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

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

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Cramers V =0.96 Traditional analysis expects to see this:

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

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

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Or this: r = 0.3

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

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

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Some alternatives to mainstream statistics Combinatorial logicCombinatorial logic Fuzzy-set analysisFuzzy-set analysis Neural network analysisNeural network analysis Data miningData mining Bayesian methodsBayesian methods Chaos/tipping point theoryChaos/tipping point theory

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

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A data matrix on SPSS

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X 1 is a necessary, but not sufficient, cause of Y The frequency of 2 k combinations of 3 binary causal variables plus binary outcome

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A fuzzy set

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X 1 is a necessary, but not sufficient, condition for Y to occur The degree of membership of X 1 sets a ceiling on the degree of membership of Y

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X 1 is a sufficient, but not necessary, condition for Y to occur High membership of X 1 acts as a floor for high membership of Y

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Some other alternatives Neural network analysisNeural network analysis Data miningData mining Bayesian methodsBayesian methods Chaos/tipping point theoryChaos/tipping point theory

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