Like The Cognitive Science of Rationality, this is a post for beginners. Send the link to your friends!

Science is broken. We know why, and we know how to fix it. What we lack is the will to change things.

In 2005, several analyses suggested that most published results in medicine are false. A 2008 review showed that perhaps 80% of academic journal articles mistake "statistical significance" for "significance" in the colloquial meaning of the word, an elementary error every introductory statistics textbook warns against. This year, a detailed investigation showed that half of published neuroscience papers contain one particular simple statistical mistake.

Also this year, a respected senior psychologist published in a leading journal a study claiming to show evidence of precognition. The editors explained that the paper was accepted because it was written clearly and followed the usual standards for experimental design and statistical methods.

Science writer Jonah Lehrer asks: "Is there something wrong with the scientific method?"

Yes, there is.

This shouldn't be a surprise. What we currently call "science" isn't the *best* method for uncovering nature's secrets; it's just the first set of methods we've collected that *wasn't totally useless* like personal anecdote and authority generally are.

As time passes we learn new things about how to do science better. The Ancient Greeks practiced some science, but few scientists tested hypotheses against mathematical models before Ibn al-Haytham's 11th-century *Book of Optics* (which also contained hints of Occam's razor and positivism). Around the same time, Al-Biruni emphasized the importance of repeated trials for reducing the effect of accidents and errors. Galileo brought mathematics to greater prominence in scientific method, Bacon described eliminative induction, Newton demonstrated the power of consilience (unification), Peirce clarified the roles of deduction, induction, and abduction, and Popper emphasized the importance of falsification. We've also discovered the usefulness of peer review, control groups, blind and double-blind studies, plus a variety of statistical methods, and added these to "the" scientific method.

In many ways, the best science done today is better than ever — but it still has problems, and most science is done poorly. The good news is that we know what these problems are and we know multiple ways to fix them. What we lack is the *will* to change things.

This post won't list all the problems with science, nor will it list all the promising solutions for any of these problems. (Here's one I left out.) Below, I only describe a few of the basics.

### Problem 1: Publication bias

When the study claiming to show evidence of precognition was published, psychologist Richard Wiseman set up a registry for advance announcement of new attempts to replicate the study.

Carl Shulman explains:

A replication registry guards against publication bias, and at least 5 attempts were registered. As far as I can tell, all of the subsequent replications have, unsurprisingly, failed to replicate Bem's results. However, JPSP and the other high-end psychology journals refused to publish the results, citing standing policies of not publishing straight replications.

From the journals' point of view, this (common) policy makes sense: bold new claims will tend to be cited more and raise journal prestige (which depends on citations per article), even though this means most of the 'discoveries' they publish will be false despite their low p-values (high statistical significance). However, this means that overall the journals are giving career incentives for scientists to massage and mine their data for bogus results, but not to challenge bogus results presented by others.

This is an example of publication bias:

Publication bias is the term for what occurs whenever the research that appears in the published literature is systematically unrepresentative of the population of completed studies. Simply put, when the research that is readily available differs in its results from the results of

allthe research that has been done in an area, readers and reviewers of that research are in danger of drawing the wrong conclusion about what that body of research shows. In some cases this can have dramatic consequences, as when an ineffective or dangerous treatment is falsely viewed as safe and effective. [Rothstein et al. 2005]

Sometimes, publication bias can be more deliberate. The anti-inflammatory drug Rofecoxib (Vioxx) is a famous case. The drug was prescribed to 80 million people, but in it was later revealed that its maker, Merck, had withheld evidence of the drug's risks. Merck was forced to recall the drug, but it had already resulted in 88,000-144,000 cases of serious heart disease.

#### Example partial solution

One way to combat publication bias is for journals to only accept experiments that were registered in a public database before they began. This allows scientists to see which experiments were conducted but never reported (perhaps due to negative results). Several prominent medical journals (e.g. *The Lancet* and *JAMA*) now operate this way, but this protocol is not as widespread as it could be.

### Problem 2: Experimenter bias

Scientists are humans. Humans are affected by cognitive heuristics and biases (or, really, humans just *are* cognitive heuristics and biases), and they respond to incentives that may not align with an optimal pursuit of truth. Thus, we should expect *experimenter bias* in the practice of science.

There are many stages in research during which experimenter bias can occur:

- in reading-up on the field,
- in specifying and selecting the study sample,
- in [performing the experiment],
- in measuring exposures and outcomes,
- in analyzing the data,
- in interpreting the analysis, and
- in publishing the results. [Sackett 1979]

Common biases have been covered elsewhere on Less Wrong, so I'll let those articles explain how biases work.

#### Example partial solution

There is some evidence that the skills of rationality (e.g. cognitive override) are teachable. Training scientists to notice and meliorate biases that arise in their thinking may help them to reduce the magnitude and frequency of the thinking errors that may derail truth-seeking attempts during each stage of the scientific process.

### Problem 3: Bad statistics

I remember when my statistics professor first taught me the reasoning behind "null hypothesis significance testing" (NHST), the standard technique for evaluating experimental results. NHST uses "p-values," which are statements about the probability of getting some data (e.g. one's experimental results) *given* the hypothesis being tested. I asked my professor, "But don't we want to know the probability of the hypothesis we're testing *given* the data, not the other way around?" The reply was something about how this was the best we could do. (But that's false, as we'll see in a moment.)

Another problem is that NHST computes the probability of getting data as unusual as the data one collected by considering what might be expected if that particular experiment was repeated many, many times. But how do we know anything about these imaginary repetitions? If I want to know something about a particular earthquake, am I supposed to imagine a few dozen repetitions of that earthquake? What does that even *mean*?

I tried to answer these questions on my own, but all my textbooks assumed the soundness of the mistaken NHST framework for scientific practice. It's too bad I didn't have a class with biostatistican Steven Goodman, who says:

The p-value is almost nothing sensible you can think of. I tell students to give up trying.

The sad part is that the logical errors of NHST are old news, and have been known ever since Ronald Fisher began advocating NHST in the 1920s. By 1960, Fisher had out-advocated his critics, and philosopher William Rozeboom remarked:

Despite the awesome pre-eminence [NHST] has attained... it is based upon a fundamental misunderstanding of the nature of rational inference, and is seldom if ever appropriate to the aims of scientific research.

There are many more problems with NHST and with "frequentist" statistics in general, but the central one is this: NHST does not follow from the axioms (foundational logical rules) of probability theory. It is a grab-bag of techniques that, depending on how those techniques are applied, can lead to *different* results when analyzing the *same data* — something that should horrify every mathematician.

The inferential method that solves the problems with frequentism — and, more importantly, follows deductively from the axioms of probability theory — is Bayesian inference.

So why aren't *all* scientists using Bayesian inference instead of frequentist inference? Partly, we can blame the vigor of NHST's early advocates. But we can also attribute NHST's success to the simple fact that Bayesian calculations can be *more difficult* than frequentist calculations. Luckily, new software tools like WinBUGS let computers do most of the heavy lifting required for Bayesian inference.

There's also the problem of sheer momentum. Once a practice is enshrined, it's hard to dislodge it, even for good reasons. I took three statistics courses in university and *none* of my textbooks mentioned Bayesian inference. I didn't learn about it until I dropped out of university and studied science and probability theory on my own.

Remember the study about precognition? Not surprisingly, it was done using NHST. A later Bayesian analysis of the data disconfirmed the original startling conclusion.

#### Example partial solution

This one is obvious: teach students probability theory instead of NHST. Retrain current scientists in Bayesian methods. Make Bayesian software tools easier to use and more widespread.

### Conclusion

If I'm right that there is unambiguous low-hanging fruit for improving scientific practice, this suggests that particular departments, universities, or private research institutions can (probabilistically) out-perform their rivals (in terms of actual discoveries, not just publications) given similar resources.

I'll conclude with one particular *specific* hypothesis. If I'm right, then a research group should be able to hire researchers trained in Bayesian reasoning and in catching publication bias and experimenter bias, and have them extract from the existing literature valuable medical truths that the mainstream medical community doesn't yet know about. This prediction, in fact, is about to be tested.

Nitpick: actually last year (March 2011, per http://www.ncbi.nlm.nih.gov/pubmed/21280961 ).