Quantitative methods for the social science - Appunti esame

Methodology

A systematic, theoretical analysis of the methods applied to fields of study

A way to achieve research aims

Correct procedures

Positivism

Social phenomena are independent from the interpretation given by the subject

Social phenomena are knowable in an objective way

Formulation of universal laws (valid and unchangeable, expressed in a mathematical language)

Aim: explanation of social facts in terms of cause and effect

Procedures are mainly inductive (from particular to general)

Universal laws are derived from empirical observation

Comte and Durkheim

Neopositivism

Social reality exists outside the individual ontological realism

Social reality is objectively understandable

The meaning of a proposition is the method of its verification — the language of variables

Social reality can be studied by means of the same method as the natural sciences

Postpositivism (1960 onwards)

Probability and uncertainty: scientific laws are temporary and uncertain

Social reality is...

Mixed methods now are common in the social sciences.

Quantitative research:

• Creative process of discovery
• Prestablished itinerary
• Predetermined procedures

Five stages connected by a process:

1. Theory (deduction)
2. Hypothesis (operationalisation)
3. Data collection (data matrix)
4. Data analysis (interpretation)
5. Results (induction)

In case of a secondary analysis (already collected data) you can skip the data collection phase.

Theory — a set of organically connected propositions located at a higher level of abstraction and generalisation than empirical reality and which are derived from empirical patterns and from which empirical forecast can be derived.

For example, straight line assimilation theory: the longer an immigrant lives in a country, the more they integrate into it.

Hypothesis — a proposition that implies a relationship between two or more concepts, located on a lower level of abstraction and generalisation than the theory and which enables the theory.

to be transformed into terms that can be tested empirically.

• ex. There is a positive relationship between the time spent in the receiving country and their level of proficiency in the language of that country

Concepts in social research:

• Applied to objects
• Applied to properties (of the observed objects)

Objects of the research are subjects to which studied properties refer to

• To detect the object it is necessary to start from the property of the object
• The same properties can be applied to several empirical referents

Ex the property income. I suppose that there is a relation with the property gender. The same property (income) can be applied to different objects of research (household)

The Object is a tool which permits to establish relationships among properties (hypothesis)

Unit of analysis = a major entity used by the researcher in his study, a social object to which the properties investigated appertain (unit-individual;

unit-family;unit-organisation…)

Cases = specimens (subsets) of a given unit of analysis and it is on these that the data are recorded. They are multiple and concrete and constitute the specific objects of empirical research. They are selected through a set of rules (sampling)

Properties (ex marital status) vary in the same case over time4 fi ff fi

Properties (ex gender) vary among cases at the same time

If they do not vary they are constants

Operationalisation = from property to variable (in different ways)

• It depends on social research's interest; unit of analysis and context
• Concept: weight; property explored on a book (object of analysis); operationalisation —> o,7 kg is the variable

Operational definition is a set of rules and procedures which permit to transform a property into a variable

Operationalisation is the application to concrete cases studies (practical implementation of the operational definition)

Property = age varies among the cases

= the different ages are the states

• Operational definition and its application —> age becomes a variable and we have categories instead of states
• Indicators —> simpler 'specific' concepts that can be transformed into observational terms (can be operationalised) and linked to the 'general' concept by a relation of indication or semantic representation (each one may be linked to more than one concept - extraneous portion)

Indicator's for exploring students' academic career (examples)

• Number of years enrolled in the Course
• Number of CFU obtained
• Number of years spent abroad
• Hours of lesson per year
• Number of degree achieved (including first cycle, second cycle)

Measurement error

• Observed value = true value (concept) + systematic error + random error
• Systematic error (bias) is a consistent error (present in all the data), the mean value is not equal to 0 —> observed value tends systematically to over

orunder-estimate the true value (in the theoretical phase if we select a wrong indicator we will commit a systematic error —> no semantic representation/Indication error; in the empirical phase we can commit an operationalisation error - usually random but can be systematic:

• Selection:
  • Coverage
  • Sampling
  • Non-response
• Observation
  • Mode
  • Instrument
  • Interviewer
  • Respondent 9
• Data processing
  • Random error is a variable error (it varies both from one sample of individuals to another and in repeated observations on the same cases) —> the mean value is equal to 0
• Validity: degree to which a given procedure for transforming a concept into a variable actually operationalises the concept that it is intended to
  • ex. IQ is not considered as a valid indicator of individual’s intelligence
• Validity testing: validity is unmeasurable and linked to systematic error
  • Content validity: validation takes place

only at a purely logical level —> logical validation of the semantic relationship between the selected indicator and the concept

• Criterion-related validity: correlation between an indicator (or a set of them) and a variable (criterion) which is deemed to be correlated with the concept and its validity has been already affirmed:
• Predictive validity —> correlation between indicator and a subsequent event (criterion) - ex. To test the validity of a university entrance test (indicator) we can analyse if it's correlated with the marks obtained in subsequent exams (criterion). If there's a correlation then the indicator is valid
• Concurrent validity —> correlation between an indicator and a criterion recorded at the same moment in time - to test the validity of indicator of political conservatism/progressivism we can collect data simultaneously with the criterion (voted political party)
• Validity for known groups —> indicator is 'tested'

on subjects whose position is known with regard to the property under investigation (subjects belonging to a political party)

• Construct validity: is judged on the basis whether an indicator corresponds to theoretical expectations in terms of relationship with other variables
• Reliability is the degree to which a given procedure for transforming a concept into a variable produces the same results in tests repeated with the same empirical tools (stability) or equivalent ones (equivalence)
• Reliability is linked to a random error and measurable

Test-retest reliability: repeated administration of the same stimulus on the same subjects and calculation of the correlation between the results

Equivalence: correlation between two distinct diverse albeit similar procedures

• Split-half: reliability is indicated by the correlation between two halves of the same test
• Parallel forms: two tests are defined 'parallel' when they are assumed to gauge the same underlying

‘true value’ and to di er only in terms of random error- Internal consistency (index Cronbach’s Alpha): random errors vary not only from test to test but also from question to question —> correlation of the answers to each question with the answers to all other questions. If the index is 0 no internal consistency (0-1). Our set is reliable is at least equal to 0.7- Property has to vary —> it has to assume di erent states either from case to case at the same time or in the same cases over time- Property has to be operationalised —> di erent states must be detected and recorded in a data-matrix1. ex. Religious orientation (general property)2. states assumed by the property:- Jewish- Catholic- Muslim- Buddhism…3. Transform the property and states in a variable with modalities …- ‘Fundamentum Divisionis’ : only one classi cation criterion• Mutual exclusiveness: each case classi ed just in one category- Exhaustiveness:

All cases must be classified in one category (you can use the category 'other').

Properties may be discrete: property takes on a finite number of states.

Operationalisation process: Classification -> nominal variable/categorical variable (non-orderable states).

Operationalisation process: Ordering -> ordinal variable (ordinal states).

Ordinal variables can be studied also through scaling.

Operationalisation process: Counting -> interval/cardinal variable (countable states).

Or continuous: property takes on an infinite number of intermediate states in a given range between any of two states.