Descriptive and inferential research methods

DESCRIPTIVE STATISTICS (40HS)

Theme

Contents

Hours

Introduction

What is Statistics? Why study it? Types of statistics. Population and sample. Types of variables.

2

Descriptive statistics

14

Obtaining and organizing the data. Parameters and statistics. Frequency distributions. Histogram.

2

Measures of central tendency: Mean, median, mode for ungrouped and grouped data.

4

Dispersion measures: variance, standard deviation, coefficient of variation.

4

Relative position measures: quartiles, deciles and percentiles.

4

Probability and probability distributions

8

Elemental Probability. Sample space. Events. Probabilities of an event.

1

Additive Rules. Conditional Probability. Multiplicative rules.

3

Random Variables. Discrete and continuous probability distributions.

4

INFERENTIAL STATISTICS (40HS)

Theme

Contents

Hours

General concepts

4

Sampling and census. Random and stratified samples.

2

Distribution of sample means. Central Limit Theorem.

2

Estimation and hypothesis testing

20

Point and interval estimates (confidence intervals). Estimation of the mean of a population. Estimation error. Estimation of the proportion of a population. Sample sizes.

3

Procedure for testing a hypothesis. Null and alternative hypothesis, P-Values. One- and two-tailed tests for means 1hs

3

Hypothesis tests for a sample (“t” test).

3

Hypothesis tests for two samples (“t” test).

3

Variance analysis. ANOVA One Way.

8

SIMPLE AND MULTIPLE REGRESSION (40hs)

Theme

Contents

Hours

Linear regression of 1 predictor

14

Generalities

2

Least squared method

1

Residuals

1

Straight Adjustments

1

Normal errors in regression models

1

Inferences for regression and correlation

1

Prediction of new observations

1

Analysis of residuals and statistical tests

2

Tests for normality

2

Tests for homoscedasticity

2

Multiple Regression

10

Generalities

2

General linear model

2

Regression ANOVA

2

Estimation of means and new observations

1

Multicollinearity

1

Use of quantitative variables

1

Model selection criteria

1

1 factor, 2 and more factor, factorial, fractional, mixture and surface experiments (40 HS)

Theme

Contents

Hours

Introduction to Design of Experiments

9

Generalities

1

Basic definitions

1

Elements of Inference Review

1

Random designs

1

ANOVA for DOE

2

Graphical verification methods

1

Qualitative data

1

Statistical tests for treatment residues

1

Factorial and Fractional Experiments

8

Two-factor analysis of variance

2

The principles for the construction of factorial and fractional designs

1

2k Factorial Designs. Calculation of the effects. Confounding factors. Solving a fractional factorial design

1

Contrasts and measures of effects in treatments

2

Evaluation of a model

2

Optimization and Desirability and Testing

7

Transformation and Box-Cox procedure

2

Optimization AND desirability

2

Response surface methodology.

2

Mix Design. Factors involved in a mix design.

1

NON-PARAMETRIC STATISTICS (40 HS)

Theme

Contents

Hours

Introduction

1

Why use nonparametric statistics?

1

Nonparametric tests

15

Signs test.

3

Categorical association (Chi-square)

3

A sample. Wilcoxon test.

3

Two samples. Wilcoxon / Mann-Whitney test.

2

More than two samples. Kruskal-Wallis test.

2

Kolmogorov-Smirnov test for goodness-of-fits of distributions.

2

Resampling and boostrap

5

Resampling and boostrap

5

Nonparametric correlation

5

Spearman correlation

5

Module

Introduction Software

Eng. Jonnatan F. Aviles PhD.

Module 1

Agrim. Daniela Ballari PhD.

Module 2

Agrim. Daniela Ballari PhD.

Module 3

Eng. Jonnatan F. Aviles PhD.

Module 4

Eng. Jonnatan F. Aviles PhD.

Module 5

Agrim. Daniela Ballari PhD.