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Weak Statistical Standards Implicated In Scientific Irreproducibility
ananyo writes "The plague of non-reproducibility in science may be mostly due to scientists' use of weak statistical tests, as shown by an innovative method developed by statistician Valen Johnson, at Texas A&M University. Johnson found that a P value of 0.05 or less — commonly considered evidence in support of a hypothesis in many fields including social science — still meant that as many as 17–25% of such findings are probably false (PDF). He advocates for scientists to use more stringent P values of 0.005 or less to support their findings, and thinks that the use of the 0.05 standard might account for most of the problem of non-reproducibility in science — even more than other issues, such as biases and scientific misconduct."
I heard it more than once !!
Use Bayesian statistics.
That, and the fact that all of statistics is a joke. It's all based on the assumption that data is distributed in a bell curve. Sure, a bell curve does fit a lot of data, but we blindly assume it fits everything which just can't be true.
Doubt it makes a difference, the root of this problems us systematic errors.
Five sigma is the standard of proof in Physics. The probability of a background fluctuation is a p-value of something like 0.0000006.
Such an admonishment is fine for the computational fields, where a few more permutations can net you a p-value of 0.0005 (assuming that you aren't crunching on a 4-month cluster problem). However, biological laborations are often very expensive and take a lot of time. Furthermore, additional tests are not always possible, since it can be damn hard to reproduce specific mutations or knockout sequences without altering the surrounding interactive factors.
So, should we go for a better p-value for the experiment and scrap any complicated endeavour, or should we allow for difficult experiments and take it with a grain of salt?
Truth is expensive.
This article is statically a waste of time and certainly Irreproducibility implicated with some other concept involving 6 or 7 syllable words that most acertainly to attract freshmen geeks with bowl haircuts
If we were to insist on statistically meaningful results 90% of our contemporary journals would cease to exist for lack of submissions.
Personally, I've considered results with p values between 0.01 and 0.05 as merely 'suggestive': "It may be worth looking into this more closely to find out if this effect is real." Between 0.01 and 0.001 I'd take the result as tentatively true - I'll accept it until someone refutes it.
If you take p=0.04 as demonstrating a result is true, you're being foolish and statistically naive. However, unless you're a compulsive citation follower (which I'm not) you are somewhat at the mercy of other authors. If Alice says "In Bob (1998) it was shown that ..." I'll tend to accept it without realizing that Bob (1998) was a p=0.04 result.
Obligatory XKCD
Quattuor res in hoc mundo sanctae sunt: libri, liberi, libertas et liberalitas.
http://xkcd.com/882/
Authors need to read this: http://www.deirdremccloskey.com/articles/stats/preface_ziliak.php
It explains quite clearly why a p value 0.05 is a fairly arbitrary choice as it cannot possibly the standard for every possible study out there. Or, put it another way, be very skeptical when one sole number (namely 0.05) is supposed to be a universal threshold to decide on the significance of all possible findings, in all possible domains of science. The context of any finding still matters for its significance.
More researchers in the biological sciences are using other more rigorous methods now than the Student's t-test and a p value of 0.05. ANOVA, ANCOVA and ranking methodologies are commonplace. Many scientific findings are based on a P value below 0.01. The problem with bad science certainly involves some bad statistics, but more often it just involves bad methodology, and poor attention to the previous literature (and thus attempting to reinvent the wheel). If your findings are robust and reproducible, then the statistics work out just fine. The good news is that science is self correcting, even if sometimes the corrections seem tardy.
A brain is a terrible thing to waste... Mind? That's debatable.
Is the author mad? p < 0.05 would completely invalidate climate models! That simply can't be true, ergo p >= 0.05 is absolutely necessary in (post-normal) science.
Unreliable research
Trouble at the lab
Scientists like to think of science as self-correcting. To an alarming degree, it is not
Oct 19th 2013 |From the print edition
The Economist
First, the statistics, which if perhaps off-putting are quite crucial. Scientists divide errors into two classes. A type I error is the mistake of thinking something is true when it is not (also known as a “false positive”). A type II error is thinking something is not true when in fact it is (a “false negative”). When testing a specific hypothesis, scientists run statistical checks to work out how likely it would be for data which seem to support the idea to have come about simply by chance. If the likelihood of such a false-positive conclusion is less than 5%, they deem the evidence that the hypothesis is true “statistically significant”. They are thus accepting that one result in 20 will be falsely positive—but one in 20 seems a satisfactorily low rate.
In 2005 John Ioannidis, an epidemiologist from Stanford University, caused a stir with a paper showing why, as a matter of statistical logic, the idea that only one such paper in 20 gives a false-positive result was hugely optimistic. Instead, he argued, “most published research findings are probably false.” As he told the quadrennial International Congress on Peer Review and Biomedical Publication, held this September in Chicago, the problem has not gone away.
Dr Ioannidis draws his stark conclusion on the basis that the customary approach to statistical significance ignores three things: the “statistical power” of the study (a measure of its ability to avoid type II errors, false negatives in which a real signal is missed in the noise); the unlikeliness of the hypothesis being tested; and the pervasive bias favouring the publication of claims to have found something new.
http://www.economist.com/news/briefing/21588057-scientists-think-science-self-correcting-alarming-degree-it-not-trouble
Oh, people can come up with statistics to prove anything, Kent. 14% of people know that.
A significant problem is that many of the people who quote p values do it without understanding what a p value actually means. Getting p = 0.05 does not mean that there is only a 5% chance that the model is wrong. That is one of the fundamental misunderstandings in statistics, and I suspect that it is behind a lot of the cases of scientific irreproducibility.
Just because you are paranoid does not mean that no-one is out to get you.
TOo many scientists in fields like geophysics and biology and other fields have been implicated in too many coverups and hoaxes with regards to liberal frauds like evolution and global warming. At this point the public has become almost completely opposed to almost all science and instead are relying on engineering to move society forward. Ultimately the only way to avoid this kind of problem is to appoint some layperson judges who can use simple common sense to pick out those scientific theories that should be funded and those that should not, rather than allowing corrupt liberal scientists to pick and choose their own pet agendas at taxpayer expense.
http://www.youtube.com/watch?v=HtMX_0jDsrw
So it gives you a very valid excuse to assume that the value distribution of some quantity occurring in nature will follow a Normal distribution when you know nothing else about it.
But there's the crux: it remains an assumption; a hypothesis, and fortunately it's usually a *testable* hypothesis. It's the responsibility of a researcher to check if it holds, and to see how problematic it is when it doesn't.
If something has a normal distribution, its square or its square root (or another power) doesn't have a Normal distribution. Take for example the diameter, surface area, and volume of berries. The diameter (goes with the radius, r), the surface area (goes with r^2), and the volume of berries (goes with r^3). They cannot all be Normally distributed at the same time, so assuming any of them is starts you out on shaky foundation.
Okay, here's the real problem with scientific studies.
All science is data compression, and all studies are are intended to compress data so that we can make future predictions. If you want to predict the trajectory of a cannonball, you don't need an almanac cross referencing cannonball weights, powder loads, and cannon angles - you can calculate the arc to any desired accuracy with a set of equations that fit on half a page. The half-page compresses the record of all prior experience with cannonball arcs, and allows us to predict future arcs.
Soft science studies typically make a set of observations which relate two measurable aspects. When plotted, the data points suggest a line or curve, and we accept the linear-regression (line or polynomial) as the best approximation for the data. The theory being that the underlying mechanism is the regression, and unrelated noise in the environment or measurement system causes random deviations of observation.
This is the wrong method. Regression is based on minimizing squared error, which was chosen by Laplace for no other reason that it is easy to calculate. There's lots of "rationalization" explanations of why it works and why it's "just the best possible thing to do", but there's no fundamental logic that can be used to deduce least squares from from fundamental assumptions.
Least squares introduces several problems:
1) Outliers will skew the values, and there is no computable way to detect or deal with outliers (source).
2) There is no computable way to determine whether the data represent a line or a curve - it's done by "eye" and justified with statistical tests.
3) The resultant function frequently looks "off" to the human eye, humans can frequently draw better matching curves; meaning: curves which better predict future data points.
4) There is no way to measure the predictive value of the results. Linear regression will always return the best line to fit the data, even when the data is random.
The right way is to show how much the observation data is compressed. If the regression function plus data (represented as offsets from the function) take fewer bits than the data alone, then you can say that the conclusions are valid. Further, you can tell how relevant the conclusions are, and rank and sort different conclusions (linear, curved) by their compression factor and choose the best one.
Scientific studies should have a threshold of "compresses data by N bits", rather than "1-in-20 of all studies are due to random chance".
Having quickly skimmed the paper, I'll give an example of the problem. .54 .65 .74 .83 .88 .96 .94 .98
I couldn't quickly find a real data set that was easy to interpret, so I'm going to make up some data.
Chance to die before reaching this age
Age woman man
80
85
90
95
We have a person who is 90 years old. Taking the null hypothesis to be that this person is a man, we can reject the hypothesis that this is a man with greater than 95 percent confidence (p=0.04). However, if we do a Bayesian analysis assuming prior probabilities of 50 percent for the person being a man or a woman, we find that there is a 25 percent chance that the person is a man after all (as women are 3 times more likely to reach age 90 than men are.)
(Having 11 percent signs in my post seems to have given /. indigestion so I've had to edit them out.)
Quattuor res in hoc mundo sanctae sunt: libri, liberi, libertas et liberalitas.
Johnson found that a P value of 0.05 or less — commonly considered evidence in support of a hypothesis in many fields including social science — still meant that as many as 17–25% of such findings are probably false (PDF).
.
Found? Was he unaware that using a threshold of 0.05 means a 20% probability that a finding is a chance result - by definition ?
More interesting, IMO, is that statistical doesn't tell you what the scale of an effect is. There can be a trivial difference between A and B even if the difference is statistically significant. People publish it anyway.
Sheesh, evil *and* a jerk. -- Jade
A surprising number of senior scientists are not aware of the problems introduced by ending an experiment based on achieving a certain significance level. By taking the significance as the criterion of the experiment, you don't actually know anything about the significance. Your highly significant result may just be a fluctuation because, had you continued, the high signal-to-noise ratio could well dissipate. Too often I've heard senior scientists advising junior scientists: You've got three sigma, publish. But, proper procedure is to design an experiment to run for a certain duration and then find out what the result is.
Medicine has a formal means to end a trial early if a medicine turns out to be dangerous or particularly helpful. This is an ethical consideration. But, it does make the trial results void.
At one level, they are right that unreproducible results are usually not fraud, but are simply fluctuations that make a study look promising leading to publication. But raising the standard of statistical significance will not really improve the situation. The most important uncertainties in most scientific studies are not random. You can't quantify them assuming a gaussian distribution. There are all kind of choices made in acquiring, processing, and presenting data. The incentives that scientists have are all pushing them to look for ways to obtain a high profile result. We make our best guesses trying to be honest, but when a set of guesses leads to a promising result we publish it and trust further study to determine whether our guesses were fully justified. There is one step that would improve the situation. We need to provide a mechanism to receive career credit for reproducing earlier results or for disproving earlier results. At the moment, you get no credit for doing this. And you will never get funding to do it. The only way to be successful is to spit out a lot of papers and have some of them turn out to be major results that others build on. The number of papers that turn out to be wrong is of no consequence. No one even notices except a couple of researchers who try to build on your result, fail, and don't publish. In their later papers they will probably carefully dance around the error so as not to incur the wrath of a reviewer. If reproducing earlier results was a priority, then we would know earlier which results were wrong and could start giving negative career credit to people who publish a lot of errors.
Ahhh!! it's 1/20, not two percent. Of course, it's 5%.
The bigger problem is the habit of confusing correlation with cause.
I do not fail; I succeed at finding out what does not work.
This is a geek website, not a "research" website so stop talking a bunch of crap about a bunch of crap. I'm providing silly examples so don't focus upon them. Most researchers suck at stats and my attempt at explaining should either help out or show that I don't know what I'm talking about. Take your pick.
"p=.05" is a stat that reflects the likelihood of rejecting a true null hypothesis. So, lets say that my hypothesis is that "all cats like dogs" and my null hypothesis is "not all cats like dogs." If I collect a whole bunch of imaginary data, run it through a program like SPSS, and the results turn out that my hypothesis is correct then I have a .05 percent chance that the software is wrong. In that particular imaginary case, I would have committed a Type I Error. This error has a minimal impact because the only bad thing that would happen is some dogs get clawed on the nose and a few cats get eaten.
Now, on a typical experiment, we also have to establish beta which is the likelihood of committing a type II error, that is, accepting a false null hypothesis. So let's say that my hypothesis is that "Sex when desired makes men happy" and my null hypothesis is "Sex only when women want it makes men happy." It's not a bad thing if #1 is accepted but the type II error will make many men unhappy.
Now, this is a give and take relationship. Every time that we make p smaller (.005, .0005, .00005, etc.) for "accuracy," then the risk of committing a type II error increases. A type II error when determining what games 15 year olds like to play doesn't really matter if we are wrong but if we start talking about drugs and false positives then the increased risk of a type II error really can make things ugly.
Next, there are guideline for determining a how many participants are needed for lower p (alpha) values. Social sciences (hold back your Sheldon jokes) that do studies on students might need lets say 35 subjects/people per treatment group at p=.05 whereas with a .005 might need 200 or 300 per treatment group. I don't have a stats book in front of me but .0005 could be in the thousands. Every adjustment impacts a different item in a negative fashion. You can have your Death Star or you can have Luke Skywalker. Can't have 'em both.
Finally, there is a statistical concept of power, that is, there are stats for measuring the impact of a treatment. Basically, how much of the variance between the group A and group B can be assigned to the experimental treatment. This takes precedence in many peoples minds over simply determining if we have a correct or incorrect hypothesis. Assigning p does not answer this.
Anyways, I'm going to go have another beer. Discard this article and move onto greener pastures.
The Central Limit Theorem doesn't state that the samples are normally distributed, but their mean (average). So the average surface area, volume, and diameter will all be normally distributed for a large sample of independent berries (ie. not from same plants, and so forth).
It sounds like you have a clue about statistics. Do you know of a good forum to ask a fairly involved statistics question? I have a set of measured variables A-E which all tend to indicate the likelihood of X. The relationships are a bit complex and unknown, though, so I need help with how I should analyze the historical data in order to come up with parameters to use in the future for making "predictions" of X based on known values of A-E.
"innovative methods"??? I do not know of a single serious scientist who hasn't been lectured on the ills of weak testing (and told not to use 0.05 as some sort of magical threshold below which everything magically works).
Back when I was a wee researchling, this is literally one of the first paper I was told to read and internalise (published 20 years ago, and not even particularly breakthrough at the time).
There is absolutely no need for new evidence or further discussion of the limitations of statistical testing thresholds: anybody who cares is keenly aware of them. People who don't (particularly in some areas of social science), are just looking for a way to get their next paper out the door by any means possible.
Actually, there is a really good reason to use least-squares regression. A model that minimizes squared error is guaranteed to minimize the variance of error, obviously.
This is the wrong place for an argument (you want room 12-A) and I don't want to get into a contest, but for illustration here is the problem with this explanation.
A rule learned from experience should minimize the error, not the variance of error.
It's a valid conclusion from the mathematics, but based on a faulty assumption.
"Global Warming"?
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I always knew there was something wrong with their Pies...
http://stats.stackexchange.com/questions
\begin{rant}
Actually using statistics in the first place! I'm sick to $#@%@#$%#$TREWT#$@%$#ing death of CS papers with no statistical testing whatsoever. And don't get me started on electronic engineering.
\end{rant}
It seems like you found a lot of problems with what is taught in a stat 101 class. This is good; there are many. However, there are also solutions to these problems which you would find if you took a higher level course.
That brought a smile to my face. Thanks.
But of course, they wear white coats and are the new 'high priests' who have to be worshipped at any cost. It's not as if most scientists are concerned more with their careers and pensions than with the truth, is it...
http://stats.stackexchange.com/
If X is categorical this sounds like a case for logistic regression.
What you're talking about is the distribution of the sample means of r1, r2, r3 respectively. Those are asymptotically normally distributed, but that's not what we're talking about here.
What we were talking about is whether: r1, r2, and r3 can all be normally distributed. The reason being that people investigating the size, weight, and surface area of berries may *assume* (appealing to the Central Limit Theorem) that the quantity they're investigating can be modeled adequately through a normal distribution, and proceed to apply statistical tests based on dealing with normal distributions. For example by comparing the effect of fertilizer on berry size and weight. And it's clear that the distributions of r1, r2, and r3 cannot all be distributed normally.
So statistical tests based on the assumption that they are normally distributed will operate outside their guaranteed area of applicability, which may or may not cause them to be in error.
... but is it reproducible? :p
"I love animals! Some are cute, others are tasty, what's not to like?" - Betsy Schroeder, Jeopardy contestant
Of course it's a proven fact that 87% of all statistics are wrong. 8-)
> do want to necessitate giving some experimental medicine to 10,000 people before assessing whether it's a good idea or not?
Yes. Before giving it to a million people, we should run statistical calculations on the first 10,000 to better asses safety and efficacy.
Oh, you meant as opposed to a trial with 200 people. But that's a false dichotomy. You run run stats on the first 200 to see whether
or not it's likely safe, then run stats on 10,000 to confirm it. Which is to say, you'd wait until you managed a smaller P before announcing a conclusion. In the meantime, with a P of 0.05, you'd label it as a tentative conclusion, a likely theory.
The problem I have with least squares is that I don't like the definition of the "error". If you have two things that are correlated, one isn't necessariy a function of the other that includes some variability. If you flip the X and Y axes over - plot height against weight, rather than weight against height - then the least squares regression gives a different line. If the two errors are both minimised, but different, then neither of them is the "real" error.
Wow - brilliant insight! Thanks for that - things like this are why I come to Slashdot.
Can I discuss some ideas with you offline? thon dot 9 dot okianwarrior at spamgourmet dot com