[19] Fake Data: Mendel vs. Stapel

Diederik Stapel, Dirk Smeesters, and Lawrence Sanna published psychology papers with fake data. They each faked in their own idiosyncratic way, nevertheless, their data do share something in common. Real data are noisy. Theirs aren’t.

Gregor Mendel’s data also lack noise (yes, famous peas-experimenter Mendel). Moreover, in a mathematical sense, his data are just as lacking in noise. And yet, while there is no reasonable doubt that Stapel, Smeesters, and Sanna all faked, there is that Mendel did. Why? Why does the same statistical anomaly make a compelling case against the psychologists but not Mendel?

Because Mendel, unlike the psychologists, had a motive. Mendel’s motive is his alibi.

Excessive similarity
To get a sense for what we are talking about, let’s look at the study that first suggested Smeesters was a fabricateur. Twelve groups of participants answered multiple-choice questions. Six were predicted to do well, six poorly.  semesters3

(See retracted paper .pdf)

Results are as predicted.  The lows, however, are too similarly low. Same with highs. In “Just Post It” (SSRN), I computed this level of lack of noise had ~21/100000 chance if the data were real (additional analyses lower the odds to miniscule).

Stapel and Sanna had data with the same problem. Results too similar to be true. Even if population means were identical, samples have sampling error. Lack of sampling error suggests lack of sampling.

How Mendel is like Stapel, Smeesters & Sanna
Mendel famously crossed plants and observed the share of baby-plants with a given trait. Sometimes he predicted 1/3 would show it, sometimes 1/4. He was, of course, right. The problem, first noted by Ronald Fisher in 1911 (yes, p-value co-inventor Fisher) is that Mendel’s data also, unlike real data, lacked sampling error. His data were too-close to his predictions.

Mendel

Recall how Smeesters’ data had 27/100000 chance if data were real?
Well, Gregor Mendels’ data had 7/100000 chance (See Fisher’s 1936 paper .pdf; especially Table V).

How Mendel is not like Stapel, Smeesters, Sanna
Mendel wanted his data to look like his theory. He had a motive for lacking noise. It made his theory look better.

Imagine Mendel runs an experiment and gets 27% instead of 33% of baby-plants with a trait. He may toss out a plant or two, he may re-run the experiment; he may p-hack. This introduces reasonable doubt. P-hacking is an alternative explanation for Mendel’s anomalous data. (See e.g., Pires & Branco’s 2010 paper suggesting Mendel p-hacked, .pdf).

Sanna, Smeesters and Stapel, in contrast lack a motive. The similarity is unrelated to their hypotheses. P-hacking to get their results does not explain the degenerate results they get.

One way to think of this is that Mendel’s theory was rich enough to make point predictions, and his data are too similar to these. Psychologists seldom make point predictions, the fabricaterus had their means too similar to each other, not to theory.

Smeesters, for instance, did not need the low conditions to be similar to each other, just to be different from the high so p-hacking wouldn’t get his data to lack noise.1 Worse. p-hacking makes Smeesters’ data look more aberrant.

Before resigning his tenured position, Smeesters told the committee investigating him, that he merely dropped extreme observations aiming for better results. If this were true, if he had p-hacked that way, his low-means would look too different  from each other, not too similar. 2

If Mendel p-hacked, his data would look the way they look.
If Smeesters p-hacked, his data would look the opposite of the way they look.

This gives reasonable doubt to Mendel being a fabricateur, and eliminates reasonable doubt for Smeesters.

CODA: Stapel’s dissertation
Contradicting the committee that investigated him, Stapel has indicated that he did not fake his dissertation (e.g., in this NYTimes story .pdf).

Check out this table from a (retracted) paper based on that dissertation (.pdf).JPSP1996

These are means from a between subject design with n<20 per cell. Such small samples produce so much noise as to make it very unlikely to observe means this similar to each other.

Most if not all studies in his dissertation look this way.

 


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  1. Generic file-drawering of n.s. results will make means appear slightly surprisingly similar among the significant subset. But, not enough to raise red flags (see R code). Also, it will not explain the other anomalies in Smeesters data (e.g., lack of round numbers, negative correlations in valuations of similar items). []
  2. See details in the Nonexplanations section of  “Just Post It”, SSRN []

[18] MTurk vs. The Lab: Either Way We Need Big Samples

Back in May 2012, we were interested in the question of how many participants a typical between-subjects psychology study needs to have an 80% chance to detect a true effect. To answer this, you need to know the effect size for a typical study, which you can’t know from examining the published literature because it severely overestimates them (.pdf1; .pdf2; .pdf3).

To begin to answer this question, we set out to estimate some effects we expected to be very large, such as “people who like eggs report eating egg salad more often than people who don’t like eggs.” We did this assuming that the typical psychology study is probably investigating an effect no bigger than this. Thus, we reasoned that the sample size needed to detect this effect is probably smaller than the sample size psychologists typically need to detect the effects that they study.

We investigated a bunch of these “obvious” effects in a survey on amazon.com’s Mechanical Turk (N=697). The results are bad news for those who think 10-40 participants per cell is an adequate sample.

Turns out you need 47 participants per cell to detect that people who like eggs eat egg salad more often than those who dislike eggs. The finding that smokers think that smoking is less likely to kill someone requires 149 participants per cell. The irrefutable takeaway is that, to be appropriately powered, our samples must be a lot larger than they have been in the past, a point that we’ve made in a talk on “Life After P-Hacking” (slides).

Of course, “irrefutable” takeaways inevitably invite attempts at refutation. One thoughtful attempt is the suggestion that the effect sizes we observed were so small because we used MTurk participants, who are supposedly inattentive and whose responses are supposedly noisy. The claim is that these effect sizes would be much larger if we ran this survey in the Lab, and so samples in the Lab don’t need to be nearly as big as our MTurk investigation suggests.

MTurk vs. The Lab

Not having yet read some excellent papers investigating MTurk’s data quality (the quality is good; .pdf1; .pdf2; .pdf3), I ran nearly the exact same survey in Wharton’s Behavioral Lab (N=192), where mostly undergraduate participants are paid $10 to do an hour’s worth of experiments.

I then compared the effect sizes between MTurk and the Lab (materials .pdf; data .xls).1 Turns out…

…MTurk and the Lab did not differ much. You need big samples in both.

Six of the 10 the effects we studied were directionally smaller in the Lab sample:2

No matter what, you need ~50 per cell to detect that egg-likers eat egg salad more often. The one effect resembling something psychologists might actually care about – smokers think that smoking is less likely to kill someone – was actually quite a bit smaller in the Lab sample than in the MTurk sample: to detect this effect in our Lab would actually require many more participants than on MTurk (974 vs. 149 per cell).

Four out of 10 effect sizes were directionally larger in the Lab, three of them involving gender differences:

So across the 10 items, some of the effects were bigger in the Lab sample and some were bigger in the MTurk sample.

Most of the effect sizes were very similar, and any differences that emerged almost certainly reflect differences in population rather than data quality. For example, gender differences in weight were bigger in the Lab because few overweight individuals visit our lab. The MTurk sample, by being more representative, had a larger variance and thus a smaller effect size than did the Lab sample.3

Conclusion

MTurk is not perfect. As with anything, there are limitations, especially the problem of nonnaïvete (.pdf), and since it is a tool that so many of us use, we should continue to monitor the quality of the data that it produces. With that said, the claim that MTurk studies require larger samples is based on intuitions unsupported by evidence.

So whether we are running our studies on MTurk or in the Lab, the irrefutable fact remains:

We need big samples. And 50 per cell is not big.



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  1. To eliminate outliers, I trimmed open-ended responses below the 5th and above the 95th percentiles. This increases effect size estimates. If you don’t do this, you need even more participants for the open-ended items than the figures below suggest. []
  2. For space considerations, here I report only the 10 of 12 effects that were significant in at least one of the samples; the .xls file shows the full results. The error bars are 95% confidence intervals. []
  3. MTurk’s gender on weight effect size estimate more closely aligns with other nationally representative investigations (.pdf) []

[17] No-way Interactions

This post shares a shocking and counterintuitive fact about studies looking at interactions where effects are predicted to get smaller (attenuated interactions).

I needed a working example and went with Fritz Strack et al.’s  (1988, .pdf) famous paper [933 Google cites], in which participants rated cartoons as funnier if they saw them while holding a pen with their lips (inhibiting smiles) vs. their teeth (facilitating them).

holding pens
The paper relies on a sensible and common tactic: Show the effect in Study 1. Then in Study 2 show that a moderator makes it go away or get smaller. Their Study 2 tested if the pen effect got smaller when it was held only after seeing the cartoons (but before rating them).

In hypothesis-testing terms the tactic is:

Study Statistical Test Example
#1 Simple effect People rate cartoons as funnier with pen held in their teeth vs. lips.
#2 Two-way interaction But less so if they hold pen after seeing cartoons

This post’s punch line:
To obtain the same level of power as in Study 1, Study 2 needs at least twice as many subjects, per cell, as Study 1.

Power discussions get muddied by uncertainty about effect size. The blue fact is free of this problem: whatever power Study 1 had, at least twice as many subjects are needed in Study 2, per cell, to maintain it. We know this because we are testing the reduction of that same effect.

Study 1 with the cartoons had n=31 per-cell.1 Study 2 hence needed to increase to at least n=62 per cell, but instead the authors decreased it to n=21.  We should not make much of the fact that the interaction was not significant in Study 2

(Strack et al. do, interpreting the n.s. result as accepting the null of no-effect and hence as evidence for their theory).

The math behind the blue fact is simple enough (see math derivations .pdf | R simulations| Excel Simulations).
Let’s focus on consequences.

A multiplicative bummer
Twice as many subjects per cell sounds bad. But it is worse than it sounds. If Study 1 is a simple two-cell design, Study 2 typically has at least four (2×2 design).
If Study 1 had 100 subjects total (n=50 per cell), Study 2 needs at least 50 x 2 x 4=400 subjects total.
If Study 2 instead tests a three-way interaction (attenuation of an attenuated effect), it needs N=50 x 2 x2 x 8=1600 subjects .

With between subject designs, two-way interactions are ambitious. Three-ways are more like no-way.

How bad is it to ignore this?
VERY.
Running Study 2 with the same per-cell n as Study 1 lowers power by ~1/3.
If Study 1 had 80% power, Study 2 would have 51%.

Why do you keep saying at least?
Because I have assumed the moderator eliminates the effect. If it merely reduces it, things get worse. Fast. If the effect drops in 70%, instead of 100%, you need FOUR times as many subjects in Study 2, again, per cell. If two-cell Study 1 has 100 total subjects, 2×2 Study 2 needs 800.

How come so many interaction studies have worked?
In order of speculated likelihood:

1) p-hacking: many interactions are post-dicted “Bummer, p=.14. Do a median split on father’s age… p=.048, nailed it!” or if predicted, obtained by dropping subjects, measures, or conditions.

2) Bad inferences: Very often people conclude an interaction ‘worked’ if one effect is  p<.05  and the other isn’t. Bad reasoning allows underpowered studies to “work.”
(Gelman & Stern explain the fallacy .pdf, Nieuwenhuis et al document it’s common .pdf)

3) Cross-overs: Some studies examine if an effect reverses rather than merely goes away,those may need only 30%-50% more subjects per cell.

4) Stuff happens: even if power is just 20%, 1 in 5 studies will work

5) Bigger ns: Perhaps some interaction studies have run twice as many subjects per cell as Study 1s, or Study 1 was so high-powered that not doubling n still lead to decent power.

teeth


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  1. Study 1 was a three-cell design, with a pen-in-hand control condition in the middle. Statistical power of a linear trend with three n=30 cells is virtually identical to a t-test on the high-vs-low cells with n=30. The blue fact applies to the cartoons paper all the same. []

[16] People Take Baths In Hotel Rooms

This post is the product of a heated debate.

At a recent conference, a colleague mentioned, much too matter-of-factly, that she took a bath in her hotel room. Not a shower. A bath. I had never heard of someone voluntarily bathing in a hotel room. I think bathing is preposterous. Bathing in a hotel room is lunacy.

I started asking people to estimate the percentage of people who had ever bathed in a hotel room. The few that admitted bathing in a hotel room guessed 15-20%. I guessed 4%, but then decided that number was way too high. A group of us asked the hotel concierge for his estimate. He said 60%, which I took as evidence that he lacked familiarity with numbers.

One of the participants in this conversation, Chicago professor Abigail Sussman, suggested testing this empirically. So we did that.

We asked 532 U.S.-resident MTurkers who had spent at least one night in a hotel within the last year to recall their most recent hotel stay (notes .pdf; materials .pdf; data .xls). We asked them a few questions about their stay, including whether they had showered, bathed, both, or, um, neither.

Here are the results, removing those who said their hotel room definitely did not have a bathtub (N = 442).

Ok, about 80% of people took a normal person’s approach to their last hotel stay. One in 20 didn’t bother cleaning themselves (respect), and 12.4% took a bath, including an incomprehensible subset who bathed but didn’t shower. Given that these data capture only their most recent hotel stay, the proportion of people bathing is at least an order of magnitude higher than I expected.

 

Gender Differences

If you had told me that 12.4% of people report having taken a bath during their last hotel stay, I’d have told you to include some men in your sample. Women have to be at least 5 times more likely to bathe. Right?

Wrong.

Women bathed more than men (15.6% vs. 10.8%), but only by a small, nonsignificant margin (p=.142). Also surprising is that women and men were equally likely to take a Pigpen approach to life.

 

What Predicts Hotel Bathing?

Hotel quality: People are more likely to bathe in higher quality hotels, and nobody bathes in a one-star hotel.

 

Perceptions of hotel cleanliness: People are more likely to bathe when they think hotels are cleaner, although almost 10% took a bath despite believing that hotel rooms are somewhat dirtier than the average home.

Others in the room: Sharing a room with more than 1 person really inhibits bathing, as it should, since it’s pretty inconsiderate to occupy the bathroom for the length of time that bathing requires. More than one in five people bathe when they are alone.

 

Bathing History & Intentions

We also asked people whether they had ever, as an adult, bathed in a hotel room. Making a mockery of my mockery, the concierge’s estimate was slightly closer to the truth than mine was, as fully one-third (33.3%) reported doing so. One in three.

I give up.

Finally, we asked those who had never bathed in a hotel room to report whether they’d ever consider doing so. Of the 66.7% who said they had never bathed in a hotel room, 64.1% said they’d never consider it.

So only 43% have both never bathed in a hotel room and say they would never consider it.

Those are my people.


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[15] Citing Prospect Theory

Kahneman and Tversky’s (1979) Prospect Theory (.pdf), with its 9,206 citations, is the most cited article in Econometrica, the prestigious journal in which it appeared. In fact, it is more cited than any article published in any economics journal.1

Let’s break it down by year.prospect theory number

To be clear, this figure shows that just in 2013, Prospect Theory got about 700 citations.

Kahneman won the Nobel prize in Economics in 2002. This figure suggests a Nobel bump in citations. To examine whether the Nobel bump is real, I got citation data for other papers. I will get to that in about 20 seconds. Let’s not abandon Prospect Theory just yet.

Fan club.
Below we see which researchers and which journals have cited Prospect Theory the most. Leading the way is the late Duncan Luce with his 38 cites.

researchers

If you are wondering, Kahneman would be ranked 14th with 24 cites, and Tversky 15th with 23. Richard Thaler comes in 33rd place with 16, and DanAriely in 58th with 12.

How about journals?

journals

I think the most surprising top-5 is Management Science, it only recently started its Behavioral Economics and Judgment & Decision Making departments

Not drinking the cool-aid
The first article to cite Prospect Theory came out the same year, 1979, in Economics Letters (.pdf). It provided a rational explanation for risk attitudes differing for gains and losses. The story is perfect if one is willing to make ad-hoc assumptions about the irreversibility of decisions and if one is also willing to ignore the fact that Prospect Theory involves small stakes decisions.  Old school.

Correction: an earlier version of this post indicated the Journal of Political Economy did not cite Prospect Theory until 2005, in fact it was cited already in 1987 (.html).  

About that Nobel bump
The first figure in this blog suggests the Nobel lead to more Prospect Theory cites. I thought I would look at other 1979 Econometrica papers as a “placebo” comparison. It turned out that they also showed a marked and sustained increase in the early 2000s. Hm?

I then realized that Heckman’s famous “Sample Selection as Specification Error” paper was also published in Econometrica in 1979 (good year!) and Heckman, it turns out, got the Nobel in 2000, my placebo was no good. Whether the bump was real or spurious it was expected to show the same pattern.

So I used Econometrica 1980. The figure below shows that deflating Prospect Theory cites by cites of all articles published in Econometrica in 1980, the same Nobel bump pattern emerges. Before the Nobel, Prospect Theory was getting about 40% as many cites per year as all 1980 Econometrica articles combined. Since then that has been rising, in 2013 they were nearly tied.

ratio econometrica 1980

Let’s take this out of sample, did other econ Nobel laureates get a bump in citations? I looked for laureates from different time periods and whose award I thought could be tied to a specific paper.

There seems to be something there, though the Coase cites started increasing a bit early and Akerlof’s a bit late.2

coase Lemos


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  1. Only two psychology articles have more citations:Baron and Kenny paper introducing mediation (.pdf) with 21,746, and Bandura’s on Self-Efficacy (.html) with 9,879 []
  2. The papers: Akerlof, 1970 (..pdf) & Coase, 1960 (..pdf)   []

[14] How To Win A Football Prediction Contest: Ignore Your Gut

This is a boastful tale of how I used psychology to win dominate a football prediction contest.

Back in September, I was asked to represent my department – Operations and Information Management – in a Wharton School contest to predict NFL football game outcomes. Having always wanted a realistic chance to outperform Adam Grant at something, I agreed.

The contest involved making the same predictions that sports gamblers make. For each game, we predicted whether the superior team (the favorite) was going to beat the inferior team (the underdog) by more or less than the Las Vegas point spread. For example, when the very good New England Patriots played the less good Pittsburgh Steelers, we had to predict whether or not the Patriots would win by more than the 6.5-point point spread. We made 239 predictions across 16 weeks.

Contrary to popular belief, oddsmakers in Las Vegas don’t set point spreads in order to ensure that half of the money is wagered on the favorite and half the money is wagered on the underdog. Rather, their primary aim is to set accurate point spreads, one that gives the favorite (and underdog) a 50% chance to beat the spread.1 Because Vegas is good at setting accurate spreads, it is very hard to perform better than chance when making these predictions. The only way to do it is to predict the NFL games better than Vegas does.

Enter Wharton professor Cade Massey and professional sports analyst Rufus Peabody. They’ve developed a statistical model that, for an identifiable subset of football games, outperforms Vegas. Their Massey-Peabody power rankings are featured in the Wall Street Journal, and from those rankings you can compute expected game outcomes. For example, their current rankings (shown below) say that the Broncos are 8.5 points better than the average team on a neutral field whereas the Seahawks are 8 points better. Thus, we can expect, on average, the Broncos to beat the Seahawks by 0.5 points if they were to play on a neutral field, as they will in Sunday’s Super Bowl.2

 

My approach to the contest was informed by two pieces of information.

First, my work with Leif (.pdf) has shown that naïve gamblers are biased when making these predictions – they predict favorites to beat the spread much more often than they predict underdogs to beat the spread. This is because people’s first impression about which team to bet on ignores the point spread and is thus based on a simpler prediction as to which team will win the game. Since the favorite is usually more likely to win, people’s first impressions tend to favor favorites. And because people rarely talk themselves out of these first impressions, they tend to predict favorites against the spread. This is true even though favorites don’t win against the spread more often than underdogs (paper 1, .pdf), and even when you manipulate the point spreads to make favorites more likely to lose (paper 2, .pdf). Intuitions for these predictions are just not useful.

Second, knowing that evidence-based algorithms are better forecasters than humans (.pdf), I used the Massey-Peabody algorithm for all my predictions.

So how did the results shake out? (Notes on Analyses; Data)

First, did my Wharton colleagues also show the bias toward favorites, a bias that would indicate that they are no more sophisticated than the typical gambler?

Yes. All of them predicted significantly more favorites than underdogs.

 

Second, how did I perform relative to the “competition?”

Since everyone loves a humble champion, let me just say that my victory is really a victory for Massey-Peabody. I don’t deserve all of the accolades. Really.

Yeah, for about the millionth time (see meta-analysis, .pdf), we see that statistical models outperform human forecasters. This is true even (especially?) when the humans are Wharton professors, students, and staff.

So, if you want to know who is going to win this Sunday’s Super Bowl, don’t ask me and don’t ask the bestselling author of Give and Take. Ask Massey-Peabody.

And they will tell you, unsatisfyingly, that the game is basically a coin flip.



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  1. Vegas still makes money in the long run because gamblers have to pay a fee in order to bet []
  2. For any matchup involving home field advantage, give an additional 2.4 points to the home team []

[13] Posterior-Hacking

Many believe that while p-hacking invalidates p-values, it does not invalidate Bayesian inference. Many are wrong.

This blog post presents two examples from my new “Posterior-Hacking” (SSRN) paper showing  selective reporting invalidates Bayesian inference as much as it invalidates p-values.

Example 1. Chronological Rejuvenation experiment
In  “False-Positive Psychology” (SSRN), Joe, Leif and I run experiments to demonstrate how easy p-hacking makes it to obtain statistically significant evidence for any effect, no matter how untrue. In Study 2 we “showed” that undergraduates randomly assigned to listen to the song “When I am 64” became 1.4 years younger (p<.05).

We obtained this absurd result by data-peeking, dropping a condition, and cherry-picking a covariate. p-hacking allowed us to fool Mr. p-value. Would it fool Mrs. Posterior also? If we take the selectively reported result and feed it to a Bayesian calculator. What happens?

The figure below shows traditional and Bayesian 95% confidence intervals for the above mentioned 1.4 years-younger chronological rejuvenation effect.  Both point just as strongly (or weakly) toward the absurd effect existing.1

f2

When researchers p-hack they also posterior-hack

Example 2. Simulating p-hacks
Many Bayesian advocates propose concluding an experiment suggests an effect exists if the data are at least three times more likely under the alternative than under the null hypothesis. This “Bayes factor>3” approach is philosophically different, and mathematically more complex than computing p-values, but it is in practice extremely similar to simply requiring p< .01 for statistical significance. I hence run simulations assessing how p-hacking facilitates getting p<.01 vs getting Bayes factor>3.2

I simulated difference-of-means t-tests p-hacked via data-peeking (getting n=20 per-cell, going to n=30 if necessary), cherry-picking among three dependent variables, dropping a condition, and dropping outliers. See R-code.

f3
Adding 10 observations to samples of size n=20 a researcher can increase her false-positive rate from the nominal 1% to 1.7%. The probability of getting a Bayes factor >3 is a comparable 1.8%. Combined with other forms of p-hacking, the ease with which a false finding is obtained increases multiplicatively. A researcher willing to engage in any of the four forms of p-hacking, has a 20.1% chance of obtaining p<.01, and a 20.8% chance of obtaining a Bayes factor >3.

When a researcher p-hacks, she also Bayes-factor-hacks.

Everyone needs disclosure
Andrew Gelman and colleagues, in their influential Bayesian textbook write:

A naïve student of Bayesian inference might claim that because all inference is conditional on the observed data, it makes no difference how those data were collected, […] the essential flaw in the argument is that a complete definition of ‘the observed data’ should include information on how the observed values arose […]”
(p.203, 2nd edition)

Whether doing traditional or Bayesian statistics, without disclosure, we cannot evaluate evidence.



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  1. The Bayesian confidence interval is the “highest density posterior interval”, computed using Kruschke’s BMLR (html). []
  2. This equivalence is for the default-alternative, see Table 1 in Rouder et al, 2009 (HTML).  []

[12] Preregistration: Not just for the Empiro-zealots

I recently joined a large group of academics in co-authoring a paper looking at how political science, economics, and psychology are working to increase transparency in scientific publications. Psychology is leading, by the way.

Working on that paper (and the figure below) actually changed my mind about something. A couple of years ago, when Joe, Uri, and I wrote False Positive Psychology, we were not really advocates of preregistration (a la clinicaltrials.gov). We saw it as an implausible superstructure of unspecified regulation. Now I am an advocate. What changed?

Transparency in Scientific Reporting Figure

First, let me relate an anecdote originally told by Don Green (and related with more subtlety here). He described watching a research presentation that at one point emphasized a subtle three-way interaction. Don asked, “did you preregister that hypothesis?” and the speaker said “yes.” Don, as he relates it, was amazed. Here was this super complicated pattern of results, but it had all been predicted ahead of time. That is convincing. Then the speaker said, “No. Just kidding.” Don was less amazed.

The gap between those two reactions is the reason I am trying to start preregistering my experiments. I want people to be amazed.

The single most important scientific practice that Uri, Joe, and I have emphasized is disclosure (i.e., the top panel in the figure). Transparently disclose all manipulations, measures, exclusions, and sample size specification. We have been at least mildly persuasive, as a number of journals (e.g., Psychological Science, Management Science) are requiring such reporting.

Meanwhile, as a researcher, transparency creates a rhetorical problem. When I conduct experiments, for example, I typically collect a single measure that I see as the central test of my hypothesis. But, like any curious scientist, I sometimes measure some other stuff in case I can learn a bit more about what is happening. If I report everything, then my confirmatory measure is hard to distinguish from my exploratory measures. As outlined in the figure above, a reader might reasonably think, “Leif is p-hacking.” My only defense is to say, “no, that first measure was the critical one. These other ones were bonus.” When I read things like that I am often imperfectly convinced.

How can Leif the researcher be more convincing to Leif the reader? By saying something like, “The reason you can tell that the first measure was the critical one is because I said that publicly before I ran the study. Here, go take a look. I preregistered it.” (i.e., the left panel of the figure).

Note that this line of thinking is not even vaguely self-righteous. It isn’t pushy. I am not saying, “you have to preregister or else!” Heck, I am not even saying that you should; I am saying that I should. In a world of transparent reporting, I choose preregistration as a way to selfishly show off that I predicted the outcome of my study. I choose to preregister in the hopes that one day someone like Don Green will ask me, and that he will be amazed.

I am new to preregistration, so I am going to be making lots of mistakes. I am not going to wait until I am perfect (it would be a long wait). If you want to join me in trying to add preregistration to your research process, it is easy to get started. Go here, and open an account, set up a page for your project, and when you’re ready, preregister your study. There is even a video to help you out.


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[11] “Exactly”: The Most Famous Framing Effect Is Robust To Precise Wording

In an intriguing new paper, David Mandel suggests that the most famous demonstration of framing effects – Tversky & Kahneman’s (1981) “Asian Disease Problem” – is caused by a linguistic artifact. His paper suggests that eliminating this artifact eliminates, or at least strongly reduces, the framing effect. Does it?

This is the perfect sort of paper for a replication: The original finding is foundational and the criticism is both novel and fundamental. We read Mandel’s paper because we care about the topic, and we replicated it because we cared about the outcome.

The Asian Disease Problem

Imagine that an Asian disease is expected to kill 600 people and you have to decide between two policies designed to combat the disease. The policies can be framed in terms of gains (people being saved) or in terms of losses (people dying).

Tversky and Kahneman found that whereas 72% of people given the gain frame chose Program A’s 200 of 600 certain lives saved, only 22% of people given the loss frame chose Program C’s 400 of 600 certain deaths. This result supports prospect theory: people will take risks to avoid losses but will avoid risks to protect gains.

Just a Linguistic Artifact?

David Mandel argues that when people read “200 people will be saved” or “400 people will die” they interpret it as “at least 200 people will be saved” or “at least 400 people will die”. That small difference in interpretation would switch the finding from irrational to sensible, as the certain option would potentially save more people in the gain frame (>200 of 600 will be saved) than in the loss frame (>400 of 600 will die). Mandel resolves the ambiguity by adding the word “exactly” (“exactly 200 people will be saved”). Because the word “exactly” makes it clear that no more than 200 will be saved, he predicts that including that word will eliminate the framing effect.

In Study 2 (the study most faithful to the original), Mandel used Tversky and Kahneman’s wording and replicated their result (58% chose to save 200 people for certain; 26% chose to kill 400 people for certain). When he added “exactly,” that difference was reduced (59% vs. 43%).1

We replicated Mandel’s procedure. We showed mTurk workers the same scenario and asked the same questions. We collected ~2.5 times Mandel’s sample size; Mandel had ~38 per cell and we had ~98 per cell. (Following Mandel, we also included conditions with “at least” as a modifier; here are those results).

Unlike Mandel, we found a strong framing effect even with the use of the word “exactly” (p<.001) (materialsdata):

For completeness, we should report that Mandel emphasized a different dependent variable – a continuous measure of preference. We measured that too and it also failed to replicate his result.

In sum, our replication suggests that Tversky and Kahneman’s (1981) framing effect is not caused by this linguistic artifact.

We Could Have Just Asked Uri

When we told Uri about all this, he told us that he conducts this experiment in his class each year and that he uses the word “exactly” in his materials. The experiment has replicated every single year. For example, in the past two years combined (N=250), he observed that 63% chose to save 200 lives for sure whereas only 25% chose to let 400 die for sure.

David Mandel Responds

As is our policy, we sent a draft of this post to David Mandel to offer him the chance to respond. Please check out David’s response below. We are very thankful he took the time to do this:

I welcome this replication experiment by Joseph Simmons and Leif Nelson. I think we all agree proper replications are important regardless of how the results turn out. They have kindly offered me 150 words to reply, but that would hardly get me started. There are many points to cover, both about the replication and some of the broader issues it sparks. Joe contacted me on the Friday before the post went live with the “unwelcome news” and it’s been a weekend of changed plans, but I wanted to have a reply ready when the post goes live. Here it is on my website [and here it as a pdf]. I hope you read both. Feel free to email me if you have comments. Lastly, Joe invited me to comment on their post, but I haven’t since I cover what I might have otherwise recommended they alter in my reply. Readers can make up their own minds. 151, 152…

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  1. However, compared to the condition with the original wording, this reduction was nonsignificant (p=.293). []

[10] Reviewers are asking for it

Recent past and present
The leading empirical psychology journal, Psychological Science, will begin requiring authors to disclose flexibility in data collection and analysis starting on January of 2014 (see editorial). The leading business school journal, Management Science, implemented a similar policy a few months ago.

Both policies closely mirror the recommendations we made in our 21 Word Solution piece, where we contrasted the level of disclosure in science vs. food (see reprint of Figure 3).

2013-12-07_102828
Our proposed 21 word disclosure statement was:

We report how we determined our sample size, all data exclusions (if any), all manipulations, and all measures in the study.

Etienne Lebel tested an elegant and simple implementation in his PsychDisclosure project. Its success contributed to Psych Science‘s decision to implement disclosure requirements.

Starting Now
When reviewing for journals other than Psych Science and Management Science, what could reviewers do?

On the one hand, as reviewers we simply cannot do our jobs if we do not know fully what happened in the study we are tasked with evaluating.

On the other hand, requiring disclosure from an individual article one is reviewing risks authors taking such requests personally (reviewers are doubting them) and risks revealing our identity as reviewers.

A solution is a uniform disclosure request that large numbers of reviewers request for every paper they review.

Together with Etienne LebelDon Moore, and Brian Nosek we created a standardized request that we and many others have already begun using in all of our reviews. We hope you will start using it too. With many reviewers including it in their referee reports, the community norms will change:

I request that the authors add a statement to the paper confirming whether, for all experiments, they have reported all measures, conditions, data exclusions, and how they determined their sample sizes. The authors should, of course, add any additional text to ensure the statement is accurate. This is the standard reviewer disclosure request endorsed by the Center for Open Science [see http://osf.io/project/hadz3]. I include it in every review.


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