Oreo Preferences

Everyone loves Oreos! They are delicious and sugary and chocolatey and have excellent filling!

For your pleasure, I have done extensive research on the preferences of several different kinds of Oreos. Well, maybe not extensive research. But a bunch of research anyways!

I did a small study to compare Oreos, Oreo Double Stuf, and Oreo Thins. Here are some basic stats about the cookies in question:

Name Calories/

Serving

Serving Size Calorie/

cookie

Servings per box Cookies Calories per box
Oreo 160 3 53.3 12 36 1920
Oreo Double 140 2 70.0 15 30 2100
Oreo Thin 140 4 35.0 10 40 1400

I had 21 participants. Only 4 of my participants regularly pulls their Oreos apart. But 41% of the participants dunk their Oreos in milk! So the milk tradition is still going strong. Of these 21, 10 preferred double stuf, 8 preferred classic and 3 preferred thins.

I wanted to understand the overall preference between these cookie types versus their caloric intake. I want to determine if this data would change anyone’s mind about which cookie they eat.

I am a die-hard Double Stuf eater. I don’t understand why anyone would eat a classic Oreo. There is far too much cookie for the amount of filling. However, there is the disappointing truth that my cookie choice costs 16 calories more per cookie. And I only get 30 cookies in my box of cookies. If I’m trying to count calories the question is: do I love a single double stuf cookie 30% more than I love a single regular Oreo?  For me, there is no question. I absolutely do. Lets get into the weeds: if I prefer double stuf and my enjoyment level is an 7, but my enjoyment level of a classic is a 4. Then I enjoy my double stuf 7/4 -1 = 75% more than I enjoy the classic. So, even if I’m watching my calories, I shouldn’t switch to classic.

My participants were given a single cookie of each type as asked to rate their preferences in order (1st, 2nd, 3rd) and then to rate their enjoyment numerically from 0 to 10.  So I can also consider their answers. Do those who prefer double stuf prefer it by more than 30%?  Of the 10 people who prefer double stuf, only 5 prefer it by more than 30% of the value they gave classic. Thus, the 5 for whom double stuf is not vastly superior, they should probably stick to classic.

What about thins? An Oreo thin is only 50% of the calories of a double stuf and 66% of the calories of a classic. Of the 8 people who chose classic as their preference, do they prefer it 50% more than a thin? Only one person rated the classic more than 50% higher than they rated the thin.  Thus, 7 out of 8 people who prefer classics actually gain more enjoyment/calorie from an Oreo thin.  Additionally, 6/10 people who prefer double stuffs actually gain more enjoyment/calorie from an Oreo thin.

What about me? I was surprisingly pleased with the taste experience of the Oreo thin.  I gave the thin the same value as the double stuf: 7/10.  Therefore, if I want a single cookie, it’s actually WAY better for me to get 7 points of enjoyment out of a thin than a double stuf. As a result of this study, I buy Oreo thins instead of double stuf. What will you do?

In conclusion, although thins were the least desirable (only 3/21 people preferred them most), if you only get 1 cookie and you want to optimize your enjoyment to calorie ratio, then most people should buy thins. 16 out of 21, or 76%, of my participants would get more enjoyment/calorie from a thin than from any other Oreo.

 

 

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Posted in Communicating Math | 3 Comments

PhDs with Personality

Everyone has a personality.  At the risk of over-simplifying, I’m going to argue that there are two types of PhDs in Industry. Front-Room PhDs and Back-Room PhDs*. The distinction is that some technicians and developers enjoy talking to business clients and some do not. Your back-room PhDs probably don’t want to talk to the clients anyways, they want to write code and wear really comfortable clothing. The front-room PhDs have a desire to communicate across disciplines and bring the two groups (developers and clients) closer together.

I first came upon this phrase while reading Competing on Analytics, by Jeanne G. Harris and Thomas H. Davenport. They spend a little time talking about how companies can use analytics to propel their business forward.

“The need is for analytical experts who also understand the business in general and the particular business need of a specific decision maker. One company referred to such individuals as “front room statisticians,” distinguishing them from “backroom statisticians” who have analytical skills but who are not terribly business oriented and may also not have a high degree of interpersonal skills.

In order to facilitate this relationship, a consumer products firm with an IT-based analytical group hires what it calls PhDs with personality– individuals with heavy quantitative skills but also the ability to speak the language of the business and market their work to internal (and in some cases, external) customers.” -Competing on Analytics Pg 144

I think the individual who can understand the technical details and successfully communicate those details to the business is a rare person.  Usually it takes 2 different people to translate from technical speak to business speak. And these two people have to be really good friends and spend a lot of time talking to each other to get an accord. It’s like if you wanted to translate from a group of English speakers to a group of Japanese speakers, but the only language in common was Italian. So, you first translate your ideas into Italian and then hope the other person knows enough Italian to get the idea appropriately translated into Japanese. Small wonder things get lost in translation! The value of having a single individual who knows both languages is vast.

Aside from just reducing the number of steps in the corporate game of telephone, this person can add value and insights to the translation as well. They can say things like, “I know you really want this work completed by date X, but we’re going to have to reduce the scope of the project to get it complete by then. I can work with you to understand which pieces of your request are hard and which are easy to help create an appropriate acceptance criteria for a minimal viable product.”

The other major benefit has to do with the intrinsic value of having a seat at the table. There is a lot of conversation about how data teams can’t drive decisions if there is no one at the business table who can listen to what the client’s challenges are.  It’s critical to get a seat at the table. PhDs with Personality are the ideal type of person for this situation.  For, she (or he!) can sit at the table without pissing anyone off.  She doesn’t get lost in the weeds of the technical details and she can speak about the results of the work instead of just the technical process. She can listen and show empathy to the clients, without giving up her empathy for the developers. It’s hard to have a seat at the table if your representative keeps derailing meetings and upsetting potential clients.

By having a good balance of back-room PhDs and front-room PhDs, a team can be much more successful and complete projects that are more like to move the needle for your clients.

*I’m using the term PhD loosely here . I don’t think this discussion is limited to just PhDs, because there are many people who work in the hyper-technical space who don’t have PhDs.

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Posted in Communicating Math, data science | 4 Comments

Marketing Academic Strengths in Industry

So you wanna get an Industry job?  Great! But how do you begin to translate your CV into something non-academics want to read? How do you market your strengths?

First, we have to acknowledge that your CV took years to put together. Not just years to get experience, but years of tweaking your communication to present your best self.  Only now, the objective has changed. Instead of communicating to the 3-10 other academics who care about your area of specialization, you need to communicate your CV to people who may not have any graduate academic experience. Don’t expect to get your academic CV turned into a Industrial resume in an afternoon. It’s going to take some effort. But you have a graduate degree, you know how to put effort in.

Second, we have to acknowledge that hiring managers will spent less than 30 seconds looking at your resume.  And they tend to read the most in the upper left hand triangle of the page, and the least on the lower right.  Optimize that space. For starters, put that “, PhD” right after your name. So, if they ONLY thing they read is your name, then at least they know you did the PhD thing. Then, don’t fill the left hand side of your resume with dates, as some resume builders recommend.  Instead put your job titles over there, and make them stand out.

Finally, the most complicated part of your task is to understand your work and the Industry well enough that you can capitalize on the overlapping skills. Or, what I like to call, “Finding your dissertation sentence.”  You need to find one sentence that describes to a layperson what your work was about. For example, my dissertation was titled: “Forced Oscillators with Dynamic Hopf Bifurcations and applications to Paleoclimate.”  However, in my objective statement on my resume, I say, “My dissertation focused on identifying the driving factors in complex systems like our planet’s climate.” I spent weeks trying to figure out how to make an 90 second elevator pitch for my dissertation work.  And then more weeks streamlining it down to one sentence: “Identifying the driving factors in complex systems like our planet’s climate.” There is is. Six years of work, in one sentence.

I strongly encourage you to find your sentence.  No matter what Industrial field you go into or what your dissertation was about, you will benefit greatly from knowing your sentence. How do you find your sentence? I recommending talking about your dissertation to everyone. Mathematicians in and out of your field. Talk to you parents, pets, friends, or that guy who always talks to you on the bus (well, maybe not him- use your best judgement!).  Watch your listener for when their eyes get glassy and they tune out. When that happens you know that your explanation is too complex or too long, or both.

As you practice, first focus on the how you did your work. You may never need to prove another statement about complex fields again, but you do need to be able to clearly communicate your logic about a business problem.  You might need to be able to extrapolate to abstract concepts to allow a solution that worked in one area of your company to be applied in another. There are concrete transferrable skills that you have learned in your PhD.  But, you’ve been so problem focused (because, you have to actually finish your PhD!) that you probably haven’t noticed the skills you are learning along the way.  These skills, that you can’t yet recognize, are your strengths.

By way of example, here is a skill that every PhD has: You can do something really hard for a really long time.  This is a fundamental strength of everyone who has earned a PhD. What else is specific to your field and your experience? Keep telling your story until you figure that out!

You also need to focus on the outcomes of your work.  I proved that a popular, long-standing model will never be able to reproduce all the features of our planets δO18 data. This isn’t something that very many people on the planet actually care about, but the Industry hiring manger can understand the impact of my work.  I proved that this model formulation wasn’t valuable. Thereby making the other popular models more likely to be telling a true story about our planet. What does your work do? Try to say your outcome without using any math terms. Replace every math term with “Thing” or “do-whats-it” and then work to find non-math terms that can fill in the gaps and still make sense.

Your sentence will not come together in one day, it will take time. But you have skill that you can do something really hard for a really long time!  Apply that focus to the art of translating your work into standard english, and you’ll be a long way towards marketing yourself outside of academics.

If you would like additional context about moving into Industry or becoming a data scientist, I have a section of Social Math devoted to Data Science.  Additional explicit advice on how to write your resume I recommend 10 Things Smart PhDs do NOT Put on their Industry Resumes from CheekyPhD. It’s a really clear summary of the first steps towards making your Industrial resume .

 

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Do height restrictions matter to safety on Roller Coasters?

The conversation started with an image on how to “outsmart” the roller coaster operators for kids who are not tall enough for a certain ride:

This sparked a large controversy amongst my Facebook friends.  There were certainly people who felt that this was a terrible lesson to teach kids; that one should cheat safety rules.  And, because this is a site about mathematics, I don’t want to go into the social or moral controversy here.  You can chose to parent however you chose!  But, what I do want to do is consider how dangerous it is to do something like this. Are you subjecting your child to a more dangerous experience by cheating a 1/2 inch on the height rule? The thread seemed to illicit a lot of responses over a long period of time (which is unusual for social media), so I wanted to write up my research here for anyone else who wanted to learn more about roller coaster safety.

Rates of roller coaster accidents and deaths, as it turns out, is a hard thing to research.  There is no centralized database which collects amusement park injuries and fatalities.  Wikipedia seems to have the most comprehensive view of injury tracking, but is missing data and missing reports. Additionally, the type of information that is available to the public changes year to year; there is no way to do a trend analysis.  I’m going to make a couple of egregious assumptions:

  1. I’m going to assume that the rates of injury have not changed over the last few decades. This way I can combine studies across several years to get to meaningful numbers. evidence: In 2004, the Consumer Product Safety Commission showed that mobile rides didn’t see a statistically significant trend, though inflatable rides did show an increasing trend (between 1997 and 2004). The study didn’t cover permanent rides. So, this assumption is “Plausible”. But not bullet-proof.
  2. I’m going to assume that all the studies are accurate and they received accurate coverage from the media. This assumption is plausible, as most media sites are copying numbers from reports, but we don’t know how much we trust the reports because most are not publicly available. Most are from oversight commissions and government agencies, so it’s reasonable to believe that these are pretty accurate.

Part 1: How dangerous are roller coasters in general?

First lets look at how many children get injured for any reason. NBC reported in 2013 that 4,400 children under the age of 18 get injured every year on roller coasters. Of that group, only 67 (1.5%) are injured badly enough to go to the hospital. This group is probably* about 30% carnival rides, 30% permanent rides and 12% mobile rides (like coin-op rides in a store or a mall), with the rest being unknown.  Thus, we can guess that around 1320 injuries took place at amusement parks for minors. And 2640 for amusement and fixed-park riders.

Let’s look at amusement park injuries in total. CNN reports in 2017 that there were around 30,000 injuries at amusement parks & fixed-park rides in 2016. If we combine this with the information above, that means 2640/30,000 = 8.8% of all injuries that happen at amusement parks are to minors.

How does this relate to percentage of park goers under the age of 18?  There are no direct numbers published on this, but the US census bureau says 22.8% of the US population are under the age of 18. The IAAPA reports that the demographic which visits parks are families with kids. So I’m assuming the rate of children is higher than the national average.  So, at least 23% of park-goers are under the age of 18.  Yet, only 8.8% of the injuries are coming from minors.  Therefore, one must conclude that parks are safer for kids than adults.

How scared should you be relative to other things? Compared to other dangerous activities, sharks injured just 13 people in a year in the US. (ref). So, this is more dangerous than swimming with sharks. However, the stats show that 8,000 – 16,000 kids are injured on school buses each year. (NBC article from 2006). Thus, amusement park accidents rank somewhere between shark attacks and school bus injuries.

All of the above was about park injuries. Let’s consider the more serious case of deaths. There have been 22 deaths since 2010, so 3.1 deaths/year based on CNN’s report.  In contrast, the Consumer Product Safety Commission report from 2005 shows only 2.5 deaths per year at fixed-location rides between 1987 and 2004. Let’s compare this to other deadly things. Spiders kill 6.5-7 people every year. And 330 people get struck by lightning. For other facts about dangerous things, check out our post on the dangers of ground beef). On the scale of deadly activities, amusement parks are less dangerous than spider bites.

Part 2: How dangerous is cheating the height requirement?

Now we are in really ambiguous territory. Because the parks certainly do some analysis to determine the height requirements. But we have zero visibility into what that analysis was. So we can’t conclusively say how quickly risk of injury changes with height.

However, danger is rarely bimodal. If there is a risk from being short, it’s probably a curve and not a step function. Like, we can all agree that driving 66 mph in a 65 zone is probably not that much more unsafe than driving 65. If a cop gave you a ticket for driving 66, you’d be pissed (mph error gauge anyone?). So fudging a quarter inch on a kid might not be a huge deal. But how can we judge how quickly danger changes with height?

I’m going to hedge my bets that roller coaster safety is also a function of several other metrics which are not as easy or as feasible to collect as height. Based on all of my personal experience on indicator values of predictive functions, there are two rules for identifying indicators for various rules and restrictions.

  1. The indicator value, or input, must have some predictive power on the rate of the results. In this case, height must have some evidence for being predictive of injury.
  2. The indicator value must be accessible and easily captured. In this case, it’s possible to measure a kids height quickly and (relatively) accurately.

There are almost always other indicators you wish you had for your predictive algorithm, but can’t have.  For example, it’s not socially appropriate or feasible to give everyone a mental health test before letting them on the ride. (Though, there are many roller coaster injuries and deaths that seem to be related to mental health challenges). Similarly, it’s not socially appropriate to weigh children to see if they possess the requisite inertia to keep their butts on the seat of the coaster. Also infeasible, is to measure kids shoulder width to see if they have wide enough shoulders to not accidentally fit between the shoulder bars. I can imagine all of these metrics would provide a more predictive way to judge injury likelihood.

But based on the various explanations of roller coaster injuries I’ve read on Wikipedia and all my other research for this article, I would hedge my bets that roller coaster safety is also a function of weight and “wiggly-ness” of the kid (among other things). So, if your kid is skinny and wiggly, maybe it’s extra dangerous to cheat the height system. But if your kid can stay seated and doesn’t have a tiny frame- then maybe we have fewer concerns about cheating the height requirement. Height is probably the most easily accessible indicator for ride safety. At lot of injuries are caused by getting on and off rides (twisted ankles and wrist injuries) or by not “keeping your hands and arms inside the ride”. So, the ability of your child to follow instructions is definitely critical.  Notably, we can posit that kids are better at following instructions than adults (who over-index on amusement park injuries).

Sadly, I don’t have any numbers for anything in the above section. So, ultimately, I am unable to give a good answer to the height question. But, we can get closer: let’s look at the spread of height restrictions across rides. Presumably, the park would like their system to be as simple as possible for the ease of their guests. But, they don’t want to be unsafe. So I’m going to assume that they make as few different height restrictions as

possible.  Disneyland has height cut offs at 35″, 38″, 40″, 44″ and 52″.  If the amusement park is going to the trouble of identifying different cut-offs every 2-3″, this suggests that 2-3″ in a meaningful and important distinction, especially at smaller heights. So, let’s take Splash Mountain at 40″.  In terms of cheating the system, the danger scale starts at 0% dangerous when you are 40″, but is significantly more dangerous (perhaps not 100% dangerous, but certainly materially more dangerous) than if you are only 38″.  So, your kid has a 2 inch margin… ish.

Would I want to cheat that threshold by 1″? No, probably not. But how about by 1/4″? Or the width of a ponytail? Or the height difference of a pair of lightup sneakers versus a pair of thin-soled chucks? I don’t have data to answer that. That’s something you’ll have to decide for yourself.

Part 3: Summary

  • Riding roller coasters is less deadly than living around spiders and less dangerous for minors than riding the school bus.
  • Children under-index on injuries, sustaining less injuries than adults. (assuming as few key assumptions about the data).
  • The safe to not-safe threshold is probably 2-3″ wide, on average. So, it may be very unsafe to push the system by an inch, as suggested in the image at top.
  • I’m not making any claims on the morality of cheating the system or the parenting choice to model behavior which cheats the safety system at amusement parks.

*- Here only 25% of the 4,400 incidents per/year were location identified. So this is a generalization.

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One Line Proof

OneLineProof

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Science March Draws Controversy.

There is something about airing dirty laundry that makes everyone uncomfortable. And we scientists have some dirty laundry… And we are struggling to interface with the world about our feelings.

The Root recently published a wonderful article which highlights the racist side of some of the leaderships teams for March for Science. It’s firing up a new hastag: #MarginSci. I am a white woman in STEM who often writes about how mathematicians interact with the everyday world. And if there is one thing that I truly believe, it’s that mathematicians and scientists don’t know how to get political.

Now, I’m going to spend a couple minutes talking about a white guy, but don’t let that put you off. White guys have had all the fun for the last 100 years (well, for way longer than that! but I digress). This particular white guy gives a good example of what happens when scientists spend years trying to influence politics. I present James Hansen.  No not the puppeteer Jim Henson, this is Jim Hansen. He is wildly famous in climate science circles for putting climate change on the map and into politics. He is also pretty famous as a scientist who, maybe, perhaps overstepped his bounds of a scientists into politics?

A colleague of Jim’s wrote, “I think he thought, as did I, If we get this set of facts out in front of everybody, they’re so powerful—overwhelming—that people will do what needs to be done. Of course, that was naive on both our parts.” Politicians didn’t respond to the facts. What’s worse, Jim started get a bad reputation in science circles. As New York Times author, Elizabeth Kolbert, wrote “Hansen argues that politicians willfully misunderstand climate science; it could be argued that Hansen just as willfully misunderstands politics.” [NYTimes]. His trouble is so famous, it’s included in his wikipedia page.

This is not limited to climate science.  I have PhD-wearing friends, astrophysicists and others, who feel that Neil Degrasse Tyson shouldn’t refer to himself as a scientist anymore because, well, he’s not doing science.  He is mostly doing science outreach. In the eyes of our serious academic partners, outreach doesn’t cut it.

We, as scientists, politely, yet inexorably, push the “less serious” out of our ranks. We excommunicate them from our inner circles because they want to influence the public (and, perhaps, the politics) of science. The old boys club is strong. We kick out some white people. We push away many black people and LGBTQ folks and a lot of others besides. We, as a group, quietly fill our plenary speaker spots with white men. There are several famous articles about the plenary speaker problem, the most beautiful by Lauren Bacon. Our women in science problems are large enough and public enough that major newspapers are talking about women in Silicon Valley.  The Atlantic article is particularly compelling about this. And, one cannot write an article about this without mentioning Susan Fowler’s review of Uber. And, I’m pleased to add #MarginSci to the list of public airing of science’s dirty failings.

I attended the women’s march in my city a few months ago. I was inspired and awed by the variety of issues that came to the table at that march. There were amazing posters about all kinds of issues. And there were some amazing posters about science.

And that march was organized fast! But what happens when a bunch of scientists take a few months to organize a science march?

Scientists (and I’m including Mathematicians in this too), are a different breed. We filter, classify, organize, and sort all of life into bins. We’d like to believe our sorting systems are unbiased. In fact, one could argue that’s the entire job; to create unbiased interpretations of the world around us.  But our biases are implicit. Sometimes we see them in advance. Like with Boston’s pothole app, where they purposely set out to get the app into every vehicle maintained by the city to get better coverage than just in the rich, cell-phone having areas. Harvard Business Review talks about these hidden biases in big data science.

But sometimes we don’t see them in advance. Sometimes we are human and we do stupid things. But now we, the scientists, are all trying to get into the public sphere to raise our issues. And people are starting to look more closely at our culture. Glass houses and all that. And people are starting to see that we, maybe, do not always live up to the ivory tower we’ve built for ourselves. And people are starting to wonder, “Maybe I don’t want to march for science, because science is just giving money to rich white guys.” To these people, I urge you to reconsider.

Science funding is key to our future. Science funding got us to space.  Science funding taught us about large prime numbers for internet security, about photovoltaic cells for solar panels, about cancer treatments, and our coral reefs. The list goes on and I, for one, will march for science and people’s equality. Even though there isn’t always people’s equality in science. The science is vital to our future. Despite our dirty laundry, we must persist and resist. We must talk about our issues, all of them, and bring them forward and solve them. Scientists are great at solving problems. But not always great at people. Let’s work to teach our scientific community about how to be inclusive and how to stand up for ourselves and each other.

Just as I saw posters for science at the women’s march, I hope I will see posters about everything else at the science march.  Because all of our issues need love. And all of our issues need science. They don’t seem mutually exclusive to me.

 

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Data Science Triple Threats

Everyone likes a good list. There are some articles working around which talk about why Data Science doesn’t add business value. As a data scientist who love people, I wanted to add my voice to conversation. Here are three things that make it hard to work with a team of Data Scientists (& Engineers).

  • Data Scientists are less likely to be mobilized on incomplete information.

A data scientist, or perhaps a PhD in general, wants to fully understand the problem before choosing a solution. This is best explained in an example: There may be one business rule which turns a problem from linear to non-linear.  But, the effect of that non-linear portion is small, so the business doesn’t bother to mention it until part way through the build process. The business doesn’t understand that the data scientists might literally need to start over to incorporate that new feature. As a result, data scientists have developed a healthy suspicion of project requests. No one wants to start over because the problem wasn’t accurately described first. So, the team stalls until they believe they understand the full problem. And that can take a long time. It’s a big challenge to begin a problem fast and get quick wins while simultaneously going slowly enough to protect from future disruptions.

  • Data Scientists will not believe something until they see it with their own eyes.

This personality quirk is very important to their job.  It means they question everything, validate unknowns and solve “unsolvable” problems. (After all, if you believe your colleague who says that the problem is unsolvable… then you aren’t going to be the one to solve it!).  However, it’s challenging to have a team that won’t accept second hand knowledge. Teams are forced to include the DS in every meeting, in order to build the requisite business knowledge.  Meanwhile the DS might be pushing the meeting down a tangent which is not the main focus of the meeting.  This, in combination with #1, is a hard problem.

  • Data Scientists require leaders who are Triple Threats.

In the performing arts a Triple Threat is someone who can sing, dance and act. In Data Science, a triple threat is someone who can understand the Mathematics, the Business and the Communication necessary to be a liaison between the first two sets of people. And often these traits are negatively correlated. People who are good at Math are certainly perceived to be less good at people. Thus, Triple Threats are rare!

Incorporating mathematicians into the workplace is more valuable than ever. Finding and acquiring a triple threat can be a challenging prospect, but something which companies should not shy away from.

What can we do about these challenges? Have you made progress on solving any of these challenges? What do you think are the biggest challenges facing data scientists right now?

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