Biostatistics

To know how to obtain, organize, present and describe data sets by means of descriptive statistics. To know how to calculate the probability of an event. To know the characteristics and distribution of random variables. To know how to describe and apply methods of inferential statistics.
Handle statistical packages that allow the analysis of data obtained in research in the field of Biology.

LECTURES
1. Descriptive statistics (5 hours)
General concepts. Frequency distributions. Graphical representations. Measures of position and dispersion of a variable. Two-dimensional descriptive statistics. Frequency distributions.
2. Foundations of probability (4 hours)
Random experiment. Events and Sample Space. Conditional probability. Independence of events. Product rule, law of total probabilities and Bayes' Theorem. Applications in Biology.
3. Random variables (6 hours)
Discrete random variable: probability mass function and distribution function. Position and dispersion measures of a random variable. Distribution of two-dimensional variables. Independence of random variables. Models of discrete distributions: Bernoulli and Binomial. Continuous random variable: density function and distribution function. Measures of position and dispersion of a random variable. Models of continuous distributions: The normal distribution. Approximation of distributions.
4. Estimation and confidence intervals (5 hours)
Introduction to statistical inference. General approach to the parametric inference problem. Point estimate of a proportion. Bias and variance of an estimator. Concept of confidence interval. Confidence interval for a proportion. Point estimate of the mean and variance of a normal population. Confidence intervals for the mean and variance of a normal population.
5. Hypothesis testing (5 hours)
The problem of hypothesis testing. Hypothesis testing for the proportion. Hypothesis testing for the mean and variance of a normal population. Comparison of two means in paired samples. Comparison of two means in independent samples.
6. The simple linear regression model (5 hours)
Elements of a regression model: the linear model. Estimation of the model parameters. Inference about parameters. Covariance, correlation coefficient and determination coefficient. Decomposition of variability. The F test. Prediction.

SEMINARS (12 hours)
In the seminars there will be exercises related to each of the topics explained in the lectures.
1. Descriptive statistics (2 hours)
2. Foundations of probability 2 hours)
3. Random variables (2 hours)
4. Estimation and confidence intervals (2 hours)
5. Hypothesis testing (2 hours)
6. The simple linear regression model (2 hours)

LABORATORY (12 hours)
Introduction to R. (2 hours)
Univariate Descriptive Statistics (2 hours)
Bivariate descriptive statistics. Probability distribution models (2 hours)
Estimation and confidence intervals (2 hours)
Hypothesis testing (2 hours)
Simple linear regression (2 hours)

TUTORIALS (1 hour)
Follow-up of the development of the course and resolution of doubts.

BASIC BIBLIOGRAPHY
Milton, J.S. (2007): "Estadística para biología y ciencias de la salud", Mc Graw-Hill.

COMPLEMENTARY BIBLIOGRAPHY
Barón López F.J. (2021): "Bioestadística: Métodos y aplicaciones". Available at:
https://www.bioestadistica.uma.es/baron/bioestadistica.pdf [Accessed May 11, 2024]
Crujeiras, R.M. y Faraldo, P. (2010): "Manual de estadística básica para ciencias de la salud", Unidixital
Glover, T.; Mitchell, K. (2015): "An Introduction to Biostatistics using R", Waveland Press. Available at:
https://waveland.com/Glover-Mitchell/r-guide.pdf [Accessed May 12, 2024]
Heumann, C.; Schomaker, M.; Shalab (2016): "Introduction to Statistics and Data Analysis", Springer. Available online (through the USC Library).
Martínez González, M.A.; Sánchez Villegas, A.; Toledo Atucha , E.; Faulin Fajardo, J. (2020): "Bioestadística amigable", Elsevier.
Montanero Fernández, J.; Minuesa Abril, C. (2018): "Estadística básica para Ciencias de la salud". Available at:
http://matematicas.unex.es/~jmf/Archivos/Manual%20de%20Bioestadística.p…
[Accessed May 12, 2024]
Shahbaba, B. (2012): "Biostatistics with R", Springer. Available online (through the USC Library).
Verzani, J. (2002): "simpleR. Using R for Introductory Statistics". Available at:
https://cran.r-project.org/doc/contrib/Verzani-SimpleR.pdf [Accessed May 12, 2024]

Competencies:
Comp02: Students have developed those learning skills necessary to undertake further studies with a high degree of proficiency necessary to undertake further studies with a high degree of autonomy.

Comp05: That students have the ability to gather and interpret relevant data (usually within their area of study) in order to make judgements that are relevant data (usually within their area of study) in order to make judgements that include reflection on relevant social include reflection on relevant social, scientific or ethical issues.
Comp06: Be able to convey information both in writing and orally and to discuss ideas, problems and
and orally and to discuss ideas, problems and solutions related to Biology, in front of a general or specialised audience general or specialised public.
Comp07: Be able to integrate in interdisciplinary teams and apply theoretical and practical knowledge to
theoretical and practical knowledge to solve complex problems, participate in scientific-technical or clinical
scientific-technical or clinical projects in the bio-health field and to guarantee health and well-being.
Abilities and skills:
H/D01: Apply the theoretical and practical knowledge acquired in an integrated manner in the transmission of information/ideas and in the approach to and resolution of problems, both in academic and professional contexts.
H/D02: Know how to obtain and interpret relevant information and experimental results and draw conclusions on topics related to Biology.
H/D04: Propose, apply and interpret mathematical models and statistical methods in the field of Biology.
H/D07: Ability to search for, process, analyse and synthesise information from different sources, including the use of ICTs in the field of Biology.
H/D08: Ability to reason, argue and think critically.

Both the lectures (master classes) and seminars ((problem solving or seminars) will be in the classroom with blackboard, where the theoretical contents of the subject and the procedures for solving the problems will be explained (solving exercises and proposing others to be solved by the students).
The laboratory (computer classroom practices) will be face-to-face and it is appropriate that students can use their laptops. The computer tool R [http://www.r-project.org] will be introduced. Exercises will be solved and proposed to be solved with R by the students. This will allow us not only to put into practice the knowledge studied in the subject, but also to acquire the necessary resources to handle this computer tool.

The tests and assignments will be face-to-face and all of them are assessable.
The following scheme will be maintained:

Coursework: the coursework will be carried out throughout the four-month period. It will consist of the following elements:
-Resolution of exercises and questions associated with each subject, in which the student will use statistical techniques and the knowledge acquired in the lectures.
Through this activity the following competences, skills and abilities will be evaluated: Comp06, H/D01, H/D02, H/D08.
-Assessment of the laboratory.
This activity evaluates the following competences, skills and abilities: H/D01, H/D02, H/D07, H/D08.
The grade obtained in the continuous assessment will be kept in the two opportunities of the same course.
-Final exam: the final exam will consist of several theoretical-practical questions on the contents of the subject, which may include the interpretation of results obtained with the computer tool R, used in the practical computer teaching.
This activity evaluates the following competences, skills and abilities: Comp02, Comp06, H/D01, H/D02, H/D04, H/D07, H/D08.

The final grade, both in the first and in the second opportunity, will be the maximum of the grade in the written theoretical-practical exam, on the one hand, and of the weighted average of the continuous assessment (30%) and the grade in the written theoretical-practical exam (70%), on the other hand. Students who do not sit the written theoretical-practical exam will be ‘failed’.

Students who do not pass the course in a given year will have to repeat all the tests in the following year. The marks of any test from one year will not be retained for the following year.

It is recommended to dedicate at least an hour and a half of additional work for each hour of expository and interactive class, in addition of tutorials.

Attendance at all teaching activities.
Look up the recommended bibliography.

The students will have the materials of the course in the Virtual Campus (Moodle). In these materials are the contents (theoretical and practical) of the subject.

This guide and the criteria and methodologies described in it are subject to modifications derived from the regulations and guidelines of the USC.
Indication referring to plagiarism and improper use of technologies in the performance of tasks or tests: For cases of fraudulent performance of exercises or tests, the provisions of the "Regulations for the evaluation of the academic performance of students and the review of grades" will apply.