Course partially running (all years except the first)

Course code
Name of lecturer
Roberto Burro
Roberto Burro
Number of ECTS credits allocated
Academic sector
Language of instruction
Sem. IIA dal Feb 23, 2015 al Apr 19, 2015.

Lesson timetable

Sem. IIA
Day Time Type Place Note
Tuesday 2:00 PM - 3:40 PM lesson Lecture Hall 1.6  
Wednesday 2:00 PM - 3:40 PM lesson Lecture Hall 2.3  
Thursday 2:00 PM - 3:40 PM lesson Lecture Hall 1.6  

Learning outcomes

One of major goal of Science is to define the relationship between objects/events of the world. This course will deal the relation between "physical world" and "psychological world". The aim is to provide students with some basic notions regarding the foundations of measurement of psychological attributes. The course will teach students how to use some pratical and formal tools to measure psychological constructs.


- Understand what you are talking
- Debts of Psychology
- Conceptual errors and technical errors
- Differences between physical and psychological


The Basics
- The continuum
- The unit of measure
- The Cartesian coordinates
- The constants / variables
- The functions of linear and non-linear (and their rectification)
- Working with functions via software


- Definitions
- Empirical operations
- The scales
- The descriptive statistics


Set theory
- The concept of set
- Membership
- Graphical representation of a set
- Definition of a set. Properties and characteristics
- Empty set
- Equivalent sets
- Subsets
- Sets of parties or the family of subsets
- Universe set
- Sets of numbers

Operations between sets
- Union
- Intersection
- Disjoint sets
- Partition of a set
- Set-difference
- Complement
- Cartesian product between sets

- Binary relation between two sets
- Domain of a binary relation
- Graphical representation of a binary relation
- Codomain of a binary relation
- Relation of a binary set
- Relation inverse
- Relation of a n-ary set
- Relation can be expressed by mathematical formulas
- Properties of binary relations defined on a set

Equivalence relations
- Class of equivalence
- Partition associated with an equivalence relation
- Equivalence relation associated with a partition
- Quotient set
- Principle of contraction

Order Report
- Strict partial order
- Total strict order
- Large Partial Order
- Properties of large partial order
- Large total Order
- Total Properties of large orders
- Sets sorted

- Graphical representation of a function
- Image set of a function
- Inverse image set of a function
- Independent variables and dependent variables
- Function injection
- Function surjective
- Two-way Function
- Inverse function
- Function composed
- Reports and functional correlations
- Functions of n variables
- Relational Systems


Measurement theory
- What does it mean "to measure"?
- The concept of measurement
- Non-numerical measures
- Historical Introduction

Empirical and numerical relational systems
- Numerical relational system
- Empirical relational system

Types of empirical relational systems
- Binary empirical relational system
- Classification system
- Empirical series
- Almost empirical series
- Sorted empirical systems
- Empirical quaternary systems
- System of empirical differences
- An empirical system of finite differences and monospaced
- Systems of infinite empirical differences
- Additives systems

Types of number systems
- Numerical classification system
- Numerical Series
- Nearly numerical series
- System of numerical differences
- Additive number system
- Multiplicative number system

- Homomorphism
- Isomorphism
- Endomorphism
- Automorphism
- Properties of morphisms

Definition of measurement and measurement scale
- Definition of measurement
- Measuring
- Equivalent scales

- Representation Theorem
- Uniqueness theorem
- Permissible transformations

Types of measurement scales
- Nominal Scale
- Ordinal Scale
- Interval Scale
- Ratio Scale
- Characteristics of cumulative scales

Classificatory systems of measures: the nominal scale
- The representation theorems
- Uniqueness theorem
- Graphical representation of the representation and uniqueness theorem for the measurement of the classificatory systems
- Construction of a numerical system to a homomorphic empirical system of classification
- Nominal Scale

Size of an ordered system: the ordinal scale
- Representation Theorems
- Uniqueness theorem
- Ordinal Scale
- Construction of a scale to measure an empirical system ordered

Size differences of empirical systems: interval scales
- Representation Theorems
- Uniqueness theorem
- Construction of a measure of an empirical system of infinite differences
- Scale interval

Additive systems: scale ratio

Invariance of the statistics
- Invariance of reference
- Invariance of comparison
- General definition of significance


Introduction to Psychophysics
- The equation of Weber
- The equation of Fechner
- The equation of Thurstone
- The equation of Torgerson
- The equation of Stevens

Classical Psychophysical methods
- The method of constant stimuli
- The method of limits
- The method of adjustment

Signal detection theory
- The sensitivity of the system
- The criterion

In depth
- Calculation of the sensitivity
- Calculation of the response criterion
- The odds ratio
- The relationship between response criterion and criterion of optimal effective response
- Practical utility of the index of sensitivity and response criterion
- The schemes gain / loss
- The ROC (Receiver Operating Characteristic)
- The correction of the ROC curves
- The calculation of the sensitivity of the network using ROC
- The calculation of the response using the straight line ROC
- The invariance of the ROC straight
- The curves isocriterio

The classical methods for the one-dimensional scaling
- The method of paired comparisons
- Methods for the generation of scales equisezione
- The method of bisection
- The method of equi-section
- Methods for generating stairs partition
- The method of classification (category ranks)
- The ranking method
- The method of apparently equal intervals
- Methods for the generation of rating scales
- Methods for the generation of value scales
- The method of estimating the relationship
- The method of production report
- The method of magnitude estimation
- The method of magnitude production

Assessment methods and criteria

The exam will be a written task with 30 closed questions with 3 alternatives each and one correct answer only.

Texts for the exam:

1) Purghè Franco (1997). Metodi di psicofisica e scaling unidimensionale.

2) Teacher slides (DOWNLOAD SLIDES)

NB: book and slides take into account the same topics. Following parts of the book useful for the assessment:

Cap 1 - All

Cap 2 - From pg. 63 to pag. 67 - From pg. 71 to pg. 79 - From pg. 90 to pag. 93 - From pg. 102 to pg. 111 - From pg. 113 to pg. 115

Cap 3 - From pg. 138 to pg. 180

Cap 4 - From pg. 208 to pg. 215 - From pg. 218 to pg. 220 - From pg. 244 to pg. 251 - From pg. 264 to pg. 271 - From pg. 284 to pg. 293 - From pg. 296 to pg. 301 - From pg. 310 to pg. 311 - From pg. 320 to pg. 327

APPENDIX 1 - From pg. 343 to pg. 365