The hunt for p-values less than 0.05 has left many of science’s roadways riddled with potholes.

More than 50% of them in the biomedical literature are wrong, according to one reckoning, maybe 30% or more wherever it’s used, according to another. It’s high, but we can’t know for sure how high, according to a third. It’s definitely part of the reason more than half of studies in psychology can’t be replicated. And the lowest estimate of wrong-ness I’ve seen is 14% in biomedical research – which is still pretty high. (Details **here**, **here**, and **here**.)

The American Statistical Association (ASA) is trying to stem the tide of misuse and misinterpretation. They issued a **statement on p-values** this year. It’s the first time they ever took a position on a statistical practice. They did so because, they said, it’s an important cause of science’s reproducibility crisis.

Perhaps the ASA’s intervention will help stop the p-value’s seemingly unstoppable advance in the sciences. In psychology, according to a study by Hubbard and Ryan **in 2000**, statistical hypothesis testing – testing that calculates statistical significance – was being used by around 17% of studies in major journals in the 1920s. It pretty much exploded in the 1940s and 1950s, spreading to 85% of studies by 1960, and passing 90% in the 1970s.

How did this get so out of hand? Hubbard and Ryan argue it’s because the p-value was simple and appealing for researchers, and there was “widespread unawareness” of the test’s limitations. There is no simple alternative to replace it with, and some argued for it fiercely. So it was easier to let it take over than fight it. Hubbard and Ryan call out “the failure of professional statisticians to effectively assist in debunking the appeal of these tests”.

The ASA takes a similar line: the “bright line” of p-values at 0.05 is taught because the scientific community and journals use it so much. And they use it so much because that’s what they’re taught.

The result is a bumpy ride in the literature. Here’s my choice of the top 5 things to keep in mind to avoid p-value potholes.

**1. “Significant” in “statistically significant” doesn’t mean “important”.**

You can have a statistically significant p-value of an utterly trivial difference – say, getting better from a week-long cold 10 minutes faster. You could call that “a statistically significant difference”, but it’s no reason to be impressed.

Back in Shakespeare’s day, **significance** still didn’t have the connotation of importance. “Signify” only referred to meaning something. And as **Regina Nuzzo explains**, that’s all the developers of these tests meant in the 1920s, too: a p-value less than 0.05 just signified a result worth studying further.

**2. A p-value is only a piece of a puzzle: it cannot prove whether a hypothesis is true or not.**

This gets to the heart of misuse of p-values. The **ASA statement** could not be clearer on this:

P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.

A statistical hypothesis test is measuring an actual result against a theoretical expectation. It can’t know if the hypothesis is true or not: it just assumes that it is *not* true (a null hypothesis). And then it measures whether or not the result is far enough away from this theoretical null, to be worth more attention.

Steve Goodman says the most common misconception about a p-value of 0.05 is that “the null hypothesis has only a 5% chance of being true” [**PDF**]. You can’t rest a case on it alone, that’s for sure. It’s hard to even nail exactly what the p-value’s implications actually are – which doesn’t mean that it’s always useless [**PDF**]. So where does that leave us?

There isn’t a simple answer. The best ways to analyze data are specific to the situation. But in general, you need to be looking for several things:

*Methodological quality of the research:* No amount of statistics in the world can make up for a study that is the wrong design for the question you care about – or that’s poorly done. What or who is included can skew the value of the results too, if you want to apply the knowledge to another situation.

*Effect size: *You need to understand exactly what is being measured and how big the apparent effect is to be able to get a result into perspective.

*Understanding the uncertainty: *If there’s a p-value, you need to know exactly what it was, not only that it is under 0.05 – is it *just* under, or are there more zeros? (Or how much it is over 0.05.) But even that’s not enough. In fact, you don’t really need the p-value. You need better ways to understand the uncertainty of the estimate: and that means standard deviations, margin of error, or confidence/credible intervals. (More on this **here**, **here**, and **here**.)

*More than one study:* Certainty doesn’t come from a one-off – and especially not from a surprising one. This is why we need systematic reviews and meta-analysis. (More on that **here**, and problems to look out for **here**.)

Some argue, on the other hand, that “the answer” is simply to have a more stringent level of statistical significance than 0.05 (which is the 95% mark, or 1 in 20). Particle physicists have taken this the furthest, expecting to get a **5 sigma result** (and at least twice) before being sure. In p-value terms, that would be **0.0000003**, or 1 in 3.5 million.

Very high levels are going to be unachievable for many kinds of research. The limits to the feasible number you can have in a study for something as complicated as the effects of a drug on human beings wouldn’t come close to enough certainty anyway.

That’s not the only option, though. Bayesian statistics offer more options, with the ability to incorporate what’s known about the probability of a hypothesis being true into analysis. (More on that **here**.)

**3. More is not necessarily better: more questions or bigger datasets increase the chances of p-value potholes. **

The more common an event is, the more likely it is to reach p <0.05 in a bigger dataset. That’s good news for not throwing babies out with bathwater. But it’s bad news for fishing out more false alarms and trivial differences.

The more tests are run on a data set, the higher the risk of p-value false alarms gets. There are tests to try to account for this. (More on this **here**.)

An alternative here is for researchers to use the **false discovery rate** (FDR), which is one way of trying to achieve what people think the test for statistical significance does. That said, Andrew Gelman described the FDR as just “trying to make the Bayesian omelette without breaking the eggs” [**PDF**].

As if this whole road isn’t already hard enough to negotiate, an awful lot of researchers are putting a lot of effort into digging potholes for the rest of us. It’s so common, that many don’t even realize what they are doing is wrong.

It’s called p-hacking or data-dredging: hunting for p-values <0.05 in any dataset without a justified, pre-specified rationale for it – and without safeguards and being open about what they’ve analyzed. More on that and post hoc analyses **here**. Christie Aschwanden and FiveThirtyEight have provided a **great interactive tool** for you to see how you can p-hack your glory, too.

**4. A p-value higher than 0.05 could be an absence of evidence – not evidence of absence.**

This one is tricky terrain, too. People often choose the statistical hypothesis test as their main analysis – but then want to have their cake and eat it too if the result isn’t statistically significant. Matthew Hankins nails this practice of trying to disguise a non-statistically different result “as something more interesting” **here**.

On the other hand, if it’s important or possible that something is making a difference, you need something stronger than non-significance in a single study too (especially if it’s a small one). More on what it takes to be convincing about this **here**.

**5. Some potholes are deliberately hidden: shining the light only on p’s less than 0.05.**

This is called selective outcome reporting, and it adds outcome reporting bias – a “minus” for a study’s overall reliability. You can see it often in **abstracts**, where p-values <0.05 for factors that weren’t even the study’s primary question are highlighted – and the fact that the primary question came up short isn’t even mentioned.

In the biomedical literature, the number of studies reporting p-values in the abstract rose from **7% in 1990 to over 15% in 2014**, almost always claiming at least one p-value below 0.05 – and that’s not a good sign.

This is not always easy to spot, as researchers sometimes go to considerable lengths to hide it. Clinical trial hypotheses and planned outcome assessment are meant to be published before the trial is done and analyzed to prevent this – as well as make it obvious when a trial’s results are not published at all. (More on this at **All Trials**.) But even that isn’t enough to end the practice of biased selective reporting.

Ben Goldacre and colleagues from Oxford’s Centre for Evidence-Based Medicine are systematically studying and calling out outcome-switching in clinical trials. You can read more about this at **COMPARE**.

Pre-registering research is spreading from trials into other fields as well: read more about the campaign for **registered reports**. You can see the impact of unpublished negative results in psychology in an example in **Neuroskeptic’s post** this week.

In many ways, once you get the hang of it, the types of potholes that are out in plain sight are easier to handle – just like potholes in real life.

But especially because so many are hidden, it’s better to always go slowly and look for more solid roadway.

Wherever there are p-values, there can always be potholes.

~~~~

*More Absolutely Maybe posts related to statistical significance:*

**Statistical Significance and Its Part in Science’s Downfalls**

**Mind Your “ps”, RRs and NNTs: On Good Statistics Behavior**

**Biomedical Research: Believe It or Not?**

*And all Absolutely Maybe listicles.*

*[Update]: On 27 April I changed “measuring an actual result against a theoretical set of data” to “against a theoretical expectation”, after a comment by Doug Fletcher. It’s hard to come up with a description or conceptual analogy that works if you take it literally, but I hope this is better. (Thanks, Doug!) And I revisited this after a comment by Steve Taylor, and simplified the following sentence: instead of saying “It doesn’t know if the hypothesis it is ‘testing’ is true or not”, it then said “It can’t know if the hypothesis is true”. (Thanks, Steve!)*

*The cartoons are my own (CC-NC-ND-SA license). *(More cartoons at

**Statistically Funny**and on**Tumblr**.)*The real “signifying nothing” speech is from Shakespeare’s Macbeth.*

*The road with potholes at the top of this post is in Iceland: the photo was taken by Hansueli Krapf ( via Wikimedia Commons).*

*The flooded road with a car caught by a covered pothole is in Russia: the photo was taken by Ilya Plekhanov ( via Wikimedia Commons).*

** The thoughts Hilda Bastian expresses here at ***Absolutely Maybe*** are personal, and do not necessarily reflect the views of the National Institutes of Health or the U.S. Department of Health and Human Services.*

Figures don’t lie but liars can figure.

I’ll always remember – “Significant doesn’t really mean important.”

Thank you.

You find a lot of this. It ie either caused by a lack of knowledge of statistics, or want to lie and giggle the findings according to a researcher’s personal POV or an agenda he is working for. The most blatant example IMO being the secondhand smoke studies which could never statistically prove(using scientific proof standards- 3 standard deviations) a causation and could only prove a correlation(to 2 standard deviations) as they threw out 17% of cases, which not merely shoddy work , rather an intentional lie. Luckily for various lawyers and agenda driven groups very few people can understand statistical principles and what is considered scientifical”proof”.

Forgive any partial misstatements of terms , been 25 years since I got a piece of paper and 15 years since I did any stat work or study. BUt I still get tired of looking at all the lie, and the political correct slant numbers are perverted or dismissed with now.

Indeed, if you torture the data long enough they will confess – but as in most tortures, they will confess to anything!

Nice commentary, with good cautionary tales.

Under Tip #2, you say:

“A statistical hypothesis test is measuring an actual result against a theoretical set of data. It doesn’t know if the hypothesis it is “testing” is true or not: it just assumes that it is not true (the null hypothesis).”

The first sentence might be better as:

“A statistical hypothesis test is measuring an actual result against the results that theoretically could have occurred.”

(In tech-speak – the test statistic is tested against its sampling distribution)

The second sentence is either wrong or ambiguous. A hypothesis test always proceeds as if the null hypothesis were true (until it bumps into a sufficiently small P-value). I suggest that the word “not” should be removed.

Thanks, Doug! I think for lay people especially, what I’ve said helps to get the idea, but I changed it to “actual result against a theoretical expectation”. That’s still not literally explaining the technical process, but it’s closer to the reality than using a kind of analogy as I had done. [Note: this comment itself was updated as I thought of better wording!]

The second sentence would definitely be wrong if I took out the “not”. I see what you mean about the ambiguity, but it’s really tough to communicate the “double negative” that’s involved here for lay people. In order to statistically test people’s “real” hypotheses (that a drug might work, for example), they try to reject the null hypothesis: that the drug does not work. If you’re used to thinking that way, it’s easy to understand this. If you’re not, it’s very confusing. And I’m writing here for people who are not.

I disagree about this “not”. One must assume the null hypothesis is true in order to have a distribution for the test statistic. Only if the test statistic’s value is sufficiently extreme does one reject the assumption that the null is true and start looking for other explanations. These two sentences should say:

A statistical hypothesis test is measuring an actual result against a theoretical expectation derived from the null hypothesis. It doesn’t know if the null hypothesis is true or not: it just assumes that it is true. It also doesn’t know if the alternative hypothesis (the one we are actually interested in) is true or not and relies on these being the only two possibilities to make any inference about it.

Thanks for keeping me at it, Steve. I don’t think what you’re suggesting is easy enough to understand. But I’ve gone about it another way: I’ve shortened it to say “It can’t know whether the hypothesis is true”. That gets rid of the issue of specifying which hypothesis is being tested.

The thing that shocked me deeply is that, when I put these suggestions to a group of journal editors, they said they couldn’t do that because it would harm the impact factor of their journals. That emphasises for me the seriousness of the problems that we face.

Thanks for the citation. My preferred solution is

(a) make sure that people understand the false positive rate, and the fact that it can’t be inferred unambiguously from the P value.

(b) make journals ban the use of the terms “significant” and £non-significant”. Instead they should describe the P value in the following way: http://rsos.royalsocietypublishing.org/content/1/3/140216#comment-1889100957

Rather than the present nonsensical descriptions:

P > 0.05 not significant

P < 0.05 significant

P 0.05 very weak evidence

P = 0.05 weak evidence: worth another look

P = 0.01 moderate evidence for a real effect

P = 0.001 strong evidence for real effect

What beats me is why professional statisticians haven’t been saying this for years (well, actually they have, but only to each other, not to the users).