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ss as a whole given its equal gender split might actually prefer ice cream this sample was random in every technical sense each child had an equal chance of being selected and chance alone determined the outcome yet it is clearly not representative of the class as a whole because it fails to reflect the crucial gender balance that shapes the underlying preference distribution randomness provides no guarantee of representativeness it merely ensures equal probability of selection and probabilities do not always produce proportional outcomes in a single draw now consider the opposite case the teacher adopts a different approach instead of drawing names from a hat she deliberately selects three boys and three girls to match the class s 50 50 gender split to do this she simply chooses the first three boys and the first three girls who raise their hands this sample perfectly mirrors the class in terms of gender and since gender is the main factor influencing food preference the sample s opinions will closely track those of the whole class it is in other words highly representative yet the procedure is clearly not random the teacher does not use chance she applies a conscious non probabilistic rule furthermore she only samples children who happen to raise their hands quickly which may exclude distracted or shy pupils thus a representative sample has been produced through a non random method demonstrating that representativeness does not require randomness what these two cases show is that randomness and representativeness answer different questions randomness tells us how a sample is selected it is a feature of the selection mechanism representativeness tells us how the sample looks like it is a feature of the sample s composition a random sample may by chance fail to capture those characteristics conversely a carefully constructed quota sample may capture them accurately without any use of chance in the end both properties are valuable for different reasons randomness is important because it enables statistical inference we can calculate margins of error and confidence intervals because the selection process is known representativeness is important because it gives us confidence that our conclusions apply to the population of interest the ideal study combines both but as my sausage and ice cream example shows in practice these are two distinct ideals a random sample can be unrepresentative and a representative sample can be non random confusing the two is a common error but it remains an error nonetheless share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky what does randomisation guarantee nothing 15 jun 2026 at 17 15 posted in statistics econometrics leave a comment the point of conducting a randomised experiment is often said to be that it allows researchers to make stronger causal inferences from observed correlations this claim rests on the idea that randomisation reduces systematic differences between treatment and control groups thereby limiting the influence of confounding factors the problem with this rather simplistic view of randomisation is that the claims made on its behalf are both exaggerated and strictly speaking false even if the assignment of subjects to treatment and control groups is perfectly random sample selection almost certainly is not except in extremely rare cases proper random assignment does not compensate for a biased sample if experimental results are derived from a non representative sample there is always a risk that the findings will not generalise beyond that setting what works there may not work here randomisation therefore does not guarantee or ensure that we arrive at the correct causal conclusion while it may help us rule out certain alternative explanations randomisation in itself guarantees nothing even if both sampling and assignment were carried out in an ideally random manner standard randomised experiments provide only average effects the difficulty is that an estimate of the true average causal effect may conceal important heterogeneity the average treatment effect may be zero while some individuals experience effects of 100 and others effects of 100 for anyone considering whether to undergo treatment such heterogeneity is likely to be far more informative than the average effect alone there is almost always a trade off between bias and precision in real world settings a small amount of bias may be more than offset by a substantial gain in precision more importantly when a population exhibits significant heterogeneity the average treatment effect estimated from a sample may differ considerably from the average treatment effect in the wider population if that is the case the value of extrapolating findings from trial samples to other populations becomes highly questionable since most real world experiments and trials involve only a single randomisation the properties that would emerge over an infinite sequence of repeated randomisations provide little reassurance about the validity of the one experiment that is actually conducted it is difficult to see why knowledge of what would happen under circumstances that will never occur should make us more confident about the conclusions drawn from the single study we have performed the problem faced by many randomistas when they underestimate heterogeneity and interaction effects is not merely one of external validity when attempting to transfer regression results across periods contexts or populations it is also an internal problem affecting the millions of regression estimates produced by economists each year ideally controlled experiments can tell us with certainty what causes what effects but only given the appropriate closure assumptions making valid extrapolations from experiments whether ideal accidental natural or quasi experimental to different settings populations or target systems is far from straightforward since trials are rarely repeated properties such as unbiasedness and balance in repeated sampling tell us nothing directly about any particular trial it works there is not evidence that it will work here causes identified in an experimental setting must still be shown to possess an export warrant to the target population or system the underlying causal assumptions must be justified and without such a warrant the value of even the most rigorous and precise methods and of knowledge that holds only on average is severely limited rcts have little reach beyond describing what has occurred in the past from the perspective of future decision making and public policy they are often of limited value because they cannot tell us which background factors were held constant when the intervention was implemented nor do rcts generally provide evidence that their results are exportable to other target systems they cannot simply be assumed to yield generalisable findings the fact that something works somewhere for someone is no guarantee that it will work for us here or indeed that it works more generally randomisation may in the right circumstances help us draw causal conclusions however it is neither necessary for establishing causality nor sufficient for securing scientific validity randomisation guarantees nothing just as observational studies are vulnerable to various forms of bias so too are randomised studies and trials share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky model reification in statistics and econometrics 15 jun 2026 at 10 57 posted in economics statistics econometrics 2 comments conventional statistical methods assume that within measured covariate levels the data come from surveys with purely random selection from a sharply defined population or from experiments with purely random treatment assignment in which the researcher has complete control and understanding of every important aspect of those who entered the analysis and how they were treated the methods thus provide logically sound inferences only in ideal cases rather than correct answers for our actual imperfect applications they are however widely applied and misinterpreted in studies that fall far short of their assumptions we may view each statistical analysis as a thought experiment in a fictional small world or toy example sharply restricted by its simplifying assumptions the questions that motivated the study must be translated properly into this fictional world statistical methods then answer the questions via mathematical deductions from the assumptions but those answers apply with logical force only within a fictional world in which all the assumptions hold sander greenland since econometrics aspires to explain things in terms of causes and effects it needs many assumptions limiting model assumptions in economic science always have to be closely examined because if we are to show that the mechanisms or causes we isolate in our models are stable in the sense that they do not change when we export them to our target systems we must also demonstrate that they do not hold only under ceteris paribus conditions if they do they are of limited value to explanations and predictions of real economic systems unfortunately real world social systems are usually not governed by stable causal mechanisms or capacities the kinds of laws and relations that econometrics has established are about entities in models that presuppose invariant atomistic and additive causes but when causal mechanisms operate in the real world they mostly do so in ever changing and unstable ways if economic regularities obtain they do so as a rule only because we have engineered them for that purpose outside man made nomological machines they are rare or even non existent model reification in econometrics is evident when properties that belong strictly to models are treated as if they were real world features econometricians standardly aim to export model based mechanisms to target systems without change this metaphor itself implies reification the gap between model assumptions and messy reality is a gap that econometrics often forgets treating engineered regularities as inherent economic laws is reification pure and simple share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky why democracy outperforms dictatorship 14 jun 2026 at 10 35 posted in statistics econometrics 1 comment the power of diversity is not merely a social ideal it is a mathematical fact the diversity prediction theorem demonstrates that bringing together people who think differently generates a measurable performance advantage imagine that you fill a transparent jar with 1000 jelly beans and ask a group of students to estimate how many are inside amanda guesses 980 bob 1050 clark 1020 and david 940 individually their estimates are relatively inaccurate however when we treat the students as a collective the average of their guesses is 997 5 remarkably close to the true number the diversity prediction theorem explains why collective error average individual error prediction diversity the accuracy of a group depends both on the average quality of its members judgements and on the extent to which their predictions differ from one another if the students are sufficiently diverse making independent estimates based on different information experiences or perspectives much of the individual error effectively cancels out producing a collective estimate that is closer to the truth from an economic perspective the diversity prediction theorem challenges conventional models of rationality and efficiency diversity is not simply a matter of fairness or representation it generates a tangible advantage the most resilient and innovative economies are those that harness the power of a wide range of perspectives experiences and ways of thinking the diversity prediction theorem also provides a theoretical argument for why democratic systems often have an advantage over dictatorships they can harness the knowledge and perspectives of many different people reducing collective error and improving decision making it does not prove that democracy is always superior but it helps explain why inclusive and participatory political systems standardly outperform rule by a single leader or a narrow elite share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky rethinking the statistical toolkit 9 jun 2026 at 18 46 posted in statistics econometrics leave a comment alwyn young s 2019 article channeling fisher randomisation tests and the statistical insignificance of seemingly significant experimental results qje 134 2 offers an important methodological warning for economists and other researchers the study focuses on a concept called leverage in simple terms leverage means that some individual data points have a much bigger impact on your statistical results than others young shows that a single data point just one observation can sometimes change your conclusion completely to understand why this matters imagine you have run an experiment and found a result that is statistically significant at the 1 per cent level young demonstrates that if you remove or change just one highly leveraged observation about 35 per cent of such significant results can become insignificant conversely about 16 per cent of originally insignificant results can be turned into significant ones this raises a fundamental question how many published results in economics are actually fragile and might not survive a closer look re examining more than fifty experiments from top economics journals young highlights a serious reproducibility crisis in economics if a single observation can flip a result then the original finding is not robust instead of relying on standard regression methods which we know are sensitive to concentrated leverage young recommends randomisation inference you can read more about this in scott cunningham s causal inference the mixtape pp 148 174 this is a design based technique that uses only the random assignment of treatments in an experiment without making fragile assumptions about how the data are distributed by switching to randomisation tests researchers can obtain more robust and trustworthy p values and avoid being misled by influential outliers young s study forcefully shows one thing always check your model assumptions and especially check whether your results are driven by a single observation share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky econometrics playing tennis with the net down 17 apr 2026 at 00 26 posted in statistics econometrics comments off on econometrics playing tennis with the net down debating econometrics and its shortcomings yours truly often gets the response from econometri...
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