

4.1.2. The Kruskall-Wallis test

4.2. Tests involving k paired samples

4.2.1. The Friedman test

4.2.2. The Cochran Q test

5. Non-parametric association measures

5.1. Spearman's ordinal correlation coefficient

5.2. The coefficient of Cramer's C

5.3. The coefficient ró for tables 2x2

5.4. The Kendall correlation coefficient

5.5. The coefficient of agreement of Kendall

5.6. The K statistic for nominal data

5.7. Other measures of association

**Evaluation Methodology**

- Continuous assessment: three frequencies written during the semester (classified from 0 to 20 values each), without the restriction of minimum classification in none of them. It will be tried to divide evenly the matter taught in the chapters by the frequencies to be realized.

The student is exempt from examination, that is, is approved by continuous evaluation if the average obtained from the classification of the written frequencies, rounded to the units, is equal to or greater than 10 values.

- Evaluation by examination: students who have not obtained approval in the continuous evaluation can carry out written exam with all the subjects taught in the curricular unit (classified from 0 to 20 values). Students are considered approved to the course unit if the final grade, rounded to the units, is equal to or greater than 10 values.

**Bibliography**

- Siegel, S. (2006). *Estatísticas Não Paramétrica Para Ciências Do Comportamento*. São Paulo: Bookman

- Pereira, A. (2006). *SPSS - Guia prático de utilização, Análise de dados para as Ciências Sociais e Psicologia*. Lisboa: Edições Sílaba

**Method of interaction**

Lectures and practical classes including SPSS practice exercises.

**Software used in class**

IBM-SPSS