by Causal traps of statistics .[embedded content] Statistical reasoning certainly seems paradoxical to most people. Take for example Simpson’s paradox. From a theoretical perspective, it importantly shows that causality can never be reduced to a question of statistics or probabilities unless you are — miraculously — able to keep constant all other factors that influence the probability of the outcome studied. To understand causality we always have to relate it to a specific causal structure. Statistical correlations are never enough. No structure, no causality. Simpson’s paradox is an interesting paradox in itself, but it can also highlight a deficiency in the traditional statistical/econometric approach toward causality. Say you have 1000 observations on
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Causal traps of statistics
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Statistical reasoning certainly seems paradoxical to most people.
Take for example Simpson’s paradox. From a theoretical perspective, it importantly shows that causality can never be reduced to a question of statistics or probabilities unless you are — miraculously — able to keep constant all other factors that influence the probability of the outcome studied.
To understand causality we always have to relate it to a specific causal structure. Statistical correlations are never enough. No structure, no causality.
Simpson’s paradox is an interesting paradox in itself, but it can also highlight a deficiency in the traditional statistical/econometric approach toward causality. Say you have 1000 observations on men and an equal amount of observations on women applying for admission to university studies, and that 70% of men are admitted, but only 30% of women. Running a logistic regression to find out the odds ratios (and probabilities) for men and women on admission, females seem to be in a less favourable position (‘discriminated’ against) compared to males (male odds are 2.33, female odds are 0.43, giving an odds ratio of 5.44). But once we find out that males and females apply to different departments we may well get a Simpson’s paradox result where males turn out to be ‘discriminated’ against (say 800 males apply for economics studies (680 admitted) and 200 for physics studies (20 admitted), and 100 female apply for economics studies (90 admitted) and 900 for physics studies (210 admitted) — giving odds of 0.62 and 0.37).
Statistical patterns should never be seen as anything else than possible clues to follow. Behind observable data, there are real structures and mechanisms operating, things that are — if we really want to understand, explain and (possibly) predict things in the real world — more important to get hold of than to simply correlate and regress observable variables.
Statistics cannot establish the truth value of a fact. Never has. Never will.