# THE FUNDAMENTALS OF MEASUREMENT IN PSYCHOLOGY (2019/2020)

### Course partially running (all years except the first)

Course code
4S000609
Name of lecturer
Roberto Burro
Coordinator
Roberto Burro
Number of ECTS credits allocated
6
M-PSI/01 - GENERAL PSYCHOLOGY
Language of instruction
Italian
Period
Sem. 1B dal Nov 11, 2019 al Jan 11, 2020.

#### Learning outcomes

One of the major objectives of science is to define the relationships between objects / events in the world. This course will deal with the study of the relationships existing between "physical world" and "psychological world". The main purpose is to provide students with some basic notions regarding the measurement of psychological attributes. The course will teach students how to use some practical and formal tools to measure psychological constructs.

#### Syllabus

WHY MEASURE IN PSYCHOLOGY
- Understand what you are talking about
- Debts of Psychology
- Conceptual errors and technical errors
- Discrepancies between physical and psychological

NOTES OF MATHEMATICAL ANALYSIS AND ANALYTICAL GEOMETRY
Basic concepts
- The continuum
- The unit of measurement
- Cartesian coordinates
- The constants / variables
- Linear and non-linear functions (and their rectification)
- Work with the functions via software

MEASURE IN PSYCHOLOGY
- Definitions
- Empirical operations
- Measurement scales
- Descriptive statistics

BASIC CONCEPTS FOR MEASURING THEORY
Set theory
- The concept of a whole
- Membership
- Graphic representation of a set
- Definition of a set. Properties and characteristics
- Empty set
- Equal sets
- Subsets
- Set of parts or family of subsets
- Together universe
- Sets of numbers

Operations between sets
- Union
- Intersection
- Disjointed sets
- Partition of a whole
- Set difference
- Complement
- Cartesian product between sets

Relations
- Binary relationship between two sets
- Domain of a binary relationship
- Graphical representation of a binary relationship
- Codex of a binary relation
- Binary relationship in a whole
- Reverse relationship
- N-air relationship in a whole
- Reports expressed by mathematical formulas
- Properties of binary relations defined in a set

Equivalence relations
- Equivalence class
- Partition associated with an equivalence relation
- Equivalence report associated with a partition
- Quotient together
- Principle of contraction

Order report
- Partial narrow order
- Total strict order
- Partial large order
- Properties of partial wide orders
- Total wide order
- Properties of total wide orders
- Sorted sets

From sets to functions
- Graphical representation of a function
- Image set of a function
- Together against an image of a function
- Independent variables and dependent variables
- Injective function
- Surjective function
- Bi-univocal function
- Reverse function
- Compound function
- Functional relationships and correlations
- Functions of n variables
- Relational systems

MEASUREMENT THEORY
The theory of measurement
- What it means 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
- Ordered empirical systems
- Quaternary empirical systems
- Empirical system of differences
- Empirical system of finite and equispaced differences
- Infinite empirical systems of differences
Types of numerical systems
- Numerical classification system
- Numerical series
- Almost numerical series
- Numerical system of differences
- Numerical multiplicative system

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

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

theorems
- Representation theorem
- Theorem of uniqueness
- Permissible transformations

Types of measurement scales
- Nominal scale
- Ordinal scale
- Interval scale
- Scale to report
- Cumulative characteristics of the measurement scales

Measurements of classification systems: the nominal scale
- The representation theorems
- Theorem of uniqueness
- Graphical representation of the representation and uniqueness theorem for the measurement of classification systems
- Construction of a homomorphic numerical system to a classifying empirical system
- Nominal scale

Measure of an ordered system: the ordinal scale
- Representation theorems
- Theorem of uniqueness
- Ordinal scale
- Construction of a scale of measurement of an ordered empirical system

Measurement of empirical systems of differences: interval scales
- Representation theorems
- Theorem of uniqueness
- Construction of a measure of an infinite empirical system of differences
- Range scale

Invariance of statistics
- Reference invariance
- Comparative invariance
- General definition of significance

PSYCHOPHYSICS
Introduction to Psychophysics
- Weber's equation
- The Fechner equation
- The Thurstone equation
- The Torgerson equation
- The Stevens equation

The methods of Classical Psychophysics
- The method deglistimoli constant
- The method of limits

The theory of signal detection
- System sensitivity

Insights
- Calculation of the sensitivity index
- Calculation of the answer criterion
- The probability ratio
- Ratio between optimal response criterion and effective response criterion
- Practical utility of the sensitivity index and the response criterion
- The gain / loss schemes
- ROC (Receiver Operating Characteristic) curves
- The correction of the ROC curves
- The calculation of the sensitivity index using the ROC network
- The calculation of the response criterion using the ROC lines
- The invariance of the ROC lines
- Isocriterio curves

Classic methods for one-dimensional scaling
- The method of comparison in pairs
- The bisection method
- The method of equivalence
- The method of the following categories
- The method of rank order
- The method of perceptually equal intervals
- The constant sum method
- The classification method (category ranks)
- The ranking method
- Methods for the generation of evaluation scales
- Methods for generating reporting scales
- The ratio estimation method
- The method of report production
- The method of estimating size
- The method of production of size

 Author Title Publisher Year ISBN Note Franco Purghè METODI DI PSICOFISICA E SCALING UNIDIMENSIONALE (Edizione 1) Bollati Boringhieri 1997 9788833955841

#### Assessment methods and criteria

EDUCATIONAL MODE

The teaching methods consist of lectures dedicated to the transmission of the basic notions (as planned), key categories and fundamental application tools. Moreover, thanks to the University e-learning platform, specific materials and updating readings of the subject discipline are proposed, where deemed useful. Furthermore, throughout the academic year, the individual reception service managed by the teacher is available at the times indicated on the web pages (without having to set a specific appointment). Attending students will receive in the first lesson the complete calendar of educational activities with dates and topics covered in the lessons which are provided the timetable, the classroom and the indication of any suspension for academic reasons. No program distinction is made between attending and non-attending students.

TEXTS FOR THE EXAM

1) Purghè Franco (1997). Psychophysical and one-dimensional scaling methods. 2) Handouts provided in class by the teacher NB: text and notes show the same arguments. The text should be seen as a deepening of the dispensation, especially useful for students who have not attended the course. Here are the parts of the book useful at the end of the exam: Chapter 1 - Everything Chapter 2 - From page 63 to page 67 - From page 71 to page 79 - From page 90 to page 93 - From page 102 to page 111 - From page 113 to page 115 Chapter 3 - From page 138 to page 180 Chapter 4 - From page 208 to page 215 - Page 218 to page 220 - Page 244 to page 251 - Page 264 to page 271 - Page 284 to page 293 - Page 296 to page 301 - Page 310 to page 311 - From page 320 to page 327 APPENDIX 1 - From page 343 to page 365

EXAMINATION METHODS

NB: Following the health emergency due to Covid-19, the usual examination procedures are changed for the 2020 summer session, in accordance with the indications of the University. Specifically: "the exam will be held orally using Zoom".

The exam taken during an official call will consist of a 30-minute multiple choice question (30) (3 answers alternatives, only one of which is correct.) For the final judgment expressed in thirtieths, a correct answer has value equal to 1 point, an incorrect answer has a value equal to 0 points, an answer not given has a value equal to 0 points).