How failed replications change our effect size estimates

Yesterday I posted a very unscientific survey asking researchers to describe how failed replications changed their subjective estimates of effect sizes. The main survey asked for “ballpark estimates” of effect sizes, but an alternative interactive version allowed researchers to also report their uncertainty by specifying both the mean and variance of their posterior distributions. Thanks to everyone who participated. I won’t be analyzing any new data after this, but it’s never too late to publicly share your estimates!

Here are the questions. 

Question 1. A 2009 experiment with 50 subjects (25 per cell) is published in Psych Science. The experiment does not require any special equipment other than a questionnaire. It is not pre-registered. The results show an effect size of d=0.5. Let’s define the true effect size to be the average effect size of an infinite number of replications that the original experimenter would deem “reasonably exact” in advance. Based on this information alone, what is your ballpark subjective estimate of the true effect size?

Question 2. What if the experiment had been pre-registered? 

Question 3. Assume again that the experiment was not pre-registered. Now imagine that a pre-registered replication attempt with the same sample size estimated the effect size to be d=0.0. At the time of pre-registration, the original experimenter deemed it “reasonably exact”. Based on this replication and the original experiment, what is your ballpark subjective estimate of the true effect size?

Question 4. What if the replication attempt had 300 subjects per cell?

Here are the results.

results

Keeping in mind all the caveats about sampling bias and other issues, here are a few observations:

  • The original study reported an effect size of d=0.5, but the results for Question 1 tell us that most researchers believed the true effect size was closer to d=0.2, which is roughly in line with my own estimate. Had I allowed researchers to state their uncertainty, I suspect that many would find it quite possible that even the sign of the effect was wrong. This isn’t really surprising to me, but I think we should take a moment to reflect on what this means. When a scientist reports a result, most other researchers believe it is massively overstated. I know that there are still some researchers who want little or no changes to the status quo, but I’d like to live in a world where people actually believe the claims that scientists make. That’s why I’m a strong supporter of all the attempts to fundamentally change how scientists do research.
  • If you want people to have more confidence in your findings, pre-registration can make a big difference.
  • While it’s not apparent from the plot, almost all respondents reduced their effect size estimate upon hearing about failed replications (Question 3 and 4 compared to Question 1).
  • As some have pointed out, the original experiment falls a bit short of statistical significance. This was an oversight, as I forgot to check the p-value after changing some of the values. I don’t think this is a huge deal, since posterior estimates shouldn’t really depend too much on whether the results cross an arbitrary threshold. But apologies for the error.
  • My estimates were .25, .40, .10, .05.
  • I wish I included another question asking what people would have thought of the original study if it was conducted in 2014.

Jason Mitchell’s essay

As of yesterday I thought the debate about replication in psychology was converging on consensus in at least one respect. While there was still some disagreement about tone, basically everyone agreed that there was value in failed replications. But then this morning, Jason Mitchell posted this essay, in which he describes his belief that failed replication attempts can contain errors and therefore “cannot contribute to a cumulative understanding of scientific phenomena”. It’s hard to know where to begin when someone comes from a worldview so different from one’s own. Since there’s clearly a communication problem here, I’ll just give two examples to illustrate how I think about science.

  • Example 1. A rigorous lab conducts an experiment using a measurement device that requires special care. The effect size is d=0.5. Later, a different lab with no experience using the device tries to quickly replicate the experiment and computes an effect size of d=0.0.
  • Example 2. A small sample experiment in a field with a history of p-hacking shows an effect size of d=0.5. Another lab tries to replicate the study with a much larger sample and computes an effect size of d=0.0.

In both cases, I’d have subjective beliefs about the true effect size. For the first example, my posterior distribution might peak around d=0.4. For the second example, my posterior distribution might peak around d=0.1. In both cases, the replication would influence my posterior, but to varying degrees. In the first example, it would cause a small shift. In the second, it would cause a big shift. Reasonable people can disagree on the exact positions of the posteriors, but basically everyone ought to agree that our posteriors should incrementally adjust as we acquire new information, and that the size of these shifts should depend on a variety of factors, including the possibility of errors in either the original experiment or in the replication attempt. Maybe it’s because I’m stuck in a worldview, but none of this even seems very hard to understand. 

Jason Mitchell sees things differently. For him, all failed replications contain “no meaningful evidentiary value” and “do not constitute scientific output”. I don’t doubt the sincerity of his beliefs, but I suspect that most scientists and nonscientists alike will find these assertions to be pretty bizarre. NHST isn’t the only thing causing the crisis in psychology, but it’s pretty clear that this is what happens when people get too immersed in it. 

How I use Twitter

Next week I’m going to start a new job as a data scientist at Twitter and I am thrilled. Aside from Google search, no other website has had a more positive impact on my life than Twitter. Twitter is just so much fun, and I have learned so much from it. 

Because my experience has been so good, it saddens me to hear that some people don’t really “get” Twitter. Some people who try it feel frustrated and stop using it. Others use it occasionally but don’t really see what all the fuss is about.

I want to share my approach to using Twitter so that others can try. There are probably other ways to enjoy it, but this approach has worked well for me:

  • I don’t necessarily follow my friends, and I don’t expect them to follow me. I use Twitter for a limited set of interests, and not all of my friends tweet about those interests.
  • I generally don’t follow organizations. They tend to tweet too much and their content is often too promotional.
  • Instead, I follow opinionated people who tweet about a small set of topics that I’m interested in.
  • I make sure that my tweet stream is slow enough that I can read every tweet. I do this by limiting the number of people I follow and by making sure that I don’t follow people who tweet too much, even if they have good content.

That’s it. Follow opinionated strangers who tweet about topics you are interested in. Maybe you have a different approach that works well for you. But if you are still trying to figure out the incredible appeal of Twitter, you might want to give my approach a shot.

Is your job in another state?

National unemployment is high, but business is booming in some states. Vermont needs teachers. Nevada needs bartenders. North Dakota needs truck drivers and just about everything else.

Despite these opportunities, Americans aren’t moving much and unemployment remains high.  One reason for this is that moving can be expensive and disruptive, especially for those with families and roots in their communities. But another reason may just be lack of awareness about the opportunities in other states. That’s why I have made a new website: www.ismyjobinanotherstate.com. Enter your job skills, and the website will provide an interactive map showing where you are most in demand.

SecurityOfficerStates are ranked by their ratio of job postings to unemployment. This is a pretty good metric, but it isn’t perfect. To understand why, imagine two states with the same posting/unemployed ratio for a particular job. If you are trained for the job, you might have better luck applying in a state where the unemployed population is either untrained or unwilling to take that type of job, even though the two states have the same ratio. There also may be differences across states in the use of Indeed.com. Still, I think my results have reasonably good face validity, and the results for many jobs are close to what you would except. If you average across jobs, you get something pretty close to an independently created measure called the “Opportunity Index”.

Job posting data was collected using the Indeed.com api. Unemployment numbers came from the Bureau of Labor Statistics. For more information about how this works, see my the GitHub repository.

My Insight Data Science Project

I just finished an excellent fellowship at Insight Data Science. During our first few weeks there, each of us designed a website to demo at Insight’s sponsor companies. My website is called DealSpotter.

This all started earlier this summer when I went to Craigslist to find a used car. There were lots of good deals on Craigslist, but it took way too long to find them. When I searched for a particular model, I got hundreds of hits, but only a few of the hits included the mileage in the posting title. Since I needed the mileage to know whether I was getting a good deal, I had to click on each of the hundreds of listings. Pretty time consuming.

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A larger problem was that even if I clicked on every post, I didn’t always have a sense for what was the best deal. For example, if I had $3,000, was it better to spend it on a 2001 model with 100K miles, or a 2003 model with 140K miles?

DealSpotter is a proof-of-concept website that shows how these problems could be solved. DealSpotter grabs all the Craigslist car postings in the San Francisco Bay Area and automatically shows you the best deals. It knows how much each car should be priced, based on the model, year, and mileage. Cars that are priced lower than DealSpotter expects them to be are shown at the top of the list. DealSpotter also presents the same information in a visual format called “Graph” mode, where the best deals are highlighted in blue.

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To determine how much each car should be priced, DealSpotter doesn’t use Kelley Blue Book, which tends to overprice cars, especially newer models. Instead, DealSpotter builds its own pricing model based on the actual Craigslist market. In particular, it uses a Random Forest pricing model because, unlike smooth parametric models, Random Forests are able to detect sharp discontinuities in prices that may be caused by factors such as manufacturer design overhauls.

By selecting cars that are priced much lower than would be expected based on year and mileage, DealSpotter picks out some incredible deals, as well as the occasional clunker with an accident history. A more elaborate service might find a way to filter for accident history, but for now DealSpotter remains useful because it greatly narrows down the scope of the search for users. Once users are dealing with a handful of posts, they can easily inspect the text of the ad to determine which cars are good deals, and which have a history of accidents.

If you are in the San Francisco Bay Area and are looking for a used car, you should definitely check out my website right now. Many cars are underpriced by thousands of dollars. In the future though, I won’t be updating the listings, which will soon become outdated. Craigslist has a history of suing other services that try to improve on how their data is presented. Craigslist’s litigiousness is understandable — they curated the data after all. But it apparently has also stifled innovation. Craigslist users spend many hours of their time clicking on blue links because the website’s search and UI tools are still stuck in the 90’s. Users are also at higher risk of scams because there is no reputation system. Normally, issues like this would put a company out of business, but a combination of lawsuits and network lock-in effects have kept Craigslist at the top of classifieds services. Hopefully, we will one day get a better Craigslist. In the meantime, if you want to find an incredible deal on a car while the postings are still fresh, you should do so now.

FAQ for www.whichfamouseconomistareyoumostsimilarto.com

I made a new webpage, http://www.whichfamouseconomistareyoumostsimilarto.com

Here’s an FAQ for it.

Q. What is this and why did you make it?
A. There is a surprising amount of consensus among economists on many issues. Progressive consumption taxes and carbon taxes are good. Personal income taxes and corporate taxes are bad. Congestion pricing is good. The mortgage deduction is bad. Marijuana should be legalized. These positions are endorsed by almost every economist, both from the left and the right, but politicians in Washington tend to support the opposite.

The IGM Forum surveys an ideologically diverse group of top economists on these and other issues. I wish more people knew about their website. My new webpage, http://www.whichfamouseconomistareyoumostsimilarto.com, collects responses from the IGM forum and allows users to compare it to their own responses.

Q. Why is the economist closest to me on the graph different from the economist who actually is closest to me, according to the text below the graph?
A. Each economist can be thought of as a point in a massive 105 dimensional space, and unfortunately it’s only possible to display 2 dimensions. While you may appear close to an economist on those 2 dimensions, you may be far apart on the 103 other dimensions that you can’t see.

Q. I don’t have the expertise to answer some of these questions. Should I leave them blank or should I click “Neutral”?
A. You should leave them blank so that they do not enter the calculations. “Neutral” indicates that you have a real opinion somewhere between “Agree” and “Disagree”

Q. Every question I answer makes me move very far on the graph. This seems unreliable.
A. Do not take your graph position seriously until you have answered at least 20 questions. Your position will gradually converge as you answer more.

Q. Responses that “strongly deviate from expert consensus” are highlighted in yellow. What does that mean?
A. It means that your response deviated more that two standard deviations from the IGM panel average.

Q. I have answered only one question and it has put me in an extreme part of the graph. However my response does not get highlighted as a deviating response. Is something wrong?
A. To calculate your position in the graph, I use your past responses to make assumptions about your future responses. If you have only answered a few questions, those assumptions will be far from accurate.

Q. I just answered a question the exact same way as Economist X. But my position on the graph moved away from him/her. Why?
A. This is a natural consequence of projecting multiple dimensions onto two dimensions. To see why, take a cube-shaped object and trace your finger along the edges from one corner to the opposite corner. Viewed from some angles, your finger might sometimes appear to move away from the destination corner.

Q. I’m finding some other unexpected behavior not explained by the previous two questions.
A. There is some built-in bias resulting from mean-centering and a dummy question I added so that movement occurs after the first response. This bias will affect your position when only a few questions have been answered but it will become negligible when many questions have been answered.

Q. Why were some IGM panel economists excluded from your webpage?
A. Economists who answered less than 75% of the questions were excluded.

Q. Can you interpret what the first two principal components represent?
A. I left the axes uninterpreted because I don’t want to oversimplify things: The first two PCs only explain 20% of the variance, and they are biased by the choice of questions. But ok, I’ll bite: The horizontal axis appears to represent the left-right axis in partisan American politics, with strong weights on emotionally charged issues like school vouchers and the minimum wage. But — and I can’t stress this enough – the horizontal axis is not identical to our verbal understanding of the left-wing / right-wing continuum. Our verbal understanding of this concept corresponds to a complicated, bendy, twisty dimension within the 105 dimensional space, and it probably explains about 60% of the variance in responses. The horizontal dimension explains a meager 12% of the variance. This means that some responses that are actually left-wing will correspond to rightward movements and vice-versa. The vertical dimension is even harder to interpret. There are large weights on questions pertaining to bank regulation and monetary policy.

To give you a better sense of the dimensions, here are some questions for which answering “strongly agree” will push you far in one of the directions.

Top 5 leftward questions. 

(1) Question B: The distortionary costs of raising the federal minimum wage to $9 per hour and indexing it to inflation are sufficiently small compared with the benefits to low-skilled workers who can find employment that this would be a desirable policy.

(2) Question C: Taking into account all of the economic consequences — including effects on corporate managers’ incentives and on creditors’ expectations of how their claims will be treated in future bankruptcies — the benefits of bailing out GM and Chrysler will end up exceeding the costs.

(3) Question A: Taking into account all of the economic consequences — including the incentives of banks to ensure their own liquidity and solvency in the future — the benefits of bailing out U.S. banks in 2008 will end up exceeding the costs.

(4) Question A: The U.S government should make further efforts to shrink the size of the country’s largest banks — such as by capping the size of their liabilities or penalizing large banks more heavily through taxes or other means — because the existing regulations do not require the biggest banks to internalize enough of the “too-big-to-fail” risks that they pose.

Top 5 rightward questions

(1) Public school students would receive a higher quality education if they all had the option of taking the government money (local, state, federal) currently being spent on their own education and turning that money into vouchers that they could use towards covering the costs of any private school or public school of their choice (e.g. charter schools).

(2) Question B: Past experience of public spending and political economy suggests that if the government spent more on roads, railways, bridges and airports, many of the projects would have low or negative returns.

(3) Laws that limit the resale of tickets for entertainment and sports events make potential audience members for those events worse off on average.

(4) New technology for fracking natural gas, by lowering energy costs in the United States, will make US industrial firms more cost competitive and thus significantly stimulate the growth of US merchandise exports.

Top 5 upward questions

(1) Even if inflationary pressures rise substantially as a result of quantitative easing and low interest rates, the Federal Reserve has ample tools to rein inflation back in if it chooses to do so.

(2) Taking into account all of the economic consequences — including the incentives of banks to ensure their own liquidity and solvency in the future — the benefits of bailing out U.S. banks in 2008 will end up exceeding the costs.

(3) Even if the third round of quantitative easing that the Fed recently announced increases annual consumer price inflation over the next five years, the increase will be inconsequential.

(4) Despite relabeling concerns, taxing capital income at a permanently lower rate than labor income would result in higher average long-term prosperity, relative to an alternative that generated the same amount of tax revenue by permanently taxing capital and labor income at equal rates instead.

Top 5 downward questions

(1) Public school students would receive a higher quality education if they all had the option of taking the government money (local, state, federal) currently being spent on their own education and turning that money into vouchers that they could use towards covering the costs of any private school or public school of their choice (e.g. charter schools).

(2) Question A: The U.S government should make further efforts to shrink the size of the country’s largest banks — such as by capping the size of their liabilities or penalizing large banks more heavily through taxes or other means — because the existing regulations do not require the biggest banks to internalize enough of the “too-big-to-fail” risks that they pose.

(3) The former head of the Transportation Security Administration is correct in arguing that randomizing airport “security procedures encountered by passengers (additional upper-torso pat-downs, a thorough bag search, a swab test of carry-ons, etc.), while not subjecting everyone to the full gamut” would make it “much harder for terrorists to learn how to evade security procedures.”

(4) Question C: Unless there is a substantial default by some combination of Greece, Ireland, Italy, Portugal and Spain on their sovereign debt and commercial bank debt, plus credible reforms to prevent excessive borrowing in the future, the euro area is headed for a costly financial meltdown and a prolonged recession.