Principles and Strategies of Quantitative Data Analysis

SLC515

Research Methods for Socio-Legal Studies and Criminology

2007/2008

Outline

Foundation of QR: PositivismValidity and reliability in QRCore issues of concern in QRCritique of QR

Outline

Descriptive and inferential statisticsInferential Statistics

Crosstabs CorrelationRegression

Positivism - Historical Facts

16/17th century: blooming of European thought Beginning of modern science Auguste Comte (1798-1857):

Sociology as the “queen” of social sciences “Social physics”; idea of progress, social science works like

natural science Precise and certain methods, basing theoretical laws on

sound empirical observation Knowledge is derived from empirical evidence

19th century: natural sciences gain influence impacts thinking in social science

Positivism - Emile Durkheim (1858-1917)

Human and material phenomena are equally real but human phenomena cannot be reduced to pure material facts.

Social facts - society as a moral reality, expressed in institutions such as law, religion etc. which are external to us and constrain us.

Sociologists should describe characteristics of facts and explain how they came into being. Explanation of social facts by causes: single cause effect, law-like relationship Same general methods of scientific inquiry can be used.

Positivism - Key Elements

Social research as ‘science’ Universal laws - testing theories Cause and effect relationships between

variables Solid methods Value neutral Objectivity

Science is …

Positivism

Interpret. Soc.

Science

Critical perspectiv

eBased on strict rules procedures

Just common sense (no science)

Between the positions of positivism and interpretivism

Deductive Inductive Emancipating, empowering

Nomothetic (based on laws)

Relies on interpretations

Brain-washed, misled, conditioned

Value free Not value free Not value free

Adapted from Sarantakos (1993) Table 2.2, page 38.

Purpose of research …

Positivism Interpr. Soc.

Science

Critical perspective

To explain facts/causes/

effects

To interpret the world

To get below the surface; to expose real relations

To predict To understand social life

To disclose myths and illusions

Emphasises removing false beliefs/ideas, emancipation and empowerment

Adapted from Sarantakos (1993) Table 2.2, page 38 & 39.

Theories, Hypotheses and Research Design

Deductive approach Theory testing Derive hypotheses from theory (if… then…

sentences) and test them Research design:

Cross-sectional survey Longitudinal design Case study design Comparative design

Operationalisation

Translation of a theoretical concept into something that can be measured Example (natural sciences): temperature - degrees

Celsius, velocity - km/h

How do you measure the frustration caused by unemployment or the level of alienation in a society or a society’s satisfaction with its government?

Operational definition through indicators

Indicators

Difference between a measure and an indicator (quantities versus complex concepts)

An indicator is employed as though it were a measure of a concept.

Example: job satisfaction

Research Sites and Subjects

Depending on research design, methods and sources of data

Establish an appropriate setting:Decisions are involved: where? and who?

Sampling strategiesProbability and non-probability samplingRepresentative sample - generalizability

Collecting and Processing Data

Depends on the chosen research design: Experiments: pre- and post-testing Survey interviews: questionnaire and interviews Etc.

Gathered information is then transformed into ‘data’ Information will be quantified - coding - to be

processed by a computer

Analysing Data and Research Findings

Statistical techniques/analysis, special software Results/findings have to be interpreted based

on theoretical reflections in the beginning (verification/falsification of hypotheses)

Objectives of QR: Support or reject theoretical concepts or findings of

other studies Detecting trends, patterns Uncover common sense knowledge Building typologies

Writing up Findings and Conclusion

Results enter the public domainConference paper, article, report, thesis,

bookSignificance and validity of findingsImplications? (policy advice etc.)Presentation of quantitative data is

different than in qualitative research

Validity and Reliability

Validity, reliability and generalizability are measures of the quality, rigour and wider potential of research Validity = are you observing what you want to

observe (construct validity) Is your set of indicators really measuring what you want to

measure? Reliability = are the measures, devised for the

concept, concise (stability of measure) Stability over time, consistency of indicators (internal

reliability) and observers (inter-observer consistency)

Core Issues of Concern in QR

Measurement Causality - Explanation (dependent and

independent variable)Generalisation (representative sample)Replication Testing theory

Critique of QR

Positivism vs. interpretive social sciences

Objectivity?

Generalization - but too simplistic?

Causality

Contrasting Qualitative and Quantitative Research

Quantitative Numbers Researcher’s view Researcher distant Theory testing Static Structured Generalization Hard, reliable data Macro Behaviour Artificial setting

Qualitative Words/Text Participant’s view Researcher close Theory emergent Process Unstructured Contextual Rich, deep data Micro Meaning Natural setting

Descriptive and Inferential Statistics

Univariate Descriptive analysis of one variable (column in data

set)

Bivariate Relationship between two variables

Dependent and independent variables Relation between dependent and independent variables Differences between dependent and independent

variables

Bivariate Analysis

Questions we can ask: Is the relationship significant? If so, how strong is the relationship? In which direction does the relationship go?

Positive relationships Negative relationships

Some statistical tests: Crosstabulation Correlation Regression analysis

Cross Tabs

All levels of measurement are allowedCross tabs express common frequencies

of the categories of two different variables

Significance test: CHI SquareHow strong?: lambda, gamma, r2Which direction?: gamma, tau

Example

? High-school

Coll Uni Rowtotal

Working class

74850.4%

8713.9%

1010.2%

215.1%

86633.1%

Middle class

69446.8%

47475.6%

6768.4%

26664.9%

150157.3%

Upper class

422.8%

6610.5%

2121.4%

12330.0%

2529.6%

Column total

148456.7%

62723.9%

983.7%

41015.7%

2619100%

Example

Grouped literacy rates * Grouped GDP Crosstabulation

5 1 0 0 0 6

83.3% 16.7% .0% .0% .0% 100.0%

17.9% 3.6% .0% .0% .0% 5.6%

15 4 0 0 0 19

78.9% 21.1% .0% .0% .0% 100.0%

53.6% 14.3% .0% .0% .0% 17.8%

5 7 5 1 2 20

25.0% 35.0% 25.0% 5.0% 10.0% 100.0%

17.9% 25.0% 22.7% 16.7% 8.7% 18.7%

3 16 17 5 21 62

4.8% 25.8% 27.4% 8.1% 33.9% 100.0%

10.7% 57.1% 77.3% 83.3% 91.3% 57.9%

28 28 22 6 23 107

26.2% 26.2% 20.6% 5.6% 21.5% 100.0%

100.0% 100.0% 100.0% 100.0% 100.0% 100.0%

Count

% within Groupedliteracy rates

% within Grouped GDP

Count

% within Groupedliteracy rates

% within Grouped GDP

Count

% within Groupedliteracy rates

% within Grouped GDP

Count

% within Groupedliteracy rates

% within Grouped GDP

Count

% within Groupedliteracy rates

% within Grouped GDP

Very low literacy

Low literacy

Medium literacy

High literacy

Groupedliteracyrates

Total

Very low GDP Low GDP Medium GDP High GDPVery high

GDP

Grouped GDP

Total

Correlation

Correlations measure statistical associations, but do not allow any inferences about causal patterns

Requirement: Ordinal and interval data Normally distributed and linear relation

Coefficient: Pearson’s r (interval data) Spearman’s correlation coefficient (ordinal data)

Example

Correlations

1 .552

.000

107 107

.552 1

.000

107 109

Pearson Correlation(r)

Sig. (2-tailed)

N

Pearson Correlation(r)

Sig. (2-tailed)

N

People who read (%)

Gross domesticproduct / capita

People whoread (%)

Grossdomesticproduct /

capita

Regression Analysis

You can visualize correlation in a scatter diagram

Regression line Regression coefficients Formula: y=a+b(x) Requirements:

Interval data Normally distributed Linear relationship

Example

Controlling for Variables

Purpose of controlling for variables: e.g. exploration of variables that intervene in the relationship between other variables

Example: examination of the relationship between GDP and literacy rates in different regions of the world Independent variable: GDP Dependent variable: literacy Control variable: regions

Example

Pearson’s r was used to measure the correlation between GDP and literacy rates in three regions of the world OECD countries r=0.616 Latin America r=0.608 Africa r=0.421

Conclusion: The strength of the association between GDP and literacy rates varies between different regions. In some, GDP is a better predictor of literacy rates than in others.