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Science and the Shortcomings of Statistics
Kilrah_il writes "The linked article provides a short summary of the problems scientists have with statistics. As an intern, I see it many times: Doctors do lots of research but don't have a clue when it comes to statistics — and in the social science area, it's even worse. From the article: 'Even when performed correctly, statistical tests are widely misunderstood and frequently misinterpreted. As a result, countless conclusions in the scientific literature are erroneous, and tests of medical dangers or treatments are often contradictory and confusing.'"
In other news math may not lie but people still can, all the honesty and good statistics in the world doesnt help end-user stupidity, and there are statistically two popes per square kilometer in the vatican.
A bullet may have your name on it but splash damage is addressed "To whom it may concern."
It's not just statistics that people have a problem with...
-- Braden's law of data: All data spends some of its lifetime in an excel spreadsheet.
My doctor was explaining to me that my blood sugar readings should not have a standard deviation of more than 1/3rd of the average blood sugar reading. Just to test if he knew what it meant, I asked him what a standard deviation was. Oh the fun when he tried to bullshit his way out of that one! He eventually told me that when I plot my data in Excel I can ask it to give me statistics on the column and it would mention what the standard deviation value was. But when I pressed on and asked him what a standard deviation is, he shooed me off and told me to go look it up. Never did he confess that he had no clue.
How to Lie with Statistics by Darrell Huff. Recommended reading.
Do not mock my vision of impractical footwear
As a doctor myself, I feel I should add my $0.02...
Throughout med school we had the odd scattered lecture on statistics, and later when reading papers I used to skim over most of the maths just to look for the P value at the end (one representation of how statistically significant a result is).
However, I then took a formal stats course and was amazed at how little I understood - Monte Carlo techniques, Markov models, and even something as trivial yet important as the difference between a parametric versus a non-parametric test.
And then it struck me - most of the research I had read had applied parametric statistical tests to their data - that it, the researchers made an assumption that the underlying distribution of results would fall on a normal curve. Yet this simple assumption may be all it takes to skew the data when they should have chosen a non-parametric test instead.
So yes, stats are vitally important, badly taught, and focus too much on the maths rather than the concepts. Remember that we're doctors, not mathematicians - the last set of sums I did were in high school. If I need to analyse data, I'll probably plug it into SPSS - although now with my eyes open.
-Nano.
I think your example would be more persuasive if it involved algebra, though.
In other news math may not lie but people still can...
Usually (in science at least) it's not even a matter of lying. Part of the problem is that the multi-headed monster that statistics has become has a tendency to lead people to over-use numerical "answers" vomited up by stats packages, without really understanding what they are for, or how to interpret them.
Statistics are very useful for predicting certain things, but all too often they are submitted as "proof" of a given condition, which is dangerous. Sometimes we need to throw away statistics and start applying common sense.
You are a jerk.
You are insulting your sister because she is bad at mental math? It is a skill; one not required for extensive knowledge of the social sciences. Additionally, maybe if sales tax is simple in your state like 10%, but where I live it is 4.5% which is not always easy to get exactly right in your head.
I had a roommate who was brilliant,funny, a singer and an artist, and yet, he couldn't calculate tip to save his life, but I don't certainly hold that against him.
It is not a shortcoming of statistics that other people, like various scientists who aren't statisticians, don't know how to use or properly interpret statistics. It is a shortcoming of their knowledge.
It is not a shortcoming of the Copenhagen interpretation of quantum mechanics or the Chicago school of economics if I don't understand or know how to correctly interpret their results. It is my shortcoming and fault for not knowing enough to connect the dots.
I do statistical research some of that is through interacting with researchers in the biosciences. Often when I go to talk to a researcher and ask them if they could use some statistical or mathematical or computational assistance with their research it has almost always been a fruitful starting point to long conversations and getting into the research. Now sometimes it was simply a matter of looking at their F-test results or ANOVA scores and telling them what it meant (like with a regression model relating proportions of certain characteristics between taxa), more useful interactions for me often mean working on new algorithms or estimators or working with fitting a model from their empirical data because there isn't a reliable standard model to work off of (like intergenic distance between genes in an operon) that kind of challenge makes less engaging work worth the hassle. Maybe I'm odd because I've worked hard to have a good background in both statistics and biology, but I shouldn't be.
Although here is an observation that perhaps supports some of the intent of the article from my own experience. I was speaking with a biology graduate student and it came up that they had a biostatistics course in the department. Of course as a statistician my mind goes towards survival function, failure rate, life tables, censored data, bioassy, epidemiology, microarrays, clincal trials, topics along those lines. It turned out their course focused z tests, t tests, f tests, confidence intervals, point predictions, least squares regression, multiple regression, ANOVA, and things along these lines just with simulated problems in a lab setting. That is not necessarily a bad thing, but much of the core math was under played or missing like model assumptions and alternate formulations or things like dummy variables. The worst part was that even though they were doing well with the class they had no confidence in actually using the statistics and didn't understand how to interpret the meaning of something like a confidence interval, they knew how to calculate one, but it wasn't clear what it actually meant to them.
The corollary to the notion in the summary I'd rant and claim is that scientists overall have less than desirable skills in mathematics, statistics, and computation than those who studied those disciplines principally and that's hurting science. However many in those three disciplines really know little beyond basic results in any of the sciences which hurts the applicability of these mathematical fields to the sciences and likely hurt our ability to develop certain types of discipline specific results that can be generalized from work in application problems.
In either case whether you're a typical scientist or a typical math/stat/comp person in order to become proficient enough in the other areas it requires going an awfully long out of the way compared to any counterpart who simply does not care and goes straight through as many before have. While in some areas of research on either side it is no problem to do as has been done and not further knowledge into those other areas. Increasingly results that have the highest levels of impact are coming more and more from truly interdisciplinary research. In order to further encourage that for those who are interested in such fields (aside from making more clear what areas in any of the fields fringe to such interdisciplinary work) we need more incentive to study more than one field and/or better ways of enabling fruitful cooperation between the camps.
In reading a couple of these types of articles recently I've noticed that the articles always talk about this being a problem across all journals, but only seem to mention a couple of different disciplines - medicine usually chief among them. Has anyone heard/read anything naming a hard science (e.g. chemistry or physics) as full of bad stats? My hunch is that this happens most often in medicine because you have the combination of controlling for a lot of variables as well as inadequate mathematics training.
And lots of others. It then suggests Bayesian reasoning as an alternative to traditional statistical tests.
Most post-PhD scientists are aware of the common mistakes, but being aware that we make mistakes doesn't necessarily stop us from making them. If you chose a random set of conference proceedings, it is almost certain you will find at least one paper (and I suspect usually a dozen or more) that have statistical mistakes in them.
Peer review is not about catching mistakes, although it can on occation. Peer review is about clear communication, such that the experiment can be repeated as identically as possible and that the readers can understand the authors justification for their conclusions. At least that's what every journal article I've read on the topic indicateded was the reason for the peer review processes creation. One of my advisors asked me about it on my written preliminary exam and I needed to do a lot of reading to be prepared for the oral exam. There were several different societies that claimed to have originated the idea, but no one claimed that the purpose was to catch mistakes, fabrications, or data manipulations.
Bureaucracy expands to meet the needs of the expanding bureaucracy.-Oscar Wilde
Has it ever been demonstrated that social scientists have a worse understanding of statistics than physical scientists? I ask because my observations are the opposite. The physical scientists run a t-test and declare the matter resolved (significant or not-significant). Given the complexities of social sciences, these scientists check the assumptions required to use a test (e.g., normalcy) and have a good understanding of the statistics involved. (The obligatory exception is statistical genetics: physical science with a solid statistical basis.)
The largest demographic in american prisons are black americans. Real statistic but is it true?
Given a particular sample that indicates blacks are 60% of the prison population this would appear to be true.
But what if I said: "The largest demographic in prison is minority, non-whites." Suddenly the % jumps from 60% (black) to 80% (minority). Which is more right? This is the problem with statistics. Context.
Now I can say readily that the largest demographic in prison is actually right-handed people. The % now jumps to 90%.
But wait! There is more! The largest demographic is prison is actually people who prior to arrest were below the poverty line which jumps to 99% of the population. Again, all of the above are accurate based on a sample but which is MORE correct? Linear Algebra is coming into play here quickly....
When that kind of issue comes into play, it is the classic "Correlation != Causation" confusion. The majority of people in prison are in there because of "Being black? Being a minority? being right handed? or being poor?" None of the above. The majority of them are in there because they were convicted of a crime and sentenced. That is the causation of their imprisonment, the rest is correlation which may have a direct causation on the conviction or sentencing, but no direct causation on being in prison. (e.g. You cannot be thrown into prison for being poor, black, minority, right handed)
Same with medical research, politics, economics, etc. The price of oil rising 10% and a subsequent 5% drop in shipping orders. Measuring the significance of regessors is important but oddly never reported most of the time. Many factors get masked or shadowed by higher level regressors (e.g. being a minority masks a variety of other social and economic factors. In addition it can distort statistical work by being too broad. Asians have a variety of different economic and social factors as north american blacks versus even african immigrants.)
Back to the orignal subject:
We can take 100 prisoners and 100 non-prisoners and figure out rather quickly if being black is statistically significant in prison population. Non-prison population blacks would account for 25%-45% of the population (Depending on location). We can see that 60% of prisoners are black. There is a 20+% deviation from the norm. We can test to see the significance of that. Same with minorities. Now we find something quickly that right handed is insignificant because it doesn't deviate from the norm. We can test left-handed and right-handed populations and rule out the handed-ness of a convict being significant.
We can find the economic status is considerable MORE significant then minority or black as a status. We can determine that the reason minorities or blacks are disporotinally more prevelant in prison is that blacks and minorities have higher rates of poverty. We can extract and determine the statistical weight of POVERTY in regards to imprisonment (Since we find a high % of white in prison that are poor compared to the normal population.) Once we figure that out we can remove that and continue an investigation and figure out what weight minority and black has once we have removed POVERTY from the model (Residual analysis).
The problem in reporting is without providing the whole, comprehensive analysis you can miss important things. For instance to correct the injustice in sentencing, without reporting the weight POVERTY has in contrast to BLACK or MINORITY you may lose sight that you may have better success addressing POVERTY to normalize sentencing rather then MINORITY or BLACK (or not).
The same happens in medical reasearch. Given a cocktail of drugs wirthout having the whole analysis you may end up providing more of Medicine A versus B but lose sight that A & B are limited by the dosage of Medicine C.
Satistics are not bullshit, rather mearly observations with no intrinsic agenda or even implication of truth. Purely amoral, like a hand gun.. useful to both the good and evil.
Statistics don't lie, nor do they tell the truth. They simple show the relationship of the data as it stands. The Truth or Thruthiness of it is subjective and vulnerable to context.
-=[ Who Is John Galt? ]=-