ECTS credits ECTS credits: 4.5
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 2.25 Expository Class: 18 Interactive Classroom: 18 Total: 137.25
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Mathematics
Areas: Geometry and Topology
Center Faculty of Pharmacy
Call: Second Semester
Teaching: Sin docencia (Extinguida)
Enrolment: No Matriculable | 1st year (Yes)
- Once the information collected from a sample has been summarized and analyzed (topics covered in Mathematics and Statistics I), the objective now is, through Statistical Inference, to contrast whether a sample situation derives from a given probability model and to infer the knowledge to the population available of that model. In particular, from the data obtained through a random sample, it is a question of knowing how to apply the appropriate statistical procedures to infer unknown characteristics of the population and calculate the error margins of the estimate.
- Apply, through the use of a statistical package, the concepts of regression, contrasts and confidence intervals to physical, chemical, biological data from medical-pharmaceutical databases and interpret the results.
- Provide an elementary capacity for the design of experiments according to statistical criteria.
UNIT 1: INTRODUCTION TO STATISTICAL INFERENCE. ESTIMATE
1.1 Population and sample.
1.2 Parameter. Statistical.
1.3 Distribution of different statistics. Central limit theorem.
1.4 Point estimate. Properties of the estimators.
1.5 Estimation by confidence intervals: basic concepts. Confidence level.
1.6 Confidence intervals for mean, variance and proportion.
1.7 Determination of the sample size.
TOPIC 2: CONTRASTS OF HYPOTHESIS
2.1 Statistical hypothesis. Formulation and method.
2.2 Types of error. Decision criteria. Critical level or p-value. Power of a contrast. 2.3 Interpretation of a hypothesis test. Relationship between confidence intervals and hypothesis tests.
2.4 Contrasts with a sample: for a mean, for a proportion and for a variance.
2.5 Contrasts with two samples: comparison of two variances; comparison of two means (independent samples, paired samples); comparison of two proportions.
2.6 Confidence intervals for the difference of means, difference of proportions and quotient of variances.
UNIT 3: THE CHI-SQUARE TEST
3.1 Contrasts for categorical data: contingency tables. Chi-square test. 2 × 2 tables. Study design. Homogeneity tests. Contrasts of independence.
3.2 Goodness of fit tests: Pearson's chi-square test; the Kolmogorov-Smirnov contrast; contrasts of normality.
UNIT 4: REGRESSION AND CORRELATION
4.1 Introduction. General concepts.
4.2 Regression: least squares method, regression lines.
4.3 Total variance. Residual variance and explained variance.
4.4 Correlation: linear correlation coefficient.
4.5 Other regression models: the exponential model and the potential model.
4.6 Hypothesis testing for regression parameters: ANOVA.
Basic
– Milton, J.S.,“Estadística para Biología y Ciencias de la Salud” Tercera edición ampliada. McGraw-Hill Interamericana, Madrid, 2007.
- Notes on the subject, available in the virtual course.
Complementary
– Cao Abad, R., Francisco Fernández M., y otros, Introducción a la estadística y sus aplicaciones, Ed. Pirámide (Grupo Anaya, S.A.), Madrid, 2001.
– Colton, T., Estadística en Medicina, Ed. Masson-Litle, Brown, S.A., Barcelona, 1995.
– Martín Andrés, A.; Luna del Castillo, J. de D., Bioestadística para las Ciencias de la Salud, Ed. Norma S.L. (4ª edición), Madrid, 1994.
– Peña Sánchez de Rivera, D., Estadística Modelos y métodos. I. Fundamentos, Alianza editorial, S.A., Madrid, 2000.
- Samuels, Myra L; Witmer, J., Fundamentos de Estadística para las Ciencias de la Vida, Ed. Pearson Educación, 2012.
– Sánchez M.; Frutos G.; Cuesta, P.L., Estadística y Matemáticas Aplicadas. Edición dirigida a los estudios de Farmacia, Editorial Síntesis S.A., Madrid, 1996.
Transversal competences.
CP01 Critical and self-critical ability.
CI01 Capacity for analysis and synthesis.
CI07 Basic computer skills.
CI08 Information management skills (ability to search and analyze information from a variety of sources).
CI09 Troubleshooting.
CI10 Decision making.
CS01 Ability to apply knowledge in practice.
CS03 Ability to learn.
Specific competences.
FM01 Apply knowledge of Mathematics to pharmaceutical sciences.
FM02 Apply computational and data processing techniques in relation to information related to physical, chemical and biological data.
FM03 Design experiments based on statistical criteria.
FM04 Evaluate scientific data related to medicines and medical devices. FM05 Use statistical analysis applied to pharmaceutical sciences.
Since the subject is fundamentally practical, special interest will be put in developing the contents with simplicity, without sacrificing precision.
- Conferences in large groups: in each class time will be devoted to the introduction, presentation or illustration of a theoretical question, and the rest to solving problems or exercises related to said question.
- Interactive classes in small groups: Students will be given exercise and problem bulletins, which will correspond to the contents of each of the program topics. The student will try, with the help of the work of the previous point, to solve them, or if necessary, to solve them in the classroom, with her active participation.
- Interactive classes with a computer for small groups: Data entry and coding (practices with EXCEL) for later use in a statistical package (R software). Attendance at these classes is compulsory and at the end of them there will be an exam.
- Tutorials in very small groups will be dedicated, individually or in groups, to solving doubts and particular difficulties that arise, and to the individualized monitoring of each student.
- The qualification of each student will be made through continuous evaluation and the completion of the final tests set in the Faculty's exam calendar. You must have completed and passed the computing practices.
- In cases of fraudulent completion of exercises or tests, the provisions of the "Regulations for the evaluation of academic performance of students and review of grades" will apply.
- The student's grade will be the sum of 60% of the final exam grade and 40% of the one corresponding to the continuous assessment.
- Continuous evaluation will be done through written controls, resolution of problem bulletins, student participation in the classroom and tutorials. The student will know his continuous evaluation qualification before the final exam.
- Controls will be during school hours. They will have a maximum duration of 1 hour. The day and time in which each control will take place, as well as the subject under examination, will be announced in advance.
- The final test will consist of solving problems similar to those worked in class.
- In the second opportunity, the same evaluation conditions and the grade of the continuous evaluation of the first opportunity will be maintained.
- The computer practices already carried out and approved will remain approved in the successive academic years.
- Students who repeat the subject may request that their continuous assessment grade from the previous year be taken into account.
-Evaluation of skills.
On the exam: FM03, FM05, CI01, CI09, CI10, CP01 and CS01.
In laboratory practices: FM02, FM05, CI07 and CI08. In interactive classes: FM04, FM05, CI09, CI10, CP01, CP02, CS01 and CS03.
WORK IN THE CLASSROOM (in hours)
Large group lectures 23.
Interactive classes in small groups 10.
Small group interactive computer classes 10.
Tutorials in very small or individualized groups 2.
Total contact hours 44.
STUDENT'S PERSONAL WORK
Individual or group autonomous study 45.
Writing exercises, conclusions or other work 13.5.
I work with a computer 9.
Exams and Review 2.
Total hours of personal work of the student 6.5.
In the course a lot of time is spent solving exercises.
Obviously, it is considered a fundamental aspect in learning the subject, therefore it is recommended:
- Try to solve the problems of the newsletters.
- Use the bibliography to consolidate the knowledge and techniques that allow the resolution of the problems proposed in the bulletins.
- Go to tutorials to be able to solve the doubts that arise throughout the course.
- Use the virtual classroom of the USC to access the didactic material.
CONTINGENCY PLAN
In case we have to go to Scenarios 2 or 3,
Contents
The following changes would be made to the program:
a) In section 2.3, the heading: Relationship between confidence intervals and hypothesis tests is removed.
b) Section 3.2 would be deleted in its entirety. 3.2 Goodness of fit tests: Pearson's chi-square test; the Kolmogorov-Smirnov contrast; contrasts of normality
c) In section 4.5, the heading is removed: The potential model
Methodology
a) Scenario 2: distancing 1. The lecture classes will respect the capacity of the classroom, and may be broadcast at the fixed time, or recorded for viewing through the Equipment platform.
b) Scenario 3: closure of facilities
1. The lectures will be replaced by explanatory videos of the didactic material that is already available to students, both on the Teams platform and in the virtual course.
2. The interactive classes will be replaced by the delivery of weekly problem bulletins. The submission of at least two solved problems from a newsletter will count as an aid for continuous evaluation.
3. The laboratory practices, on the dates already scheduled, will consist of viewing explanatory videos and the completion of a work by the students.
Evaluation
- The controls will be carried out online through the virtual course and will be during school hours.
- The continuous evaluation will be carried out through written and telematic controls, and the delivery of resolved bulletins.
- The final exam will be face-to-face unless authorized by the Faculty. In this case, it will be done electronically (Teams platform and / or virtual course). At the beginning of the exam, each student will have at their disposal in the virtual campus a personalized approach with problems similar to those proposed and solved in the subject. He must solve them within the period indicated and deliver in the corresponding task of the virtual campus of the subject a copy of the solutions, written by hand, in a good quality PDF file.
- The student's grade will be the sum of 60% of the final exam grade and 40% of the one corresponding to the continuous assessment.
- In the second opportunity, the same evaluation conditions and the grade of the continuous evaluation of the first opportunity will be maintained.
Enrique Macías Virgós
Coordinador/a- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813153
- quique.macias [at] usc.es
- Category
- Professor: University Professor
Antonio M. Gómez Tato
- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813151
- antonio.gomez.tato [at] usc.es
- Category
- Professor: University Lecturer
Jose Carlos Diaz Ramos
- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813363
- josecarlos.diaz [at] usc.es
- Category
- Professor: University Lecturer
Miguel Dominguez Vazquez
- Department
- Mathematics
- Area
- Geometry and Topology
- Phone
- 881813156
- miguel.dominguez [at] usc.es
- Category
- Researcher: Ramón y Cajal
Alberto Rodriguez Vazquez
- Department
- Mathematics
- Area
- Geometry and Topology
- a.rodriguez [at] usc.es
- Category
- Ministry Pre-doctoral Contract
Juan Manuel Lorenzo Naveiro
- Department
- Mathematics
- Area
- Geometry and Topology
- jm.lorenzo [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 11:00-12:00 | Grupo B/CLE_02 | Galician | 5035 Animal Physiology Seminar Room |
| 13:00-14:00 | Grupo A/CLE_01 | Spanish | 5035 Animal Physiology Seminar Room |
| 17:30-18:30 | Grupo C/CLE_03 | Spanish | 5035 Animal Physiology Seminar Room |
| Tuesday | |||
| 11:00-12:00 | Grupo B/CLE_02 | Galician | 5035 Animal Physiology Seminar Room |
| 13:00-14:00 | Grupo A/CLE_01 | Spanish | 5035 Animal Physiology Seminar Room |
| 17:30-18:30 | Grupo C/CLE_03 | Spanish | 5035 Animal Physiology Seminar Room |
| Wednesday | |||
| 11:00-12:00 | Grupo B/CLE_02 | Galician | 5035 Animal Physiology Seminar Room |
| 13:00-14:00 | Grupo A/CLE_01 | Spanish | 5035 Animal Physiology Seminar Room |
| 17:30-18:30 | Grupo C/CLE_03 | Spanish | 5035 Animal Physiology Seminar Room |
| Thursday | |||
| 11:00-12:00 | Grupo B/CLE_02 | Galician | 5035 Animal Physiology Seminar Room |
| 13:00-14:00 | Grupo A/CLE_01 | Spanish | 5035 Animal Physiology Seminar Room |
| 17:30-18:30 | Grupo C/CLE_03 | Spanish | 5035 Animal Physiology Seminar Room |
| Friday | |||
| 11:00-12:00 | Grupo B/CLE_02 | Galician | 5035 Animal Physiology Seminar Room |
| 13:00-14:00 | Grupo A/CLE_01 | Spanish | 5035 Animal Physiology Seminar Room |
| 17:30-18:30 | Grupo C/CLE_03 | Spanish | 5035 Animal Physiology Seminar Room |