2019_20
University
Rovira y Virgili
Educational guide 
Faculty of Oenology
A A 
english 
Bachelor's Degree in Oenology (2014)
 Subjects
  STATISTICS
   Contents
Topic Sub-topic
1. Introduction to data analysis. 1.1. Concept of Statistics. Contents of Statistics.
1.2. Concept of population, sample, individual and random variable.
1.3. Classification of the statistical variables.
1.4. Position parameters.
1.5. Dispersion parameters.

2. Random variables. 2.1. Concept of probability and properties.
2.2. Concept of random variable.
2.3. Discrete random variables: probability function and distribution function.
2.4. Continuous random variables: density function and distribution function.
2.5. Expected value.
2.6. Variance.

3. Models of probability distribution. 3.1. Discrete distributions: Bernoulli, binomial, Poisson, uniform.
3.2. Continuous distributions: uniform, exponential, normal.
3.3. General normal law. Reduced normal law: N(0,1).
3.4. Distributions deduced from the normal: khi-squared, Student’s t and Snedecor’s F.
3.5. Convergence to the normal law: central limit theorem.
3.6. Use of statistical tables.

4. Theory of estimation. 4.1. Concept of estimator and parameter. Point estimation and interval estimation.
4.2. Properties of estimators: bias, efficiency and consistency.
4.3. Some methods of estimation: method of moments and method of maximum likelihood.
4.4. Notion of confidence interval. Confidence coefficient.
4.5. Determination of confidence intervals for: a mean, a difference between means, a variance, a ratio between variances, a proportion and a difference between proportions.

5. Hypothesis testing. 5.1. Statistical hypotheses. Types of hypotheses.
5.2. Concept of critical region and acceptance region.
5.3. Types of errors. Power of a test. Significance level.
5.4. Applying hypothesis testing to: a mean, a difference between means, a variance, a ratio between variances, a proportion and a difference between proportions.

6. Analysis of variance. 6.1. General concepts about the analysis of variance.
6.2. One-way design.
6.3. Two-way design without interaction. Random blocks.
6.4. Two-way design with interaction.

7. Linear regression. 7.1. Simple linear regression model.
7.2. Estimation of the regression line by the least squares method.
7.3. Goodness-of-fit measures.
7.4. Significance testing.
7.5. Prediction intervals.
7.6. Non linear regression.
7.7. Multiple linear regression.

8. Numerical methods. 8.1. Error analysis.
8.2. Zeros of functions.
8.3. Solving systems of linear equations.
8.4. Numerical integration.
8.5. Numerical solution of differential equations.