Statistic Math Quotes

Scientists and inventors of the USA (especially in the so-called "blue state" that voted overwhelmingly against Trump) have to think long and hard whether they want to continue research that will help their government remain the world's superpower. All the scientists who worked in and for Germany in the 1930s lived to regret that they directly helped a sociopath like Hitler harm millions of people. Let us not repeat the same mistakes over and over again.

Another mistaken notion connected with the law of large numbers is the idea that an event is more or less likely to occur because it has or has not happened recently. The idea that the odds of an event with a fixed probability increase or decrease depending on recent occurrences of the event is called the gambler's fallacy. For example, if Kerrich landed, say, 44 heads in the first 100 tosses, the coin would not develop a bias towards the tails in order to catch up! That's what is at the root of such ideas as "her luck has run out" and "He is due." That does not happen. For what it's worth, a good streak doesn't jinx you, and a bad one, unfortunately , does not mean better luck is in store.

The lottery is a tax on poor people and on people who can’t do math. Rich people and smart people would be in the line if the lottery were a real wealth-building tool, but the truth is that the lottery is a rip-off instituted by our government. This is not a moral position; it is a mathematical, statistical fact. Studies show that the zip codes that spend four times what anyone else does on lottery tickets are those in lower-income parts of town. The lottery, or gambling of any kind, offers false hope, not a ticket out.

It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that there must be something mysterious about the normal law since mathematicians think it is a law of nature whereas physicists are convinced that it is a mathematical theorem.

Todd, trust math. As in Matics, Math E. First-order predicate logic. Never fail you. Quantities and their relation. Rates of change. The vital statistics of God or equivalent. When all else fails. When the boulder's slid all the way back to the bottom. When the headless are blaming. When you do not know your way about. You can fall back and regroup around math. Whose truth is deductive truth. Independent of sense or emotionality. The syllogism. The identity. Modus Tollens. Transitivity. Heaven's theme song. The night light on life's dark wall, late at night. Heaven's recipe book. The hydrogen spiral. The methane, ammonia, H2O. Nucleic acids. A and G, T and C. The creeping inevibatility. Caius is mortal. Math is not mortal. What it is is: listen: it's true.

open a basic math book, and make sure you are really good at multiplying, dividing, compounding, probability, and statistics.

Numbers never lie, after all: they simply tell different stories depending on the math of the tellers.

Conventional wisdom nor scientific, mathematical prove of randomness in life could do nothing to deter human's curiosity for the unknown, however small the chance of a positive outcome maybe.

A remarkably consistent finding, starting with elementary school students, is that males are better at math than females. While the difference is minor when it comes to considering average scores, there is a huge difference when it comes to math stars at the upper extreme of the distribution. For example, in 1983, for every girl scoring in the highest percentile in the math SAT, there were 11 boys. Why the difference? There have always been suggestions that testosterone is central. During development, testosterone fuels the growth of a brain region involved in mathematical thinking and giving adults testosterone enhances their math skills. Oh, okay, it's biological. But consider a paper published in science in 2008. The authors examined the relationship between math scores and sexual equality in 40 countries based on economic, educational and political indices of gender equality. The worst was Turkey, United States was middling, and naturally, the Scandinavians were tops. Low and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries it's statistically insignificant. And by the time you examine the most gender equal country on earth at the time, Iceland, girls are better at math than boys. Footnote, note that the other reliable sex difference in cognition, namely better reading performance by girls than by boys doesn't disappear in more gender equal societies. It gets bigger. In other words, culture matters. We carry it with us wherever we go.

One sample is poor statistics, my math prof used to say.

The number of people who think they understand statistics dangerously dwarfs those who actually do, and maths can cause fundamental problems when badly used.

I don't believe in the glory and the dream. I believe in statistics.

IT WAS EASIER FOR PEOPLE to be good at something when more of us lived in small, rural communities. Someone could be homecoming queen. Someone else could be spelling-bee champ, math whiz or basketball star. There were only one or two mechanics and a couple of teachers. In each of their domains, these local heroes had the opportunity to enjoy the serotonin-fuelled confidence of the victor. It may be for that reason that people who were born in small towns are statistically overrepresented among the eminent.68 If

Why did math matter so much? Some reasons were practical: More and more jobs required familiarity with probability, statistics, and geometry. The other reason was that math was not just math. Math is a language of logic. It is a disciplined, organized way of thinking. There is a right answer; there are rules that must be followed. More than any other subject, math is rigor distilled. Mastering the language of logic helps to embed higher-order habits in kids’ minds: the ability to reason, for example, to detect patterns and to make informed guesses. Those kinds of skills had rising value in a

If college admissions officers are going to encourage kids to take the same AP math class, why not statistics? Almost every career (whether in business, nonprofits, academics, law, or medicine benefits from proficiency in statistics. Being an informed, responsible citizen requires a sound knowledge of statistics, as politicians, reporters, and bloggers all rely on "data" to justify positions. [p.98]

Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special theory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity. This last paper contains no references and quotes to authority. All of them are written in a style unlike any other theoretical physicist's. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.

Marianne, how’s your statistics?” “Math is my worst subject.” “But you can program?” “Of course. I’m not illiterate.

Sometimes the job of a data scientist is to know when you don't know enough.

On Rachel's show for November 7, 2012: Ohio really did go to President Obama last night. and he really did win. And he really was born in Hawaii. And he really is legitimately President of the United States, again. And the Bureau of Labor statistics did not make up a fake unemployment rate last month. And the congressional research service really can find no evidence that cutting taxes on rich people grows the economy. And the polls were not screwed to over-sample Democrats. And Nate Silver was not making up fake projections about the election to make conservatives feel bad; Nate Silver was doing math. And climate change is real. And rape really does cause pregnancy, sometimes. And evolution is a thing. And Benghazi was an attack on us, it was not a scandal by us. And nobody is taking away anyone's guns. And taxes have not gone up. And the deficit is dropping, actually. And Saddam Hussein did not have weapons of mass destruction. And the moon landing was real. And FEMA is not building concentration camps. And you and election observers are not taking over Texas. And moderate reforms of the regulations on the insurance industry and the financial services industry in this country are not the same thing as communism. Listen, last night was a good night for liberals and for democrats for very obvious reasons, but it was also, possibly, a good night for this country as a whole. Because in this country, we have a two-party system in government. And the idea is supposed to be that the two sides both come up with ways to confront and fix the real problems facing our country. They both propose possible solutions to our real problems. And we debate between those possible solutions. And by the process of debate, we pick the best idea. That competition between good ideas from both sides about real problems in the real country should result in our country having better choices, better options, than if only one side is really working on the hard stuff. And if the Republican Party and the conservative movement and the conservative media is stuck in a vacuum-sealed door-locked spin cycle of telling each other what makes them feel good and denying the factual, lived truth of the world, then we are all deprived as a nation of the constructive debate about competing feasible ideas about real problems. Last night the Republicans got shellacked, and they had no idea it was coming. And we saw them in real time, in real humiliating time, not believe it, even as it was happening to them. And unless they are going to secede, they are going to have to pop the factual bubble they have been so happy living inside if they do not want to get shellacked again, and that will be a painful process for them, but it will be good for the whole country, left, right, and center. You guys, we're counting on you. Wake up. There are real problems in the world. There are real, knowable facts in the world. Let's accept those and talk about how we might approach our problems differently. Let's move on from there. If the Republican Party and the conservative movement and conservative media are forced to do that by the humiliation they were dealt last night, we will all be better off as a nation. And in that spirit, congratulations, everyone!

But consider a paper published in Science in 2008.1 The authors examined the relationship between math scores and sexual equality in forty countries (based on economic, educational, and political indices of gender equality; the worst was Turkey, the United States was middling, and, naturally, the Scandinavians were tops). Lo and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries, it’s statistically insignificant. And by the time you examine the most gender-equal country on earth at the time, Iceland, girls are better at math than boys.

None of us was normal. But “normal,” as I’d learned in math, was just a statistical concept, an averaged smoothing out of all diverse and interesting permutations to some hypothetical midpoint so generalized it was unlikely to surprise or offend. Or to delight. Normal was nice. Normal was bland. Normal was damned boring. Our differences, our own brand of crazy, were what made each of us special and unique and fascinating.

Ethan’s parents constantly told him how brainy he was. “You’re so smart! You can do anything, Ethan. We are so proud of you, they would say every time he sailed through a math test. Or a spelling test. Or any test. With the best of intentions, they consistently tethered Ethan’s accomplishment to some innate characteristic of his intellectual prowess. Researchers call this “appealing to fixed mindsets.” The parents had no idea that this form of praise was toxic. 　　Little Ethan quickly learned that any academic achievement that required no effort was the behavior that defined his gift. When he hit junior high school, he ran into subjects that did require effort. He could no longer sail through, and, for the first time, he started making mistakes. But he did not see these errors as opportunities for improvement. After all, he was smart because he could mysteriously grasp things quickly. And if he could no longer grasp things quickly, what did that imply? That he was no longer smart. Since he didn’t know the ingredients making him successful, he didn’t know what to do when he failed. You don’t have to hit that brick wall very often before you get discouraged, then depressed. Quite simply, Ethan quit trying. His grades collapsed. What happens when you say, ‘You’re so smart’ 　　Research shows that Ethan’s unfortunate story is typical of kids regularly praised for some fixed characteristic. If you praise your child this way, three things are statistically likely to happen: 　　First, your child will begin to perceive mistakes as failures. Because you told her that success was due to some static ability over which she had no control, she will start to think of failure (such as a bad grade) as a static thing, too—now perceived as a lack of ability. Successes are thought of as gifts rather than the governable product of effort. 　　Second, perhaps as a reaction to the first, she will become more concerned with looking smart than with actually learning something. (Though Ethan was intelligent, he was more preoccupied with breezing through and appearing smart to the people who mattered to him. He developed little regard for learning.) 　　Third, she will be less willing to confront the reasons behind any deficiencies, less willing to make an effort. Such kids have a difficult time admitting errors. There is simply too much at stake for failure. 　　  　　What to say instead: ‘You really worked hard’ 　　What should Ethan’s parents have done? Research shows a simple solution. Rather than praising him for being smart, they should have praised him for working hard. On the successful completion of a test, they should not have said,“I’m so proud of you. You’re so smart. They should have said, “I’m so proud of you. You must have really studied hard”. This appeals to controllable effort rather than to unchangeable talent. It’s called “growth mindset” praise.

Perfect moments, what did they even mean? They were blind luck, that was all. Coincidences. Statistical anomalies. I did some Googling and it turned out somebody had actually bothered to do the math on this, a real actual Cambridge University mathematician named John Littlewood (1885-1977; thank you, Wikipedia). He proposed that if you define a miracle as something with a probability of one in a million, and if you’re paying close attention to the world around you eight hours a day, every day, and little things happen around you at a rate of one per second, then you’d observe about thirty thousand things every day, which means about a million things a month. So, on average, you should witness one miracle every month (or every thirty-three-and-one-third days, if we’re being strictly accurate). It’s called Littlewood’s law. So, there you have it, a miracle a month. They’re not even that special.

Baseball also has statistical rigor. Its gurus have an immense data set at hand, almost all of it directly related to the performance of players in the game. Moreover, their data is highly relevant to the outcomes they are trying to predict. This may sound obvious, but as we’ll see throughout this book, the folks building WMDs routinely lack data for the behaviors they’re most interested in. So they substitute stand-in data, or proxies. They draw statistical correlations between a person’s zip code or language patterns and her potential to pay back a loan or handle a job. These correlations are discriminatory, and some of them are illegal.

About 4,400 years ago 8 people stepped off Noah’s ark. According to the United Nations Population Growth Statistics, the world’s population grows at about .47% per year. That is the growth rate for all civilizations who kept records. Suppose you put $8.00 in the bank 4,400 years ago and received .47% a year. How much money would you have? What a coincidence! It would be about $7,000,000,000. That’s kind of odd, because 4,400 years ago 8 people stepped off the ark and now we have about 7,000,000,000 people on planet earth. God’s math works! Compound interest is something we teach to seventh-graders. You don’t have to be a professor to figure this out. A twelve-year-old can do the calculation. Ask any seventh-grader, the algebraic equation looks like this: A=P (1+r/n)t . . . where "A " is the ending amount (about 7,000,000,000 in this case), "P " is the beginning amount (8 in this case), "r " is the interest rate (.47% in this case), "n " is the number of compoundings a year (1 in this case), and "t " is the total number of years (4,400 in this case).

What’s more, attempting to score a teacher’s effectiveness by analyzing the test results of only twenty-five or thirty students is statistically unsound, even laughable. The numbers are far too small given all the things that could go wrong. Indeed, if we were to analyze teachers with the statistical rigor of a search engine, we’d have to test them on thousands or even millions of randomly selected students.

Luck is not some esoteric, godlike phenomenon. Luck is countable but undefinable. Luck easily can be explained by a number of factors acting in favour of a person. These factors' behaviour could be statistically proved, and the probability of such a result is possible. So, it is not an unexplainable event. Actually, the miracle would be if these events (luck) are not in presence in our life. So, make your luck!"

In my opinion, defining intelligence is much like defining beauty, and I don’t mean that it’s in the eye of the beholder. To illustrate, let’s say that you are the only beholder, and your word is final. Would you be able to choose the 1000 most beautiful women in the country? And if that sounds impossible, consider this: Say you’re now looking at your picks. Could you compare them to each other and say which one is more beautiful? For example, who is more beautiful— Katie Holmes or Angelina Jolie? How about Angelina Jolie or Catherine Zeta-Jones? I think intelligence is like this. So many factors are involved that attempts to measure it are useless. Not that IQ tests are useless. Far from it. Good tests work: They measure a variety of mental abilities, and the best tests do it well. But they don’t measure intelligence itself.

Terrible as this is, there’s worse news. An article in the New York Times points out a statistic that should make our nation’s leaders tremble… suspension rates, kindergarten through high school, have nearly doubled from the early 1970s through 2006. Whatever is happening with our test scores, something else, something catastrophic, is going on in our schools. As countless teachers across America can testify, disruptive kids are hijacking our classrooms.

In college, except for the obligatory courses, I avoided science, math, and accounting—all the normal preparations for business. I was on the arts side of school, and along with the usual history, psychology, and political science, I also studied metaphysics, epistemology, logic, religion, and the philosophy of the ancient Greeks. As I look back on it now, it’s obvious that studying history and philosophy was much better preparation for the stock market than, say, studying statistics. Investing in stocks is an art, not a science, and people who’ve been trained to rigidly quantify everything have a big disadvantage

But consider a paper published in Science in 2008. The authors examined the relationship between math scores and sexual equality in forty countries (based on economic, educational, and political indices of gender equality; the worst was Turkey, the United States was middling, and, naturally, the Scandinavians were tops). Lo and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries, it’s statistically insignificant. And by the time you examine the most gender-equal country on earth at the time, Iceland, girls are better at math than boys.

There are no single guys who don’t have at least one major flaw, and a flaw, I might add, that would stop you from dating them – even if everything else was great. Why? Simple math. Women are interesting and honest and sensitive. Most men are not. There is only one normal, decent single guy for every five women in this city. This is what’s known as the Great Male Statistic. Girls don’t want to face the GMS. They want to believe there’s someone for everyone. The truth hurts. You only start coming to terms with the GMS when you’re twenty-six or twenty-seven. It actually killed Sylvia Plath. She finally found this guy in grad school who she thought was so great, and she married him, and he cheated on her.

Equally important, statistical systems require feedback—something to tell them when they’re off track. Without feedback, however, a statistical engine can continue spinning out faulty and damaging analysis while never learning from its mistakes. Many of the WMDs I’ll be discussing in this book, including the Washington school district’s value-added model, behave like that. They define their own reality and use it to justify their results. This type of model is self-perpetuating, highly destructive—and very common. If the people being evaluated are kept in the dark, the thinking goes, they’ll be less likely to attempt to game the system. Instead, they’ll simply have to work hard, follow the rules, and pray that the model registers and appreciates their efforts. But if the details are hidden, it’s also harder to question the score or to protest against it.

There are several different frameworks one could use to get a handle on the indeterminate vs. determinate question. The math version is calculus vs. statistics. In a determinate world, calculus dominates. You can calculate specific things precisely and deterministically. When you send a rocket to the moon, you have to calculate precisely where it is at all times. It’s not like some iterative startup where you launch the rocket and figure things out step by step. Do you make it to the moon? To Jupiter? Do you just get lost in space? There were lots of companies in the ’90s that had launch parties but no landing parties. “But the indeterminate future is somehow one in which probability and statistics are the dominant modality for making sense of the world. Bell curves and random walks define what the future is going to look like. The standard pedagogical argument is that high schools should get rid of calculus and replace it with statistics, which is really important and actually useful. There has been a powerful shift toward the idea that statistical ways of thinking are going to drive the future.” —PETER THIEL

A remarkably consistent finding, starting with elementary school students, is that males are better at math than females. While the difference is minor when it comes to considering average scores, there is a huge difference when it comes to math stars at the upper extreme of the distribution. For example, in 1983, for every girl scoring in the highest percentile on the math SAT, there were eleven boys. Why the difference? There have always been suggestions that testosterone is central. During development, testosterone fuels the growth of a brain region involved in mathematical thinking, and giving adults testosterone enhances some math skills. Oh, okay, it’s biological. But consider a paper published in Science in 2008.1 The authors examined the relationship between math scores and sexual equality in forty countries (based on economic, educational, and political indices of gender equality; the worst was Turkey, the United States was middling, and, naturally, the Scandinavians were tops). Lo and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries, it’s statistically insignificant. And by the time you examine the most gender-equal country on earth at the time, Iceland, girls are better at math than boys.

This happens because data scientists all too often lose sight of the folks on the receiving end of the transaction. They certainly understand that a data-crunching program is bound to misinterpret people a certain percentage of “he time, putting them in the wrong groups and denying them a job or a chance at their dream house. But as a rule, the people running the WMDs don’t dwell on those errors. Their feedback is money, which is also their incentive. Their systems are engineered to gobble up more data and fine-tune their analytics so that more money will pour in. Investors, of course, feast on these returns and shower WMD companies with more money. And the victims? Well, an internal data scientist might say, no statistical system can be perfect. Those folks are collateral damage. And often, like Sarah Wysocki, they are deemed unworthy and expendable. Big Data has plenty of evangelists, but I’m not one of them. This book will focus sharply in the other direction, on the damage inflicted by WMDs and the injustice they perpetuate. We will explore harmful examples that affect people at critical life moments: going to college, borrowing money, getting sentenced to prison, or finding and holding a job. All of these life domains are increasingly controlled by secret models wielding arbitrary punishments.

The radial patterning of Protestantism allows us to use a county’s proximity to Wittenberg to isolate—in a statistical sense—that part of the variation in Protestantism that we know is due to a county’s proximity to Wittenberg and not to greater literacy or other factors. In a sense, we can think of this as an experiment in which different counties were experimentally assigned different dosages of Protestantism to test for its effects. Distance from Wittenberg allows us to figure out how big that experimental dosage was. Then, we can see if this “assigned” dosage of Protestantism is still associated with greater literacy and more schools. If it is, we can infer from this natural experiment that Protestantism did indeed cause greater literacy.16 The results of this statistical razzle-dazzle are striking. Not only do Prussian counties closer to Wittenberg have higher shares of Protestants, but those additional Protestants are associated with greater literacy and more schools. This indicates that the wave of Protestantism created by the Reformation raised literacy and schooling rates in its wake. Despite Prussia’s having a high average literacy rate in 1871, counties made up entirely of Protestants had literacy rates nearly 20 percentile points higher than those that were all Catholic.18 FIGURE P.2. The percentage of Protestants in Prussian counties in 1871.17 The map highlights some German cities, including the epicenter of the Reformation, Wittenberg, and Mainz, the charter town where Johannes Gutenberg produced his eponymous printing press. These same patterns can be spotted elsewhere in 19th-century Europe—and today—in missionized regions around the globe. In 19th-century Switzerland, other aftershocks of the Reformation have been detected in a battery of cognitive tests given to Swiss army recruits. Young men from all-Protestant districts were not only 11 percentile points more likely to be “high performers” on reading tests compared to those from all-Catholic districts, but this advantage bled over into their scores in math, history, and writing. These relationships hold even when a district’s population density, fertility, and economic complexity are kept constant. As in Prussia, the closer a community was to one of the two epicenters of the Swiss Reformation—Zurich or Geneva—the more Protestants it had in the 19th century. Notably, proximity to other Swiss cities, such as Bern and Basel, doesn’t reveal this relationship. As is the case in Prussia, this setup allows us to finger Protestantism as driving the spread of greater literacy as well as the smaller improvements in writing and math abilities.

Frankly, we hesitate to pile on the data, since even when numbers are persuasive, they are not galvanizing. A growing collection of psychological studies show that statistics have a dulling effect, while it is individual stories that move people to act. In one experiment, research subjects were divided into several group, and each person was asked to donate $5 to alleviate hunger abroad. One group was told the money would go to Rokia, a seven-year-old girl in Mali. Another group was told that the money would go to address malnutrition among 21 million Africans. The third group was told that the donations would go to Roka, as in the first group, but this time her own hunger was presented as part of a background tapestry of global hunger, with some statistics thrown in. People were much more willing to donate to Rokia than to 21 million hungry people, and even a mention of the larger problem made people less inclined to help her. In another experiment, people were asked to donate to a $300,000 fund to fight cancer. One group was told that the money would be used to save the life of one child, while another group was told it would save the lives of eight children. People contributed almost twice as much to save one child as to save eight. Social psychologists argue that all this reflects the way our consciences and ethical systems are based on individual stories and are distinct from the parts of our brain concerned with logical and rationality. Indeed, when subjects in experiments are first asked to solve math problems, thus putting in play the parts of the brain that govern logic, afterward they are less generous to the needy.

If you dislike Michigan winters so much,” Connell said, “why did you move here? Why didn’t you stay in New York?” At least there she’d be away from wild lumber camps and towns. The sunshine in her face disappeared. She took a longer drink of coffee before looking at him. The heartache in her expression socked him in the stomach. “I wish we could have stayed. Then maybe Daisy wouldn’t have gotten herself into this predicament.” Her voice was soft. “If you find her, do you think you’ll move back?” “There’s nothing left for us there. No one who wants us. No one who ever did.” She spoke so low, he wasn’t sure he’d heard her correctly. And he couldn’t help wondering what had happened to the rest of her family and how she had ended up with the cranky old photographer. “When I find Daisy—not if,” she said, her voice growing louder and ringing with the passion he’d heard before. “When I find her, I’ll never let her go. And I’ll give her the kind of home she deserves—finally.” He took a slurp of coffee, not quite sure how to answer her. If he did the math, he could come up with the slim percentage she had of finding her sister, especially alive. But he didn’t think she’d be too happy with the statistic. “I’m old enough now that I’ll be able to get a job and find a place for the two of us,” she said, looking him directly in the eyes, as if somehow she could convince him. “I’ll take care of her. We’ll make it this time.” He prayed she was right. But he had the gut feeling she was in for far more challenges than she expected. But who was he to contradict her and discourage her plans? He hardly knew her. In a few short weeks, she’d move on with Oren to another town and Connell would likely never see her again. And yet, down in the dark depths of her eyes, there was a spark that drew him in, a flicker of loneliness and longing, and it tugged on him, pulling him deeper. . . . And he was afraid

Frederick Mosteller, who would later found Harvard’s statistics department, was there. So was Leonard Jimmie Savage, the pioneer of decision theory and great advocate of the field that came to be called Bayesian statistics.* Norbert Wiener, the MIT mathematician and the creator of cybernetics, dropped by from time to time. This was a group where Milton Friedman, the future Nobelist in economics, was often the

experience as an electronics engineer, researcher, and mathematician makes him an ideal editor for reference books and tutorials. He has authored several titles for the McGraw-Hill DeMYSTiFied series (a group of home-schooling and self-teaching volumes), including Everyday Math Demystified, Physics Demystified, and Statistics Demystified, all perennial bestsellers. Stan has also written more than 20 other books and dozens of magazine articles. His work

The overall lesson of this chapter is that statistical malfeasance has very little to do with bad math.

Today, algorithm design draws not only on computer science, math, and engineering but on kindred fields like statistics and operations research.

Why do things happen the way they do? Is there some kind of order in all this chaos that we just don't see, or is it all, as the mathematically minded people would like us to believe, just random coincidence? If you put one hundred apes in a room, they'll tell you, with one hundred typewriters, and given an infinite amount of time and bananas, one of them would eventually churn out the complete Oxford dictionary. It's all statistical math and probability. The odds of winning the lottery are greater than the odds of getting struck by lightning, but someone wins, don't they? And people get hit by lightning disturbingly more often that you would think. Their point is, eventually all things happen. No matter how philosophically unprejudiced you are, you can't argue with statistical probabilities. But you can certainly give the mathematicians some substantial cud to chew on, can't you? For instance, sure, everything may be eventual from a statistical point of view, but what happens to the formula if you plug in when a particular thing happens? The fortuitousness of the timing? Or combine a particular coincidence with other seemingly non-related coincidences that might have occurred within the same general time frame? We've all had it happen. It's one of our favorite phrases: "Why me? Why now?" Well, when you take the "when" into account, all kinds of very interesting and un-mathematical things begins to happen. The coincidence becomes too coincidental to be a coincidence.

I have always had an uncomfortable relationship with math. I don’t like numbers for the sake of numbers. I am not impressed by fancy formulas that have no real-world application. I particularly disliked high school calculus for the simple reason that no one ever bothered to tell me why I needed to learn it. What is the area beneath a parabola? Who cares?

They draw statistical correlations between a person’s zip code or language patterns and her potential to pay back a loan or handle a job. These correlations are discriminatory, and some of them are illegal.

In practice, Bacon’s method doesn’t bother scientists, or most reasonable people, because the chances of being wrong, while present, are usually in a practical sense very small. It is, for example, theoretically possible that chemical processes taking place in your body could cause you to spontaneously combust, but we don’t live our lives worrying about it because the probability is extremely small. That is why math and statistics have become such important parts of science: they quantify the relative probability that a conclusion is true or false.

I think science always becomes something else,” Krakauer said. "It’s become engineering, it becomes maps, it becomes statistics. It keeps being not itself. If you look at what science is, minus the math or the engineering, it’s more like the humanities. That’s the deep dark secret: Science is not its instruments.

We suffer massive levels of crime that did not exist even 30 years ago, overwhelmingly at the hands of “people of color.” Though our media and government do everything possible to skew the statistics, we know who is to blame. Blacks commit seven times the violent crimes than do whites and are only one-seventh of the total population. Do the math: Blacks are 50 times more likely to commit violent crime than the average white. In the last 30 years, 45,000 Americans have been killed in interracial murders, overwhelmingly black on white. Almost as many as the number of Americans lost in Vietnam and much more than the 34,000 killed in Korea.

Politicians use statistics in the same way that a drunk uses lampposts—for support rather than illumination,” said Andrew Lang.

The numbers produced by statistics are the start of finding the answer, not the end. It takes a bit of common sense and clever insight to go from the statistics to the actual answer.

Compared to the human brain, machine learning isn’t especially efficient. A child places her finger on the stove, feels pain, and masters for the rest of her life the correlation between the hot metal and her throbbing hand. And she also picks up the word for it: burn. A machine learning program, by contrast, will often require millions or billions of data points to create its statistical models of cause and effect. But for the first time in history, those petabytes of data are now readily available, along with powerful computers to process them. And for many jobs, machine learning proves to be more flexible and nuanced than the traditional programs governed by rules.

The expression ‘There are three kinds of lies: lies, damned lies, and statistics’ was popularised by Mark Twain and attributed by him, in his autobiography, to the nineteenth-century British Prime Minister Benjamin Disraeli.

Statistics can easily fool us if used incorrectly, or if we fail to take in the whole picture of what’s going on. The situation is even worse when data are presented in a way that’s deliberately misleading – as often happens in advertising and politics. Without resorting to outright lies, there are plenty of ways to distort data to create a false impression.

Haese is a money grubbing goondah trying to exploit teachers by making them buy an online subscription every 12 months. Boycott Haese!!!

Second, like most other statistical inference, regression analysis builds only a circumstantial case. An association between two variables is like a fingerprint at the scene of the crime. It points us in the right direction, but it’s rarely enough to convict. (And sometimes a fingerprint at the scene of a crime doesn’t belong to the perpetrator.) Any regression analysis needs a theoretical underpinning: Why are the explanatory variables in the equation? What phenomena from other disciplines can explain the observed results? For instance, why do we think that wearing purple shoes would boost performance on the math portion of the SAT or that eating popcorn can help prevent prostate cancer? The results need to be replicated, or at least consistent with other findings.

In statistics, this phenomenon is known as Simpson’s Paradox: when a whole body of data displays one trend, yet when broken into subgroups, the opposite trend comes into view for each of those subgroups.

At heart, statistics is always about making judgment calls. It is the science of educated guesses, if you like. It looks like maths, it smells like maths, but there's none of the perfect certainty we associate with maths.

In statistics, this phenomenon is known as Simpson’s Paradox: when a whole body of data displays one trend, yet when broken into subgroups, the opposite trend comes into view for each of those subgroups. The damning conclusion in the Nation at Risk report, the one that spurred the entire teacher evaluation movement, was drawn from a grievous misinterpretation of the data.

Cellular biologist Glen Rein, Ph.D., conceived of a series of experiments to test healers’ ability to affect biological systems. [...] In Dr. Rein’s experiment, he first studied a group of ten individuals who were well practiced in using techniques that Heart-Math teaches to build heart-focused coherence. They applied the techniques to produce strong, elevated feelings such as love and appreciation, then for two minutes, they held vials containing DNA samples suspended in deionized water. When those samples were analyzed, no statistically significant changes had occurred. A second group of trained participants did the same thing, but instead of just creating positive emotions (a feeling) of love and appreciation, they simultaneously held an intention (a thought) to either wind or unwind the strands of DNA. This group produced statistically significant changes in the conformation (shape) of the DNA samples. In some cases the DNA was wound or unwound as much as 25 percent! A third group of trained subjects held a clear intent to change the DNA, but they were instructed not to enter into a positive emotional state. In other words, they were only using thought (intention) to affect matter. The result? No changes to the DNA samples. [...] Only when subjects held both heightened emotions and clear objectives in alignment were they able to produce the intended effect. An intentional thought needs an energizer, a catalyst—and that energy is an elevated emotion.

Exponential functions appear in many real-world situations: population growth, technological growth, product value over time, compounded interest, radioactive decay, statistical analysis, ...

Furthermore, academic fads have been forced upon successive generations of elementary and secondary school students, including the “New Math,” the “Open Classroom,” “Values Clarification,” “Cooperative Learning,” “Outcome-Based Education,” “No Child Left Behind,” and more recently “Common Core” and “Race to the Top,” for which trillions of dollars have been and are being wasted on inferior educational outcomes. Even the once-heralded school lunch program is not safe from statist overreach, where billions of dollars are spent on federally mandated lunches that many students refuse to eat.23

And the rest of us? We should grasp the basics of math and statistics-certainly better than most of us do today-but still follow what we love. The world doesn't need millions of mediocre mathematicians, and there's plenty of opportunity for specialists in other fields. Even in the heart of opportunity for specialists in other fields. Even in the heart of the math economy, at IBM Research, geometers and engineers work on teams with linguists and anthropologists and cognitive psychologists. They detail the behavior of humans to those who are trying to build mathematical models of it. All of these ventures, from Samer Takriti's gang at IBM to the secretive researchers laboring behind the barricades at the National Security Agency, feed from the knowledge and smarts of diverse groups. The key to finding a place on such world-class teams is not necessarily to become a math whiz but to become a whiz at something. And that something should be in an area that sparks the most enthusiasm and creativity within each of us. Somewhere on those teams, of course, whether it's in advertising, publishing, counterterrorism, or medical research, there will be at least a few Numerati. They'll be the ones distilling this knowledge into numbers and symbols and feeding them to their powerful tools.

Seven years after A Nation at Risk was published with such fanfare, researchers at Sandia National Laboratories took a second look at the data gathered for the report. These people were no amateurs when it came to statistics—they build and maintain nuclear weapons—and they quickly found the error. Yes, it was true that SAT scores had gone down on average. However, the number of students taking the test had ballooned over the course of those seventeen years. Universities were opening their doors to more poor students and minorities. Opportunities were expanding. This signaled social success. But naturally, this influx of newcomers dragged down the average scores. However, when statisticians broke down the population into income groups, scores for every single group were rising, from the poor to the rich.

In baseball, we count everything,” Babe said. “Baseball’s a math teacher’s dream for teaching kids arithmetic. It’s numbers and statistics. It’s long division and decimals. I

I took 17 computer science classes and made an A in 11 of them. 1 point away from an A in 3 of them and the rest of them didn't matter. Math is a tool for physics,chemistry,biology/basic computation and nothing else. CS I(Pascal Vax), CS II(Pascal Vax), Sr. Software Engineering, Sr. Distributed Systems, Sr. Research, Sr. Operating Systems, Sr. Unix Operating Systems, Data Structures, Sr. Object Oriented A&D, CS (perl/linux), Sr. Java Programming, Information Systems Design, Jr. Unix Operating Systems, Microprocessors, Programming Algorithms, Calculus I,II,III, B Differential Equations, TI-89 Mathematical Reasoning, 92 C++ Programming, Assembly 8086, Digital Computer Organization, Discrete Math I,II, B Statistics for the Engineering & Sciences (w/permutations & combinatorics) -- A-American Literature A-United States History 1865 CLEP-full year english CLEP-full year biology A-Psychology A-Environmental Ethics

The modulus (%) and the floor division (//) operations are not valid for complex numbers.

Reason #1: Downtime Aids Insights Consider the following excerpt from a 2006 paper that appeared in the journal Science: The scientific literature has emphasized the benefits of conscious deliberation in decision making for hundreds of years… The question addressed here is whether this view is justified. We hypothesize that it is not. Lurking in this bland statement is a bold claim. The authors of this study, led by the Dutch psychologist Ap Dijksterhuis, set out to prove that some decisions are better left to your unconscious mind to untangle. In other words, to actively try to work through these decisions will lead to a worse outcome than loading up the relevant information and then moving on to something else while letting the subconscious layers of your mind mull things over. Dijksterhuis’s team isolated this effect by giving subjects the information needed for a complex decision regarding a car purchase. Half the subjects were told to think through the information and then make the best decision. The other half were distracted by easy puzzles after they read the information, and were then put on the spot to make a decision without having had time to consciously deliberate. The distracted group ended up performing better. Observations from experiments such as this one led Dijksterhuis and his collaborators to introduce unconscious thought theory (UTT)—an attempt to understand the different roles conscious and unconscious deliberation play in decision making. At a high level, this theory proposes that for decisions that require the application of strict rules, the conscious mind must be involved. For example, if you need to do a math calculation, only your conscious mind is able to follow the precise arithmetic rules needed for correctness. On the other hand, for decisions that involve large amounts of information and multiple vague, and perhaps even conflicting, constraints, your unconscious mind is well suited to tackle the issue. UTT hypothesizes that this is due to the fact that these regions of your brain have more neuronal bandwidth available, allowing them to move around more information and sift through more potential solutions than your conscious centers of thinking. Your conscious mind, according to this theory, is like a home computer on which you can run carefully written programs that return correct answers to limited problems, whereas your unconscious mind is like Google’s vast data centers, in which statistical algorithms sift through terabytes of unstructured information, teasing out surprising useful solutions to difficult questions. The implication of this line of research is that providing your conscious brain time to rest enables your unconscious mind to take a shift sorting through your most complex professional challenges. A shutdown habit, therefore, is not necessarily reducing the amount of time you’re engaged in productive work, but is instead diversifying the type of work you deploy.

Statistical malfeasance has very little to do with bad math. Judgement an integrity turn out to be surprisingly important. A detailed knowledge of statistics does not deter wrongdoing any more than a detailed knowledge of the law averts criminal behavior.