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description= 15 posts published by Lars Syll during August 2015;
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than the inherent uselessness of the methodology hmm that doesn t sound very convincing maybe we should apply yet another smell test a non trivial part of teaching statistics is made up of learning students to perform significance testing a problem i have noticed repeatedly over the years however is that no matter how careful you try to be in explicating what the probabilities generated by these statistical tests p values really are still most students misinterpret them this is not to blame on students ignorance but rather on significance testing not being particularly transparent conditional probability inference is difficult even to those of us who teach and practice it a lot of researchers fall pray to the same mistakes so given that it anyway is very unlikely than any population parameter is exactly zero and that contrary to assumption most samples in social science and economics are not random or having the right distributional shape why continue to press students and researchers to do null hypothesis significance testing testing that relies on weird backward logic that students and researchers usually don t understand statistical significance doesn t say that something is important or true and since there already are far better and more relevant testing that can be done it is high time to give up on this statistical fetish jager and leek may well be correct in their larger point that the medical literature is broadly correct but i don t think the statistical framework they are using is appropriate for the questions they are asking my biggest problem is the identification of scientific hypotheses and statistical hypotheses of the theta 0 variety based on the word empirical title i thought the authors were going to look at a large number of papers with p values and then follow up and see if the claims were replicated but no they don t follow up on the studies at all what they seem to be doing is collecting a set of published p values and then fitting a mixture model to this distribution a mixture of a uniform distribution for null effects and a beta distribution for non null effects since only statistically significant p values are typically reported they fit their model restricted to p values less than 0 05 but this all assumes that the p values have this stated distribution you don t have to be uri simonsohn to know that there s a lot of p hacking going on also as noted above the problem isn t really effects that are exactly zero the problem is that a lot of effects are lots in the noise and are essentially undetectable given the way they are studied jager and leek write that their model is commonly used to study hypotheses in genetics and imaging i could see how this model could make sense in those fields but i don t see this model applying to published medical research for two reasons first i don t think there would be a sharp division between null and non null effects and second there s just too much selection going on for me to believe that the conditional distributions of the p values would be anything like the theoretical distributions suggested by neyman pearson theory so no i don t at all believe jager and leek when they write we are able to empirically estimate the rate of false positives in the medical literature and trends in false positive rates over time they re doing this by basically assuming the model that is being questioned the textbook model in which effects are pure and in which there is no p hacking andrew gelman indeed if anything this underlines how important it is and on this noah smith and yours truly agree not to equate science with statistical calculation all science entail human judgement and using statistical models doesn t relieve us of that necessity working with misspecified models the scientific value of significance testing is actually zero even though you re making valid statistical inferences statistical models and concomitant significance tests are no substitutes for doing real science or as a noted german philosopher once famously wrote there is no royal road to science and only those who do not dread the fatiguing climb of its steep paths have a chance of gaining its luminous summits in its standard form a significance test is not the kind of severe test that we are looking for in our search for being able to confirm or disconfirm empirical scientific hypothesis this is problematic for many reasons one being that there is a strong tendency to accept the null hypothesis since they can t be rejected at the standard 5 significance level in their standard form significance tests bias against new hypotheses by making it hard to disconfirm the null hypothesis and as shown over and over again when it is applied people have a tendency to read not disconfirmed as probably confirmed standard scientific methodology tells us that when there is only say a 10 probability that pure sampling error could account for the observed difference between the data and the null hypothesis it would be more reasonable to conclude that we have a case of disconfirmation especially if we perform many independent tests of our hypothesis and they all give about the same 10 result as our reported one i guess most researchers would count the hypothesis as even more disconfirmed most importantly we should never forget that the underlying parameters we use when performing significance tests are model constructions our p values mean next to nothing if the model is wrong as eminent mathematical statistician david freedman writes i believe model validation to be a central issue of course many of my colleagues will be found to disagree for them fitting models to data computing standard errors and performing significance tests is informative even though the basic statistical assumptions linearity independence of errors etc cannot be validated this position seems indefensible nor are the consequences trivial perhaps it is time to reconsider statistical significance tests do not validate models in journal articles a typical regression equation will have an intercept and several explanatory variables the regression output will usually include an f test with p 1 degrees of freedom in the numerator and n p in the denominator the null hypothesis will not be stated the missing null hypothesis is that all the coefficients vanish except the intercept if f is significant that is often thought to validate the model mistake the f test takes the model as given significance only means this if the model is right and the coefficients are 0 it is very unlikely to get such a big f statistic logically there are three possibilities on the table i an unlikely event occurred ii or the model is right and some of the coefficients differ from 0 iii or the model is wrong so share on facebook opens in new window facebook share on x opens in new window x share on bluesky opens in new window bluesky perfect day private 11 aug 2015 at 15 06 posted in varia comments off on perfect day private a newly wedded couple celebrating in the garden of their summer residence fourteen years ago feels like it was yesterday rethinking expectations 11 aug 2015 at 09 55 posted in economics 1 comment the tiny little problem that there is no hard empirical evidence that verifies rational expectations models doesn t usually bother its protagonists too much rational expectations überpriest thomas sargent has defended the epistemological status of the rational expectations hypothesis arguing that since it focuses on outcomes and does not pretend to have behavioral content it has proved to be a powerful tool for making precise statements precise yes but relevant and realistic i ll be dipped in their attempted rescue operations rational expectationists try to give the picture that only heterodox economists like yours truly are critical of the rational expectations hypothesis but on this they are simply eh wrong let s listen to nobel laureate edmund phelps hardly a heterodox economist and what he has to say emphasis added question in a new volume with roman frydman rethinking expectations the way forward for macroeconomics you say the vast majority of macroeconomic models over the last four decades derailed your microfoundations approach can you explain what that is and how it differs from the approach that became widely accepted by the profession answer in the expectations based framework that i put forward around 1968 we didn t pretend we had a correct and complete understanding of how firms or employees formed expectations about prices or wages elsewhere we turned to what we thought was a plausible and convenient hypothesis for example if the prices of a company s competitors were last reported to be higher than in the past it might be supposed that the company will expect their prices to be higher this time too but not that much this is called adaptive expectations you adapt your expectations to new observations but don t throw out the past if inflation went up last month it might be supposed that inflation will again be high but not that high q so how did adaptive expectations morph into rational expectations a the scientists from chicago and mit came along to say we have a well established theory of how prices and wages work before we used a rule of thumb to explain or predict expectations such a rule is picked out of the air they said let s be scientific in their mind the scientific way is to suppose price and wage setters form their expectations with every bit as much understanding of markets as the expert economist seeking to model or predict their behavior the rational expectations approach is to suppose that the people in the market form their expectations in the very same way that the economist studying their behavior forms her expectations on the basis of her theoretical model q and what s the consequence of this putsch a craziness for one thing you re not supposed to ask what to do if one economist has one model of the market and another economist a different model the people in the market cannot follow both economists at the same time one if not both of the economists must be wrong another thing it s an important feature of capitalist economies that they permit speculation by people who have idiosyncratic views and an important feature of a modern capitalist economy that innovators conceive their new products and methods with little knowledge of whether the new things will be adopted thus innovations speculators and innovators have to roll their own expectations they can t ring up the local professor to learn how the professors should be ringing up the speculators and aspiring innovators in short expectations are causal variables in the sense that they are the drivers they are not effects to be explained in terms of some trumped up causes q so rather than live with variability write a formula in stone a what led to rational expectations was a fear of the uncertainty and worse the lack of understanding of how modern economies work the rational expectationists wanted to bottle all that up and replace it with deterministic models of prices wages even share prices so that the math looked like the math in rocket science the rocket s course can be modeled while a living modern economy s course cannot be modeled to such an extreme it yields up a formula for expectations that looks scientific because it has all our incomplete and not altogether correct understanding of how economies work inside of it but it cannot have the incorrect and incomplete understanding of economies that the speculators and would be innovators have q one of the issues i have with rational expectations is the assumption that we have perfect information that there is no cost in acquiring that information yet the economics profession including federal reserve policy makers appears to have been hijacked by robert lucas a you re right that people are grossly uninformed which is a far cry from what the rational expectations models suppose why are they misinformed i think they don t pay much attention to the vast information out there because they wouldn t know what to do what to do with it if they had it the fundamental fallacy on which rational expectations models are based is that everyone knows how to process the information they receive according to the one and only right theory of the world the problem is that we don t have a right model that could be certified as such by the national academy of sciences and as long as we operate in a modern economy there can never be such a model bloomberg the rational expectations hypothesis presumes consistent behaviour where expectations do not display any persistent errors in the world of rational expectations we are always on average hitting the bull s eye in the more realistic open systems view there is always the possibility danger of making mistakes that may turn out to be systematic it is because of this presumably that we put so much emphasis on learning in our modern knowledge societies so where does all this leave us i think john kay sums it up pretty well a scientific idea is not seminal because it influences the research agenda of phd students an important scientific advance yields conclusions that differ from those derived from other theories and establishes that these divergent conclusions are supported by observation yet as prof sargent disarmingly observed such empirical tests were rejecting too many good models in the programme he had established with fellow nobel laureates bob lucas and ed prescott in their world the validity of a theory is demonstrated if after the event and often with torturing of data and ad hoc adjustments that are usually called imperfections it can be reconciled with already known facts calibrated since almost everything can be explained in this way the theory is indeed universal no other approach is necessary or even admissible share on facebook opens in new window facebook share on x opens in new window x 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