Large-N && Small-N
Analysis in Innovation
studies
Beyond the quantitative-qualitative divide
OPENINNOVA::David Lopez
Creative Commons Attribution ShareAlike 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/ )

Two main approaches to social science

analysis:
Quantitative Qualitative
analysis analysis
Quantitative versus Qualitative Analysis in Social Sciences
OpenInnova:David López

Quantitative analysis:

◦ Large-N approach (extensive use of cross-
sectional data)
Theory
Empirical
Model
Data
Multivariate
Analysis
Large N approach. Provides answers to: what causes
revolutions ? OpenInnova:David López

Qualitative analysis:

◦ Small-N approach (qualitative comparisons of
cases)
Cases
“Soft Qualitative
Model” analysis
Causal
chains
Small-N approach. Provides answers to: what caused the
French revolution ? OpenInnova:David López

 When it comes to policy analysis, such as innovation
regimes and R&D, statistical inference is not
enough, holistic approaches are needed in order to:
◦ Explore several combinations and their consequences.
◦ Conduct context-specific assessments.
 For instance: What It takes to avoid poverty ?
◦ Does college education make a difference for married white
males from families with good incomes ?
◦ And college education for unmarried black females from
low-income families ?
Moreover, what about scenarios with limited data

such as OECD innovation database for instance ?
Small-N analysis in policy research (innovation is about policy
after all) OpenInnova:David López

 Small-N approaches consider cases as combinations
of causally relevant conditions
College High Parent High Poverty Number
Educated Parental College AFQT avoidance of cases
income educated Score
1 0 0 0 0 0 30
2 0 0 0 1 0 3
3 0 0 1 0 ? 4
….
16 1 1 1 1 1 23
Causal conditions Outcome
Goal of the analysis: Identify different combinations of

case characteristics explicitly linked to poverty
avoidance.
Small-N Analysis by example: Avoiding poverty (I) López
OpenInnova:David

But…. what do we mean by “High parental

income” ???
 How strong is the inference:
 CollegeAvoiding poverty
Charles Ragin suggests Fuzzy-set logic.

High
High parental
parental income
income
Low
Low
parental
parental
income
income
Small-N Analysis : Fuzzy-set approach OpenInnova:David López

Y
Xi
Xi→Y
Consistenc y ( X i Yi ) (min( X i , Yi )) (Xi)
Small-N Analysis: Sufficiency && Consistency
OpenInnova:David López

Xi
Y
Y →Xi
Consistenc y (Y i Xi) (min( X i , Y i )) (Y i )
Small-N Analysis: Necessity && ConsistencyOpenInnova:David López

Y Y Y
Xi2
Xi
Xi
Xi1
Xi→Y Xi→Y
X1* X2 →Y
Coverage ( X i Yi ) (min( X i , Y i )) (Y i )
Small-N Analysis: Sufficiency && Coverage OpenInnova:David López

Data from 18 European countries (Ragin 2008).
COUNTRY SURVIVED BREAKDOWN DEVELOPED URBAN LITERATE INDUSTRIAL STABLE
Austria 0,01 0,99 0,74 0,14 0,98 0,76 0,35
Belgium 0,98 0,02 0,99 0,89 0,96 0,98 0,96
Czech 0,85 0,015 0,42 0,96 0,97 0,91 0,87
Estonia 0,12 0,88 0,15 0,07 0,96 0,02 0,87
Finland 0,64 0,36 0,43 0,03 0,98 0,09 0,51
France 0,98 0,02 0,97 0,02 0,97 0,83 0,93
Germany 0,01 0,99 0,85 0,83 0,98 0,96 0,23
Greece 0,03 0,97 0,05 0,1 0,11 0,38 0,35
Hungary 0,41 0,59 0,08 0,2 0,81 0,08 0,09
Ireland 0,91 0,09 0,62 0,04 0,96 0,02 0,93
Italy 0,01 0,99 0,25 0,11 0,38 0,49 0,51
Netherland 0,98 0,02 0,97 0,99 0,99 0,94 0,99
Poland 0,12 0,88 0,03 0,22 0,55 0,02 0,02
Portugal 0,01 0,99 0,02 0,01 0,02 0,12 0,02
Romania 0,25 0,75 0,02 0,03 0,15 0,02 0,78
Spain 0,03 0,97 0,04 0,41 0,08 0,22 0,14
Sweden 0,98 0,02 0,93 0,15 0,99 0,7 0,87
UK 0,98 0,02 0,98 0,98 0,99 0,98 0,96
Outcome
fzQCA in Action: Democracies in interwar Europe (1918-1936)
OpenInnova:David López

DEVELOPED URBAN LITERATE INDUSTRIAL STABLE number survivedconsist
1 1 1 1 1 3 0.884337
1 0 1 0 1 1 0.773810
1 1 0 0 0 0 0.741379
1 1 0 0 1 0 0.736842
1 1 0 1 0 0 0.727273
1 1 0 1 1 0 0.727273
1 0 1 1 1 2 0.725352
0.5 1 1 1 0 1 0 0.712871
1 1 1 0 0 0 0.694737
0 1 1 1 1 1 0.675497
1 0 1 0 0 0 0.674556
0 1 1 0 0 0 0.627907
0 1 1 0 1 0 0.620000
1 0 0 0 0 0 0.594595
1 0 0 0 1 0 0.589041
0 1 0 0 1 0 0.589041
1 0 0 1 1 0 0.577465
1 0 0 1 0 0 0.577465
0 1 0 1 1 0 0.552239
0 1 1 1 0 0 0.528846
0 0 1 0 1 2 0.508197
0 0 1 0 0 2 0.506173
0 1 0 1 0 0 0.493333
0 1 0 0 0 0 0.484615
1 1 1 1 0 1 0.392857
1 0 1 1 0 1 0.379310
0 0 1 1 1 0 0.370629
0 0 1 1 0 0 0.370629
0 0 0 0 1 2 0.306977
0 0 0 1 1 0 0.287879
0 0 0 1 0 0 0.248366
0 0 0 0 0 3 0.225543
fzQCA in Action: Democracies in interwar Europe (1918-1936)
OpenInnova:David López

DEVELOPED URBAN LITERATE INDUSTRIAL STABLE number survivedconsist
1
1 1 1 1 1 3 0.884337
0
0 0 0 0 0 3 0.225543
1
1 0 1 0 1 1 0.775352
0
0 0 1 0 1 2 0.508197
0
0 0 1 0 0 2 0.506173
0
0 0 0 0 1 2 0.306977
0
1 0 1 0 1 1 0.773810
0
0 1 1 1 1 1 0.675497
0
1 1 1 1 0 1 0.392857
0
1 0 1 1 0 1 0.379310
Consistent
enough
0.75
Non consistent
fzQCA in Action: Democracies in interwar Europe (1918-1936)
OpenInnova:David López

Least parsimonious solution (remainders not considered)

If all five conditions are present then is sufficient for a democracy to

survive.
But NOTurban and NOTindustrial does not really seem to matter

much:
DEVELOPED*LITERATE*STABLE  SURVIVAL
fzQCA in Action: Democracies in interwar Europe (1918-1936)
OpenInnova:David López

Considering Breakdown instead of Survival as the outcome of interest:

Two sufficient conditions emerge:

NOT DEVELOPED * NOT URBAN * NOT INDUSTRIAL  BREAKDOWN

DEVELOPED*LITERATE*INDUSTRIAL*NOT STABLE  BREAKDOWN

fzQCA in Action: Democracies in interwar Europe (1918-1936)
OpenInnova:David López

Nested analysis approach (Evan S. Lieberman)
The best of both worlds ? Just adding extra workload ?
OpenInnova:David López

Triangulation
Nested analysis approach (Evan S. Lieberman)
The best of both worlds ? Just adding extra workload ?
OpenInnova:David López