
Course unit
MATHEMATICAL TOOLS FOR PSYCHOLOGISTS
PSP5070177, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2017/18
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
MAT/07 
Mathematical Physics 
6.0 
Course unit organization
Period 
First semester 
Year 
3rd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
42 
108.0 
No turn 
Examination board
Examination board not defined
Prerequisites:

The mathematical knowledge necessary for the admission to the undergraduate course in Psychological Science is assumed. 
Target skills and knowledge:

The probability that a woman of age 40 has breast cancer is about 1 per cent. If she has breast cancer, the probability that she tests positive on a screening mammogram is 90 percent. If she does not have breast cancer, the probability that she nevertheless tests positive is 9 percent. What are the chances that a woman who tests positive actually has breast cancer? This class presents some basic techniques for the analysis of the uncertainty inherent in statistical information, with the goal of providing a correct evaluation and communication of risk. Basic notions of elementary probability theory and of Bayesian probability are introduced and discussed, and their application is illustrated in problems connected with the medical and psychological practice. 
Examination methods:

Written final exam with open questions or quizzes (46 exercises; duration: 7090 minutes). The written exam verifies that the expected learning outcomes are actually acquired by the students through applicative questions, possibly including brief theoretical questions regarding the material presented in class.
The students will also make an oral presentation of a selected topic during class (topics chosen and researched by the students, under guidance of the instructor, working in groups of 34 people). Attendance to other students' presentations is considered part of the required coursework. 
Assessment criteria:

Grading is based on the results of the final written test, and on the performance in the oral presentation (the presentation contributes about 20% to the final course grade). 
Course unit contents:

Uncertainty in statistical information. Problems related to the evaluation of risk and communication of risk. Realworld examples. Bayesian inferences through the use of probabilities and by means of natural frequencies. Suitability of the latter for a more intuitive and direct insight in both risk estimation and in a transparent representation of risk. Examples focussing on the correct judgement of the probabilistic predictive value of medical diagnostic tests, and aiming at avoiding misleading risk information. Evaluation of the effect of interventions: Relative risk and Absolute Risk, and Relative and Absolute Risk Reduction (or Increase); Number Needed to Treat or to Harm [ARR, RR, RRR, NNT, NNH]. 
Planned learning activities and teaching methods:

Class lectures, with presentation of the main points mentioned above. Some theory and many examples. Recitations and exercises to complement the theoretical parts, also directly involving students in both individual and group work. The main focus is on realworld applications of the topics treated during the coursework. 
Additional notes about suggested reading:

The textbook is required reading, and further material is made available through moodle during class. See also the extra reading material indicated in the references below. 
Textbooks (and optional supplementary readings) 

MAIN TEXTBOOK  Gerd Gigerenzer, Calculated Risk. New York: Simon & Schuster, 2002.

Auxiliary reading material  Gerd Gigerenzer et al., Helping Doctors and Patients Make Sense of Health Statistics. : Association for Psychological Science, 2008. http://library.mpibberlin.mpg.de/ft/gg/GG_Helping_2008.pdf

Auxiliary reading material  Stephanie Kurzenhäuser, Natural frequencies in medical risk communication: improving statistical thinking in physicians and patients. Dissertation: FU Berlin, 2003. http://www.diss.fuberlin.de/diss/servlets/MCRFileNodeServlet/FUDISS_derivate_000000001633/00_kurzenhaeuser.pdf

Auxiliary reading material  M. R. Spiegel, Theory & Problems Of Probability & Statistics. New York: Schaum Mc Graw Hill, 1998.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Interactive lecturing
 Working in group
 Questioning
 Problem solving
 Loading of files and pages (web pages, Moodle, ...)
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
Sustainable Development Goals (SDGs)

