Small N - Large N: Some Alternatives

Research Methods Festival, Oxford, July 2006 Small N - Large N: Some Alternatives Ray Kent University of Stirling

Limitations of mainstream quantitative methods • The focus is on the variable • The thinking in linear • The main pattern sought is covariation

Traditional analysis expects to see this: Cramer’s V =0.96

Or this: (Var Y) r = 0.86 (Var X)

But we often get this: Phi (Cramer’s V) = 0.37 Lambda = 0.0 Heavy television viewing is a sufficient, but not necessary condition for large expenditure on convenience food

Or this: r = 0.3

Further limitations • Not good at handling causal or logical relationships • Poor at handling complexity

Some common misuses • The use (even reliance) on statistical inference on non-random samples or total populations • Causal inferences based on establishing covariation • Poor, vague wording of hypotheses

Some alternatives to mainstream statistics • Combinatorial logic • Fuzzy-set analysis • Neural network analysis • Data mining • Bayesian methods • Chaos/tipping point theory

Combinatorial logic Instead of comparing variable distributions, we see cases as combinations of characteristics

A data matrix on SPSS

The frequency of 2k combinations of 3 binary causal variables plus binary outcome X1 is a necessary, but not sufficient, cause of Y

A fuzzy set

X1 is a necessary, but not sufficient, condition for Y to occur The degree of membership of X1sets a ceiling on the degree of membership of Y

X1 is a sufficient, but not necessary, condition for Y to occur High membership of X1 acts as a floor for high membership of Y

Some other alternatives • Neural network analysis • Data mining • Bayesian methods • Chaos/tipping point theory

Small N - Large N: Some Alternatives