Statistical Analysis

Objectives

1. Describe a random variable; understand probabilistic models and probabilities calculation
2. Characterise the Binomial and Normal distributions; compute probabilities
3. Understand the concept of sampling distribution,explain and apply the Central Limit Theorem
4. Explain the impact of the sample size on the sampling distribution
5. Understand and investigate the properties of estimators
6. Build and interpret confidence intervals
7. Calculate the sample size given the precision of the point estimate
8. Formulate the hypothesis of the statistical test and decide based on an appropriate test
9. Explain the two types of error in statistical tests
10. Calculate and interpret the p-value
11. Make inferences about the mean,proportion, difference between means and proportions, variance and ratio of variances
12. Verify the assumptions of ANOVA, obtain the ANOVA table, apply the F-test and post-hoc tests
13. Distinguish parametric & nonparametric test procedures
14. Perform nonparametric hypothesis tests

General characterization

Code

200185

Credits

7.5

Responsible teacher

Docente a designar

Hours

Weekly - Available soon

Total - Available soon

Teaching language

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

Prerequisites

Bibliography

- Hogg, R. V., Tanis, E. A. (2010). Probability and Statistical Inference. 8th Edition, New Jersey: Pearson/Prentice-Hall.
- Newbold, P., Carlson, W. L., Thorne, B. (2012). Statistics for Business and Economics. 8th Edition, Boston: Pearson.
- Tutorials and other materials provided by the teacher.

Teaching method

The curricular unit is based on theoretical and pra ctical lessons. A variety of instructional strategies will be applied, including lectures, slide show demonstrations, step-by-step applications (with and without software), questions and answers. The sessions include presentation of concepts and methodologies, solving examples, discussion and interpretation of results. The practical component is geared towards solving problems and exercises, including discussion and interpretation of results. A set of exercises to be completed independently in extra-classroom context is also proposed.

Evaluation method

Evaluation:
1st call: pro ject (20%), 1st test (40%), 2nd test (40%)
2nd call: final exam (100%)

Subject matter

1. RANDOM VARIABLES
- Probabilistic models
- Discrete r.v.
- Continuous r.v.

2. PROBABILITY DISTRIBUTIONS
- Binomial, Poisson, Normal
- Approximation of Binomial to Normal
- t, Chi-square, F

3. SAMPLING DISTRIBUTIONS
- Sampling statistics & sampling distributions
- Distribution of sampling mean and sampling proportion

4. POINT ESTIMATION
- Unbiasedness, efficiency, consistency

5. INTERVAL ESTIMATION
- CI for mean, proportion, variance
- CI for difference between means and between proportions
- Sample size determination

6. HYPOTHESIS TESTING
- Concepts
- Tests for mean,proportion, variance, difference between means and between proportions, ratio between variances
- Tests for correlation coefficient

7. ANALYSIS OF VARIANCE
- One-way ANOVA with fixed effects
- Multiple comparison tests
- Tests to the equality of k variances

8. NONPARAMETRIC TESTS
- Introduction
- Distribution fitting tests
- Comparing independent and paired-samples
- Spearman¿s rank correlation test

Programs

Programs where the course is taught: