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Posted 22 Jul 16 by arbelos in Fun math

This is another “fun with math” post meant to impart simple math knowledge that could make the world a better place.

If you aren’t a statistician/math aficionado/empirical economist, you’ve probably never thought about what a “percentage point” is or how it’s different from a “percent”. Frankly, I hadn’t either until one of my advisers in graduate school asked if I was reporting results in percent or percentage points. The realization that there was a difference was eye-opening. Basically, a “percentage point” is always out of 100, whereas a “percent” is always relative to some baseline rate. We can also think of percentage point as telling us something on an absolute scale and a percent as telling us something on a relative scale.

Let me give you an example of why it matters. What sounds scarier, if I tell you that your probability of getting into a fatal car crash is 50 percent higher when driving over the speed limit or if I tell you that your probability of getting into a fatal car crash is 0.5 percentage points higher when driving over the speed limit? Chances are, the first one sounds a lot worse. But the 50% number is relative to some baseline crash rate, which is probably very very low (maybe 1 in a million if we’re talking about a day’s worth of driving). So multiplying that by 1.5 still leaves you pretty safe. By contrast, raising your risk of a fatal car crash by 0.5 percentage points brings it from 0.0001% to 0.5001% - more than a 5000% increase! (By the way, “%” usually refers to “percent”. If you want to talk about percentage points, you should just write it out.)

Why should you care about this difference? Because it’s often helpful to know differences in percentage points rather than percent, especially when it comes to rare events. For example, the risks of birth defects rise dramatically in percent/relative terms with the mother’s age, but the percentage points/absolute changes are actually pretty small. According to this page, 20 year old women have about a 0.19% chance of having a baby with some chromosomal anomalies, whereas 40-year-old women have a 1.52% chance. If you calculate the percent increase in risk, it’s huge, almost 800%. But the percentage point change is clearly much smaller, just 1.33.  

Moral of the story - as a rule of thumb, if you want to scare or impress someone, use percent. If someone is trying to scare or impress YOU, ask them what the percentage point/raw difference is.

Posted 29 Jun 16 by arbelos in Fun math

Search for “What successful people do” and you’ll find dozens of articles and books divulging the secrets. Success could be measured by learning a language, starting a business, having good relationships with people, being happy, etc. Typically, the writers will find some “successful” people and scrutinize their strategies. But what few people realize is that looking at what successful people do is not enough to figure out whether a particular strategy is associated with a higher probability of success. Why? Because you need to (at least) know the rate at which “normal” people employ that strategy!

Let me give you a simple example. Suppose that you read in a book that 80 percent of “successful” people get up at or before 6am every day. 80 percent - that’s a lot! But suppose then I tell you that 80 percent of “normal” people get up at or before 6am every day. All of a sudden, the strategy of getting up at 6am doesn’t look so impressive – it’s just something that all people do. If I tell you that 90 percent of normal people get up at 6am, then it looks like you’re better off sleeping in!

Conversely, just because a strategy is rare among “successful” people doesn’t mean that it’s not a good strategy for success. Let’s go back to the 6am example and say that only 10 percent of successful people get up at or before 6am every day. Is it beneficial to sleep in then? Not if I tell you that only 2 percent of “normal” people get up that early – then successful people are 5 times more likely to get up early than normal ones! So it’s vital to know the rate of a behavior in the “general population” if you want to understand its correlation with “success”.

Of course, I have to end this post with a “correlation-is-not-causation” cautionary tale, as every good scientist should. Suppose I tell you that 90 percent of successful people get up later than 6am (as in the previous example), but only 10 percent of “normal” people do (so success = 9 times more likely to get up later than 6am!). Does this mean sleeping in will bring you good fortune? Absolutely not. It’s very possible (and maybe even likely) that success allows you to “rest on your laurels” and relax, so it’s being successful that causes sleeping in, not the other way around.

Lesson over.

Posted 20 Jun 16 by arbelos in General

For the longest time, I didn’t say anything about my views on gun control publicly. I dislike prolonged Facebook arguments where people seem to be speaking past each other. But, meh, you only have one life to live, and I don’t want to keep my mouth shut for all of it.

So here goes: dear people who say “guns don’t kill people, people kill people”, do you really think that someone could do just as much damage with a knife/axe/sword/crossbow or your other weapon of choice? If you yourself had to face an attacker, would you rather have it be someone with a knife/axe/sword/crossbow or a gun? No one is saying that ONLY guns kill people, but they sure as hell make it a lot easier. Also, maybe restaurants shouldn’t give people forks and knives? After all, forks and knives don’t eat the food, people eat the food.

And people who say “limiting gun access would only hurt law-abiding citizens; the criminals will get their guns somewhere else”, I hope you support full legalization of all drugs and free access to prescription drugs, including opiate painkillers. Because in your world, if it’s just as easy for a criminal to get an illegal gun as a legal one, the same logic should apply to drugs, right? But I suspect most who are so vehemently against any additional restrictions on guns don’t have the same view about drugs.

I’m not saying we should ban guns. In fact, I don’t know what the optimal gun policy looks like, but there are plenty of experts out there who have some good ideas. But what I’m sure about is that there is definitely a way to reduce gun violence through more gun control and saying there isn’t is either dishonest or stupid or both (ok, the other alternative is that you’re a nihilist). Resisting more gun control at all costs is simply irresponsible. That is all.

Posted 11 Jun 16 by arbelos in General

Inevitably, there comes an election cycle where people start talking about moving to Canada if Candidate X wins the race. Of course, this is mostly an expression of a dislike for a candidate rather than a serious intention. As far as I can tell, there was no statistical increase in out-migration to Canada when Bush Jr. won, for example.

Now Candidate X is Donald Trump, and I think it’s time for me to finally speak up and say “Shut up about moving to Canada and do something useful instead!” Talking about moving to Canada is about as lazy as you can get in helping avoid this outcome. So instead of making that your next Facebook post, go and convince someone else not to vote for Donald Trump. As much as you hate to admit it, you very likely know people who will vote for him if you don’t do something about it. Don’t believe? Go ask your friends who they’re planning on voting for. Eventually, you will find at least one person who will say (maybe hesitatingly) “Donald Trump.”

The next thing to say to such a person is not “How could you possibly be so stupid?” or “Our friendship is over!” even if that’s what you’re thinking. What you should do next is find out why that person thinks Donald Trump is the best option this country has and listen to the answer. Don’t assume that anyone who’s willing to vote for Trump is crazy or racist – they may be, but telling them that won’t convince them not to vote for Trump. Instead, engage in a discussion with them about whether their reasons for voting for Trump are justified. Tell them why you’re not voting for Trump and why you think he’s the wrong choice for America in general (other than “He’s an orange-faced idiot”). Help them see that voting for Trump is not in their best interest. Yes, this is a lot harder than lamenting the sad state of American politics, threatening to move to Canada, and calling Trump supporters names. But it’s also a lot more productive. You might even learn something along the way!

To give you some ideas, I will tell you why I think Trump is the absolutely the wrong choice. To keep my posts from getting too long, I’ll do one reason per post. So today will be reason #1 why no one should vote for Donald Trump: we should not let anyone with absolutely no political experience be President, regardless of how smart they are, how much money they’ve made, or how good their ideas are. We don’t let pilots straight out of flight school fly international jetliners – they have to fly regional jets for a while. No one gets to build a house or a bridge until they’ve built something smaller – again, no matter how brilliant they are. Anyone who wants to be President should first do something easier – Congressman, governor, even city mayor. It’s too important of a job to trust to someone completely inexperienced at that particular job.

I know that one of the reasons people support Trump is because they’re tired of politicians’ crap. I very much sympathize with that sentiment. But the solution to that is to look for better politicians, not to take a chance on someone who has never held political office. The better politicians are out there and they can rise to the top. We put the current ones in charge and we can replace them. But let’s start from the bottom up and not the top. Too many lives are at stake to let inexperienced pilots fly 500-person planes; too many lives are affected by the US President for us to pick someone who has no experience governing.

Posted 05 Mar 16 by arbelos in Musings on Economics

Most people are taught in introductory economics courses that they should ignore "sunk costs" (costs that cannot be recovered) in their introductory economics courses. But sometimes decisions involving sunk costs can be tricky, as a recent example I came across illustrates.

I have a "friend" who booked a spring break trip to the Dominican Republic with her two kids and husband nine months in advance. About two weeks before they were scheduled to leave, she realized they didn't have a passport for their younger son. They didn't forget, they didn't procrastinate, they didn't think he DIDN'T need a passport (their older daughter had one) - they just didn't think about it. It's one of those inexplicable things like a woman who doesn't realize she's pregnant until she goes into labor. On top of that, American changed their flight itinerary in a way that would make them have to spend a night in Chicago on the way there and probably on the way back. So they were not happy.

As it turned out, it was possible to get a passport on such short notice, but it would involve driving to Chicago (which is 2.5 hours away) during a work day with the son. But the question is, should they do that? Or should they cancel their vacation and stay home? Unsurprisingly, the answer depends on whether or not the airfare and hotel are refundable.

If the trip is not refundable (= sunk cost), it should make my friend MORE likely to go on this vacation than if it's refundable. Why? Because then the (marginal) cost of the nice vacation becomes the time and effort to drive to Chicago, the two nights' hotel stay in Chicago, and the unpleasantness of dealing with all that. That's not too bad for a fancy week-long vacation in the Dominican Republic. On the other hand, if the trip is fully refundable, then you have the costs already listed PLUS the money paid for the trip (because you could get the money back, it's as though it's still sitting in your bank account and you're considering whether to buy the trip). And while my friend was willing to buy the trip when the flights were easier and the document issue was not on her mind, adding these things into the mix tipped the balance against the trip.

As it turns out, the trip was almost fully refundable, so the family decided to cancel the trip. The moral of the story is that whether or not a cost is sunk changes the marginal cost of doing something and you should consider that next time you forget that you need a passport to go to Canada and find yourself without one.

And I'll be staying in Champaign over spring break...

Posted 04 Feb 16 by arbelos in Science

Recently, the CDC recommended that sexually active women who don’t use birth control don’t drink. I’m not talking about not drinking heavily or not getting buzzed. Not drinking at all. Not even a little bit. Not even half a glass of wine. Because who knows what could happen? Even though there seems to be no good evidence that drinking half a glass of wine here and there will do anything bad to your baby, even if you know you’re pregnant (see here, here, and here, for example), why risk it?

So in the spirit of not risking, I think the CDC should extend their recommendations to women who aren’t on birth control to include: no skydiving, no skiing, no biking, no hot tubs, no ibuprofen, no caffeine, no deli meats, and no jogging. Wait, you say. But can’t pregnant women jog? Yes, but we actually don’t know whether it’s safe or not. Even though there isn’t good evidence that it’s NOT safe, why risk it? Clearly, pregnant women shouldn’t sprint, so maybe jogging is bad too.

Oh, and let’s not forget that pregnant women and their unborn babies die in car accidents all the time (here’s one from yesterday). I’m surprised the CDC has not recommended that pregnant women not get into cars. Or even non-pregnant ones. Let’s stay at home barefoot like nature intended.

Update: this article does a great job discussing other issues with the new CDC recommendations. Summary: CDC, I'm very very disappointed in you.

Posted 02 Feb 16 by arbelos in Science

There has been a lot of sickness around my household, prompting me to try to figure out what I could do to prevent myself from getting sick. I found myself taking probiotic pills, even though the germs around my house were not the kind a probiotic could help against. I also drank vitamin C mixes and in general kept wondering about what other non-clinically-tested thing I could take that maybe marginally works. And then I remembered one thing that we know works very well in many situations - sugar pills, aka placebos. In fact, they sometimes work even when people know they're taking a placebo (see here and here). So here's my great business idea: someone should sell placebo pills that people can take when they feel sick.

Now I know what you're going to say - there are many "placebos" out there in the form of homeopathic treatments and herbal remedies. Those things, however, are fairly expensive. Although there's some evidence that more expensive placebos provide more relief (see here and here), the market needs some cheap placebos too. And the best part is that you don't even have to deceive people. In fact, I was surprised to see that no one makes such a thing already (if you want to have a good laugh, google "placebo pills"). You're welcome.

Posted 27 Jan 16 by arbelos in Musings on Economics

Vaccines prevent diseases and that's awesome because even relatively mild diseases like measles and chickenpox kill or disable a minor share of the people they infect. So it is without a doubt that vaccines have prevented billions of sick days and saved many many lives (don't even go there, anti-vaxxers).

But there's another important benefit of vaccines that I've never seen highlighted - the time they save the parents by reducing the amount of time they have to spend taking care of sick children (I had this epiphany last week when both of my children were sequentially sick and home from daycare). And if your child is constantly home sick, even with routine childhood diseases, it makes it difficult to hold down a job. Undoubtedly, in the pre-vaccines era, this burden would have fallen largely on women. Of course, children still get sick, but my guess is that vaccines made it significantly easier for women with children to hold steady jobs. So the research question is, "What is the effect of vaccines on female labor supply?" Potential title of paper: "Vaccines and Female Labor Supply". You're welcome. 

Posted 10 Jan 16 by arbelos in Simply Amusing

Over the past few years, I've noticed an interesting pattern on my Facebook feed - lots of my friends were sharing articles about how to handle/understand introverts. I was surprised because I didn't think introverts were so rare that there was a need for special instructions about how to deal with them and because some of the people posting did not seem like introverts to me. So I decided to ask my friends (a) if they thought they were an introvert/extrovert and (b) if they thoughts their FRIENDS/FAMILY considered them an introvert or extrovert. A few days ago, I posted a SurveyMonkey questionnaire with those two questions on my Facebook feed.

Of course, lots of caveats apply to my discussion of the results. I'm not a psychologist and this is not research. I didn't define extrovert/introvert either in the questionnaire or in this post, so presumably people just went with their own ideas of who these types are (you can read about the "official" differences here). The people who completed the questionnaire are almost certainly not random. From the two questions, it was probably pretty obvious what I was trying to get at. This post is NOT peer reviewed and may be duplicating existing efforts. Etc, etc.

Anyway, here are the results. Of the 74 people who took my survey, 48 (65%!) considered themselves introverts. This is quite high! The best stat I could (quickly) find says that about half the U.S. population can be classified as an introvert. So this either means that my friends are different (this link claims that people with higher IQ are more likely to be introverts, so maybe my friends are just smart) or that people tend to identify more with the idea of being an introvert, even if an official test would not classify them as an introvert. I also consider myself an introvert, so maybe I'm just more likely to befriend introverts. That's not the interesting part of the survey anyway.

The interesting part is that only half (24) of the self-identified introverts thought that their family and friends would classify them as an introvert. The rest either didn't know (11 people) or thought that their family would classify them as an extrovert (13). So if you extrapolate from this, at least a quarter of all introverts think that they're misclassified by their loved ones. Maybe that's why they were posting all those news articles in the first place!

Now what about the extroverts? There were 23 of them (a few people who took the survey didn't know whether they were introverts or extroverts). A whopping 22 said their family and friends also consider them extroverts and 1 person didn't know. Not a single extrovert said that their friends/family thought they were an introvert!

This is roughly in line with what I was expecting, at least qualitatively. And maybe you're also not surprised, but I think it's nice to confirm ideas with data (subject to many caveats). Thanks to everyone who took the survey!

Posted 21 Oct 15 by arbelos in General

One of my colleagues recently put up a story on her door that can be summarized by the quote "Good decisions come from experience, and experience comes from bad decisions". I can certainly relate to that sentiment. I learned how to make most of the good decisions I make the hard way (and some from watching others make good/bad decisions). But the main reason I want to share this quote is because I think, among many things, it applies to doing research in economics. In particular, I can attest that "Doing good research comes from experience, and experience comes from doing bad research"; "Writing good papers comes from experience, and experience comes from writing bad papers"; and "Making good presentations comes from experience, and experience comes from making bad presentations."

A related sentiment that one of my MIT professors expressed when I was in grad school is that you have to give X bad presentations before you start giving good presentations and you have to write X bad papers before you start writing good papers (X was not specified; I suspect that it's a lot higher for me than it was for that professor). The moral of this is that you should start writing papers and presenting ASAP so you can make it through the bad ones and get to the good ones!

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