Applied statistics

The recommended background knowledge corresponds to that acquired in the course units Data Analytics and Mathematical Analysis I, with particular emphasis on the former.

The classes are, in accordance with the curriculum, theoretical-practical, planned and prepared to actively involve students at various moments or throughout the entire class.

In the theoretical part, which introduces concepts, fundamental results and methods, the expository method will tend to be used, interspersed with tasks that encourage more active participation from all students. These tasks include asking questions to and by students, either orally and/or on a platform, and also proposing debate/discussion in small groups on some aspect/topic presented.

The practical part will be devoted to the full development of the listed skills, through the commented exemplification of procedures and/or problem solving under the guidance/tutoring of the teacher, encouraging independent work or work in small groups. There will be a strong interaction between theory and practice, giving, whenever possible, a central role to the visualisation and treatment of concrete and real situations.

Good monitoring of classes by students requires regular attendance and a willingness to remain involved beyond the classroom, with the start or completion of tasks agreed in class.

Statistics is a discipline with a wide range of applications across diverse fields of knowledge and professional domains, particularly within the business sciences. Data-driven decision-making relies on statistical knowledge applied throughout the entire process, from planning to data analysis and interpretation. In this course unit, a selection of inferential statistical methods for data analysis will be addressed.

Intended learning outcomes:

Upon successful completion of this course unit, students will be able to:

• Solve problems involving uncertainty scenarios that can be described in probabilistic terms.
• Identify and apply statistical inference methods, such as estimation, hypothesis testing, and regression, appropriate to the solution of real-world problems.
• Develop simple statistical or econometric studies.

Skills to be developed:

• Use fundamental concepts of probability and discrete and continuous theoretical distributions to model random phenomena.
• Apply statistical inference methods, namely confidence intervals and parametric and non-parametric hypothesis tests, to the analysis of real data.
• Build, estimate and analyse simple linear regression models, assessing their adequacy and interpreting the results obtained.
• Interpret statistical results, recognising the limitations of the methods used and the impact of uncertainty on decision-making.
• Plan and develop simple statistical studies, from problem formulation to the analysis and presentation of results.
• Use software tools to support statistical data analysis, namely the software introduced in the course unit.

1. Framework: statistical thinking

2. Probabilities and theoretical distributions
2.1. Fundamental concepts and theorems
2.2. Discrete and continuous random variables
2.3. Discrete and continuous theoretical distributions

3. Statistical inference
3.1. Introduction
3.2. Confidence intervals for different population parameters
3.3. Parametric hypothesis tests for different population parameters
3.4. Nonparametric tests

4. Linear regression model
4.1. Introduction
4.2. Estimation and inference
4.3. Model assessment

In accordance with the Academic Regulations of the of the 1st Cycle of Studies of the IPC, the following two assessment regimes are proposed.

1) Periodic assessment

• This regime consists of two assessment tests to be carried out during the teaching period, either during class time or during the period outside classes designated for the administration of tests.
• Each test is graded on a scale of 0–10, with a minimum mark of 3.5 required in each test.
• Access to this assessment regime does not require class attendance, although attendance is strongly recommended.
• The tests are computer-based, and students are required to use the statistical analysis software introduced in class, namely Microsoft Excel and JASP (https://jasp-stats.org/).
• These tests are closed-book.
• The content assessed in each test corresponds to the one covered up to the class immediately preceding the test.
• In the event that a student fails to attend a test, regardless of the reason, no resit will be scheduled and a mark of 0 (zero) will be awarded.
• Under this regime, the student’s final mark is obtained by summing the marks of the two tests, provided that each meets the minimum required mark.
• Failure to meet the minimum mark requirement results in failure under this assessment regime.

2) Assessment by examination

• This assessment regime consists of a single examination, graded on a scale of 0–20, to be held on the date specified in the official examination schedule.
• The examination is computer-based, and students are required to use the statistical analysis software introduced in class, namely Microsoft Excel and JASP (https://jasp-stats.org/).
• The examination is closed-book.
• The student’s final mark corresponds to the mark obtained in the examination.

Final rules:

• Under either assessment regime, a passing grade is awarded with a final mark, rounded to the nearest whole number, of at least 10.
• Under either assessment regime, grade improvement may be obtained by taking the examination during the examination period in which the student is registered for grade improvement.

NAO