Statistical Analysis Quotes

Science of yoga and ayurveda is subtler than the science of medicine, because science of medicine is often victim of statistical manipulation.

The lesson is that no amount of sophisticated statistical analysis is a match for the historical experience that ‘stuff happens’.

In the business people with expertise, experience and evidence will make more profitable decisions than people with instinct, intuition and imagination.

By the time your perfect information has been gathered, the world has moved on.

What nature hath joined together, multiple regression analysis cannot put asunder.

So it is with statistics; no amount of fancy analysis can make up for fundamentally flawed data. Hence the expression “garbage in, garbage out.

Scientists study only those aspects of the universe that it is within their gift to study: what is observable; what is measurable and amenable to statistical analysis; and, indeed, what they can afford to study within the means and time available. Science thus emerges as a giant tautology, a "closed system". It can present us with robust answers only because its practitioners take very great care to tailor the questions.

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.

I took a course at Cal once called Statistical Analysis. And there was a guy in the course who used to make up all of his computations and he never used Sigma. He used his own initials. 'Cause he was the standard deviation.

I believe neither in luck nor in destiny,” he declared. “I trust only the science of probabilities. I have studied mathematical statistics, combinatorial analysis, mass function, and random variables, and they have never held any surprises for me. You don’t seem fully to grasp the destabilizing effect that someone like you can have on someone like me.

When our forebears asked - What is a man? - they did not expect a detailed examination of some Saturday morning shopper, Mr. John Q. Public, snatched at random from the crowded agora and forced under a microscope or onto a psychiatrist's couch. Nor did they want a statistical analysis of some cross-section of the demos for an answer. Of what good to sound learning is a man who looks like every man but in whom no man sees himself? The only use for such analyses, as our modern era shows, is in various forms of exploitation. Statistical man makes a useful abstraction for advertisers and propagandists.

Your relevance as a data custodian is your ability to analyse and interpret it. If you can’t, your replacement is due.

Regression analysis is the hydrogen bomb of the statistics arsenal.

If understanding language and other phenomena through statistical analysis does not count as true understanding, then humans have no understanding either.

Reducing intelligence to the statistical analysis of large data sets “can lead us,” says Levesque, “to systems with very impressive performance that are nonetheless idiot-savants.

The trial designed to bring the most rigorous statistical analysis to the cause of lung cancer barely required elementary mathematics to prove its point.

Blacks were ten times more likely than Whites to have their ballots rejected. The racial inequity could not be explained by income or educational levels or bad ballot design, according to a New York Times statistical analysis. That left one explanation, one that at first I could not readily admit: racism. A total of 179,855 ballots were invalidated by Florida election officials in a race ultimately won by 537 votes.

From empathy and sexuality to science inclination and extroversion, statistical analysis of 122 different characteristics involving 13,301 individuals shows that men and women, by and large, do not fall into different groups.

It is unanimously agreed that statistics depends somehow on probability. But, as to what probability is and how it is connected with statistics, there has seldom been such complete disagreement and breakdown of communication since the Tower of Babel. Doubtless, much of the disagreement is merely terminological and would disappear under sufficiently sharp analysis.

Here is one of the most important things to remember when doing research that involves regression analysis: Try not to kill anyone. You can even put a little Post-it note on your computer monitor: “Do not kill people with your research.” Because some very smart people have inadvertently violated that rule.

That so far the material has been dealt with in a rather subjective way provokes the question whether a means can be found of handling it objectively. [...] This chapter considers the applicability of the statistical tests employed by Wilson and the general problem whether the Linear B data are suited to statistical analysis.

Researchers at the University of Rochester recently pronounced “Men Are from Mars Earth, Women Are from Venus Earth,” concluding: From empathy and sexuality to science inclination and extroversion, statistical analysis of 122 different characteristics involving 13,301 individuals shows that men and women, by and large, do not fall into different groups.

I never met Meehl, but he was one of my heroes from the time I read his Clinical vs. Statistical Prediction: A Theoretical Analysis and a Review of the Evidence.

Police not enforcing laws results in a high crime rate that is formally reported as a low crime rate in police statistics.

Most people use statistics the way a drunkard uses a lamp post, more for support than illumination.

opinion-based decision making, statistical malfeasance, and counterfeit analysis are pandemic. We are swimming in make-believe analytics.

Significance unfortunately is a useful means toward a personal ends in the advance of science - status and widely distributed publications, a big laboratory, a staff of research assistants, a reduction in teaching load, a better salary, the finer wines of Bordeaux. Precision, knowledge, and control. In a narrow and cynical sense statistical significance is the way to achieve these. Design experiment. Then calculate statistical significance. Publish articles showing "significant" results. Enjoy promotion. But it is not science, and it will not last.

To be sure, it would be a mistake to underestimate the importance of the intuitive knowledge that everyone acquires about contemporary wealth and income levels, even in the absence of any theoretical framework or statistical analysis. Film and literature, nineteenth-century novels especially, are full of detailed information about the relative wealth and living standards of different social groups, and especially about the deep structure of inequality, the way it is justified, and its impact on individual lives. Indeed, the novels of Jane Austen and Honoré de Balzac paint striking portraits of the distribution of wealth in Britain and France between 1790 and 1830. Both novelists were intimately acquainted with the hierarchy of wealth in their respective societies.

No data are excluded on subjective or arbitrary grounds. No one piece of data is more highly valued than another. The consequences of this policy have to be accepted, even if they prove awkward.

If, by the virtue of charity or the funded Ennet House, you will acquire many exotic new facts. You will find out that once MA’s Department of Social Services has taken a mother’s children away for any period of time, they can always take them away again, D.S.S ., like at will, empowered by nothing more than a certain signature-stamped form. I.e. once deemed Unfit— no matter why or when, or what’s transpired in the meantime— there’s nothing a mother can do.(...)That a little-mentioned paradox of Substance addiction is: that once you are sufficiently enslaved by a Substance to need to quit the Substance in order to save your life, the enslaving Substance has become so deeply important to you that you will all but lose your mind when it is taken away from you. Or that sometime after your Substance of choice has just been taken away from you in order to save your life, as you hunker down for required A.M. and P.M. prayers , you will find yourself beginning to pray to be allowed literally to lose your mind, to be able to wrap your mind in an old newspaper or something and leave it in an alley to shift for itself, without you.(...)That certain persons simply will not like you no matter what you do. Then that most nonaddicted adult civilians have already absorbed and accepted this fact, often rather early on.(...)That evil people never believe they are evil, but rather that everyone else is evil. That it is possible to learn valuable things from a stupid person. That it takes effort to pay attention to any one stimulus for more than a few seconds.(...)That it is statistically easier for low-IQ people to kick an addiction than it is for high-IQ people.(...)That you will become way less concerned with what other people think of you when you realize how seldom they do.(...)That most Substance -addicted people are also addicted to thinking, meaning they have a compulsive and unhealthy relationship with their own thinking. That the cute Boston AA term for addictive -type thinking is: Analysis-Paralysis. That 99% of compulsive thinkers’ thinking is about themselves; that 99% of this self-directed thinking consists of imagining and then getting ready for things that are going to happen to them; and then, weirdly, that if they stop to think about it, that 100% of the things they spend 99% of their time and energy imagining and trying to prepare for all the contingencies and consequences of are never good.(...)That other people can often see things about you that you yourself cannot see, even if those people are stupid.(...)That certain sincerely devout and spiritually advanced people believe that the God of their understanding helps them find parking places and gives them advice on Mass. Lottery numbers.

Over time, managers and executives began using statistics and analysis to forecast the future, relying on databases and spreadsheets in much the same way ancient seers relied on tea leaves and goat entrails.

Over time, managers and executives began using statistics and analysis to forecast the future, relying on databases and spreadsheets in much the same way ancient seers relied on tea leaves and goat entrails. The

Be wary, though, of the way news media use the word “significant,” because to statisticians it doesn’t mean “noteworthy.” In statistics, the word “significant” means that the results passed mathematical tests such as t-tests, chi-square tests, regression, and principal components analysis (there are hundreds). Statistical significance tests quantify how easily pure chance can explain the results. With a very large number of observations, even small differences that are trivial in magnitude can be beyond what our models of change and randomness can explain. These tests don’t know what’s noteworthy and what’s not—that’s a human judgment.

Here is one of the most important things to remember when doing research that involves regression analysis: Try not to kill anyone. You can even put a little Post-it note on your computer monitor: “Do not kill people with your research.

Scholars in other disciplines found it useful, and the ideas of heuristics and biases have been used productively in many fields, including medical diagnosis, legal judgment, intelligence analysis, philosophy, finance, statistics, and military strategy.

Thinking Statistically by Uri Bram   How to Lie with Statistics by Darrell Huff   Turning Numbers into Knowledge by Jonathan G. Koomey, PhD For an examination of more advanced methods of analysis, Principles of Statistics by M. G. Bulmer is a useful reference.

During the intensive rocket bombing of London in World War II, it was generally believed that the bombing could not be random because a map of the hits revealed conspicuous gaps. Some suspected that German spies were located in the unharmed areas. A careful statistical analysis revealed that the distribution of hits was typical of a random process—and typical as well in evoking a strong impression that it was not random. “To the untrained eye,” Feller remarks, “randomness appears as regularity or tendency to cluster.

Probit analysis provides a mathematical foundation for the doctrine first established by the sixteenth-century physician Paracelsus: “Only the dose makes a thing not a poison.” Under the Paracelsus doctrine, all things are potential poisons if given in a high enough dose, and all things are nonpoisonous if given in a low enough dose. To this doctrine, Bliss added the uncertainty associated with individual results. One reason why many foolish users of street drugs die or become very sick on cocaine or heroin or speed is that they see others using the drugs without being killed. They are like Bliss’s insects. They look around and see some of their fellow insects still alive. However, knowing that some individuals are still living provides no assurance that a given individual will survive. There is no way of predicting the response of a single individual.

Only years later—as an investigative journalist writing about poor scientific research—did I realize that I had committed statistical malpractice in one section of the thesis that earned me a master’s degree from Columbia University. Like many a grad student, I had a big database and hit a computer button to run a common statistical analysis, never having been taught to think deeply (or at all) about how that statistical analysis even worked. The stat program spit out a number summarily deemed “statistically significant.” Unfortunately, it was almost certainly a false positive, because I did not understand the limitations of the statistical test in the context in which I applied it. Nor did the scientists who reviewed the work. As statistician Doug Altman put it, “Everyone is so busy doing research they don’t have time to stop and think about the way they’re doing it.” I rushed into extremely specialized scientific research without having learned scientific reasoning. (And then I was rewarded for it, with a master’s degree, which made for a very wicked learning environment.) As backward as it sounds, I only began to think broadly about how science should work years after I left it.

The population is angry, frustrated, bitter—and for good reasons. For the past generation, policies have been initiated that have led to an extremely sharp concentration of wealth in a tiny sector of the population. In fact, the wealth distribution is very heavily weighted by, literally, the top tenth of one percent of the population, a fraction so small that they’re not even picked up on the census. You have to do statistical analysis just to detect them. And they have benefited enormously. This is mostly from the financial sector—hedge fund managers, CEOs of financial corporations, and so on.

Avoid succumbing to the gambler’s fallacy or the base rate fallacy. Anecdotal evidence and correlations you see in data are good hypothesis generators, but correlation does not imply causation—you still need to rely on well-designed experiments to draw strong conclusions. Look for tried-and-true experimental designs, such as randomized controlled experiments or A/B testing, that show statistical significance. The normal distribution is particularly useful in experimental analysis due to the central limit theorem. Recall that in a normal distribution, about 68 percent of values fall within one standard deviation, and 95 percent within two. Any isolated experiment can result in a false positive or a false negative and can also be biased by myriad factors, most commonly selection bias, response bias, and survivorship bias. Replication increases confidence in results, so start by looking for a systematic review and/or meta-analysis when researching an area.

This was, he told the King, a femfatalatron, an erotifying device stochastic, elastic and orgiastic, and with plenty of feedback; whoever was placed inside the apparatus instantaneously experienced all the charms, lures, wiles, winks and witchery of all the fairer sex in the Universe at once. The femfatalatron operated on a power of forty megamors, with a maximum attainable efficiency—given a constant concupiscence coefficient—of ninety-six percent, while the system's libidinous lubricity, measured of course in kilocupids, produced up to six units for every remote-control caress. This marvelous mechanism, moreover, was equipped with reversible ardor dampers, omnidirectional consummation amplifiers, absorption philters, paphian peripherals, and "first-sight" flip-flop circuits, since Trurl held here to the position of Dr. Yentzicus, creator of the famous oculo-oscular feel theory. There were also all sorts of auxiliary components, like a high-frequency titillizer, an alternating tantalator, plus an entire set of lecherons and debaucheraries; on the outside, in a special glass case, were enormous dials, on which one could carefully follow the course of the whole decaptivation process. Statistical analysis revealed that the femfatalatron gave positive, permanent results in ninety-eight cases of unrequited amatorial superfixation out of a hundred.

1) Every cause produces a corresponding effect, so an intelligent effect is likely caused by an intelligent cause. 2) It is statistically impossible that every of billions of intelligent effects is caused by dumb luck. 3) Even if half of all intelligent effects were caused by dumb luck, who where or what is the intelligence behind the other half?

In a rigorous statistical analysis linking county-level slave ownership from the 1860 US census and public opinion data collected between 2016 and 2011 by the Cooperative Congressional Election Study (CCES), a large-scale national survey of the American electorate conducted by nearly forty universities, they find that whites residing in areas that had the highest levels of slavery in 1860 demonstrate significantly different attitudes today from whites who reside in areas that had lower historical levels of slavery: (1) they are more politically conservative and Republican leaning; (2) they are more opposed to affirmative action; and (3) they score higher on questions measuring racial resentment.

the challenges of our day-to-day existence are sustained reminders that our life of faith simply must have its center somewhere other than in our ability to hold it together in our minds. Life is a pounding surf that wears away our rock-solid certainty. The surf always wins. Slowly but surely. Eventually. It may be best to ride the waves rather than resist them. What are your one or two biggest obstacles to staying Christian? What are those roadblocks you keep running into? What are those issues that won’t go away and make you wonder why you keep on believing at all? These are questions I asked on a survey I gave on my blog in the summer of 2013. Nothing fancy. I just asked some questions and waited to see what would happen. In the days to come, I was overwhelmed with comments and e-mails from readers, many anonymous, with bracingly honest answers often expressed through the tears of relentless and unnerving personal suffering. I didn’t do a statistical analysis (who has the time, plus I don’t know how), but the responses fell into five categories.         1.        The Bible portrays God as violent, reactive, vengeful, bloodthirsty, immoral, mean, and petty.         2.        The Bible and science collide on too many things to think that the Bible has anything to say to us today about the big questions of life.         3.        In the face of injustice and heinous suffering in the world, God seems disinterested or perhaps unable to do anything about it.         4.        In our ever-shrinking world, it is very difficult to hold on to any notion that Christianity is the only path to God.         5.        Christians treat each other so badly and in such harmful ways that it calls into question the validity of Christianity—or even whether God exists. These five categories struck me as exactly right—at least, they match up with my experience. And I’d bet good money they resonate with a lot of us. All five categories have one big thing in common: “Faith in God no longer makes sense to me.” Understanding, correct thinking, knowing what you believe—these were once true of their faith, but no longer are. Because life happened. A faith that promises to provide firm answers and relieve our doubt is a faith that will not hold up to the challenges and tragedies of life. Only deep trust can hold up.

I want to write a thinkpiece about what you did to me. I want to write a critical analysis about the way you put your hands to my throat, the way you threw me against the partition wall. I want to extract a dose of worldly wisdom for all women to sap the power from that pain and into abstraction so we can all live again; I want what you did to be a statistic, I want you to be a memory, I don’t want you to be those hands on my throat.

Recently a group of researchers conducted a computer analysis of three decades of hit songs. The researchers reported a statistically significant trend toward narcissism and hostility in popular music. In line with their hypothesis, they found a decrease in usages such as we and us and an increase in I and me. The researchers also reported a decline in words related to social connection and positive emotions, and an increase in words related to anger and antisocial behavior, such as hate or kill.

The brain is a machine, and the mind is a ghost within it. The origins of self-awareness and how the mind is able to perceive, analyze, and imagine are supposedly explained by numerous schools of psychology, although in fact they study only behavior through the gathering and the analysis of statistics. The why of the mind’s existence and the how of its profound capacity to reason—especially its penchant for moral reasoning—will by their very nature remain as mysterious as whatever lies outside of time.

If we had enough data then this statistical approach would undoubtedly sort out these things, and a lot of problems are arising precisely because we haven't got enough documents for the statistical approach to be wholly valid. I know you can calculate levels of probability and so forth, but to establish this really clearly we want a lot more information than we have actually got available. This is surely our major problem that we are still at the very limits at which you can use a technique of this sort. - John Chadwick

The aim of the research is to determine what groups can be drawn up as a result of regular association of place-names. A further step is to consider whether such groups have a geographical significance. This was accepted by Palmer as a reasonable hypothesis; Wilson argued the case for it by considering possible ways in which information to be recorded on the tablets was received by the scribes. Underlying this work is the assumption that groupings may have a geographical basis, but it has still to be shown that this is a reasonable assumption.

The history of pi is only a small part of the history of mathematics, which itself is but a mirror of the history of man. That history is full of patterns and tendencies whose frequency and similarity is too striking to be dismissed as accidental. Like the laws of quantum mechanics, and in the final analysis, of all nature, the laws of history are evidently statistical in character. But what those laws are, nobody knows. Only a few scraps are evident. And of these is that the Heisels of Cleveland are more numerous than the Archimedes of Syracuse.

If the statistics of happiness depend on personal reporting, how can we be sure that anyone is as happy as they claim to be? What if they aren’t telling the truth? No, we have to assume that they are, or at least that the testing system allows for lying. So the real question lay beneath: assuming that those canvassed by anthropologists and sociologists are reliable witnesses, then surely ‘being happy’ is the same as ‘reporting yourself happy’? Whereupon any subsequent objective analysis – of brain activity, for instance – becomes irrelevant. To say sincerely that you are happy is to be happy. At which point, the question disappears.

Price mostly meanders around recent price until a big shift in opinion occurs, causing price to jump up or down. This is crudely modeled by quants using something called a jump-diffusion process model. Again, what does this have to do with an asset’s true intrinsic value? Not much. Fortunately, the value-focused investor doesn’t have to worry about these statistical methods and jargon. Stochastic calculus, information theory, GARCH variants, statistics, or time-series analysis is interesting if you’re into it, but for the value investor, it is mostly noise and not worth pursuing. The value investor needs to accept that often price can be wrong for long periods and occasionally offers interesting discounts to value.

Headed, appropriately enough, by the succinct title “BREVITY,” the minute began: “To do our work, we all have to read a mass of papers. Nearly all of them are far too long. This wastes time, while energy has to be spent in looking for the essential points.” He set out four ways for his ministers and their staffs to improve their reports. First, he wrote, reports should “set out the main points in a series of short, crisp paragraphs.” If the report involved discussion of complicated matters or statistical analysis, this should be placed in an appendix. Often, he observed, a full report could be dispensed with entirely, in favor of an aide-mémoire “consisting of headings only, which can be expanded orally if needed.” Finally, he attacked the cumbersome prose that so often marked official reports. “Let us have an end to phrases such as these,” he wrote, and quoted two offenders: “It is also of importance to bear in mind the following considerations…” “Consideration should be given to the possibility of carrying into effect…” He wrote: “Most of these woolly phrases are mere padding, which can be left out altogether, or replaced by a single word. Let us not shrink from using the short expressive phrase, even if it is conversational.” The resulting prose, he wrote, “may at first seem rough as compared with the flat surface of officialese jargon. But the saving of time will be great, while the discipline of setting out the real points concisely will prove an aid to clear thinking.

The human brain is by far the most complex object known to exist in the entire universe, containing more neurons than there are billions of stars in the Milky Way. The brain and the mind are very different things, and the latter is as mysterious as the former is complex. The brain is a machine, and the mind is a ghost within it. The origins of self-awareness and how the mind is able to perceive, analyze, and imagine are supposedly explained by numerous schools of psychology, although in fact they study only behavior through the gathering and the analysis of statistics. The why of the mind’s existence and the how of its profound capacity to reason—especially its penchant for moral reasoning—will by their very nature remain as mysterious as whatever lies outside of time.

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.

This irrelevance of molecular arrangements for macroscopic results has given rise to the tendency to confine physics and chemistry to the study of homogeneous systems as well as homogeneous classes. In statistical mechanics a great deal of labor is in fact spent on showing that homogeneous systems and homogeneous classes are closely related and to a considerable extent interchangeable concepts of theoretical analysis (Gibbs theory). Naturally, this is not an accident. The methods of physics and chemistry are ideally suited for dealing with homogeneous classes with their interchangeable components. But experience shows that the objects of biology are radically inhomogeneous both as systems (structurally) and as classes (generically). Therefore, the method of biology and, consequently, its results will differ widely from the method and results of physical science.

On Friday, August 9, for example, amid a rising tide of urgent war matters, he found time to address a minute to the members of his War Cabinet on a subject dear to him: the length and writing style of the reports that arrived in his black box each day. Headed, appropriately enough, by the succinct title “BREVITY,” the minute began: “To do our work, we all have to read a mass of papers. Nearly all of them are far too long. This wastes time, while energy has to be spent in looking for the essential points.” He set out four ways for his ministers and their staffs to improve their reports. First, he wrote, reports should “set out the main points in a series of short, crisp paragraphs.” If the report involved discussion of complicated matters or statistical analysis, this should be placed in an appendix. Often, he observed, a full report could be dispensed with entirely, in favor of an aide-mémoire “consisting of headings only, which can be expanded orally if needed.” Finally, he attacked the cumbersome prose that so often marked official reports. “Let us have an end to phrases such as these,” he wrote, and quoted two offenders: “It is also of importance to bear in mind the following considerations…” “Consideration should be given to the possibility of carrying into effect…” He wrote: “Most of these woolly phrases are mere padding, which can be left out altogether, or replaced by a single word. Let us not shrink from using the short expressive phrase, even if it is conversational.” The resulting prose, he wrote, “may at first seem rough as compared with the flat surface of officialese jargon. But the saving of time will be great, while the discipline of setting out the real points concisely will prove an aid to clear thinking.” That evening, as he had done almost every weekend thus far, he set off for the country.

I am perpetually—sometimes darkly—amused by the workings of my mind, which can often seem less rational than I would like to believe they are. The human brain is by far the most complex object known to exist in the entire universe, containing more neurons than there are billions of stars in the Milky Way. The brain and the mind are very different things, and the latter is as mysterious as the former is complex. The brain is a machine, and the mind is a ghost within it. The origins of self-awareness and how the mind is able to perceive, analyze, and imagine are supposedly explained by numerous schools of psychology, although in fact they study only behavior through the gathering and the analysis of statistics. The why of the mind’s existence and the how of its profound capacity to reason—especially its penchant for moral reasoning—will by their very nature remain as mysterious as whatever lies outside of time.

Beauty is not the goal of competitive sports, but high-level sports are a prime venue for the expression of human beauty. The relation is roughly that of courage to war. The human beauty we’re talking about here is beauty of a particular type; it might be called kinetic beauty. Its power and appeal are universal. It has nothing to do with sex or cultural norms. What it seems to have to do with, really, is human beings’ reconciliation with the fact of having a body. Of course, in men’s sports no one ever talks about beauty or grace or the body. Men may profess their “love” of sports, but that love must always be cast and enacted in the symbology of war: elimination vs. advance, hierarchy of rank and standing, obsessive statistics, technical analysis, tribal and/or nationalist fervor, uniforms, mass noise, banners, chest-thumping, face-painting, etc. For reasons that are not well understood, war’s codes are safer for most of us than love’s." - from "Federer Both Flesh and Not

Bose’s creative use of statistical analysis was reminiscent of Einstein’s youthful enthusiasm for that approach. He not only got Bose’s paper published, he also extended it with three papers of his own. In them, he applied Bose’s counting method, later called “Bose-Einstein statistics,” to actual gas molecules, thus becoming the primary inventor of quantum-statistical mechanics. Bose’s paper dealt with photons, which have no mass. Einstein extended the idea by treating quantum particles with mass as being indistinguishable from one another for statistical purposes in certain cases. “The quanta or molecules are not treated as structures statistically independent of one another,” he wrote.48 The key insight, which Einstein extracted from Bose’s initial paper, has to do with how you calculate the probabilities for each possible state of multiple quantum particles. To use an analogy suggested by the Yale physicist Douglas Stone, imagine how this calculation is done for dice. In calculating the odds that the roll of two dice (A and B) will produce a lucky 7, we treat the possibility that A comes up 4 and B comes up 3 as one outcome, and we treat the possibility that A comes up 3 and B comes up 4 as a different outcome—thus counting each of these combinations as different ways to produce a 7. Einstein realized that the new way of calculating the odds of quantum states involved treating these not as two different possibilities, but only as one. A 4-3 combination was indistinguishable from a 3-4 combination; likewise, a 5-2 combination was indistinguishable from a 2-5. That cuts in half the number of ways two dice can roll a 7. But it does not affect the number of ways they could turn up a 2 or a 12 (using either counting method, there is only one way to roll each of these totals), and it only reduces from five to three the number of ways the two dice could total 6. A few minutes of jotting down possible outcomes shows how this system changes the overall odds of rolling any particular number. The changes wrought by this new calculating method are even greater if we are applying it to dozens of dice. And if we are dealing with billions of particles, the change in probabilities becomes huge.

Due to the various pragmatic obstacles, it is rare for a mission-critical analysis to be done in the “fully Bayesian” manner, i.e., without the use of tried-and-true frequentist tools at the various stages. Philosophy and beauty aside, the reliability and efficiency of the underlying computations required by the Bayesian framework are the main practical issues. A central technical issue at the heart of this is that it is much easier to do optimization (reliably and efficiently) in high dimensions than it is to do integration in high dimensions. Thus the workhorse machine learning methods, while there are ongoing efforts to adapt them to Bayesian framework, are almost all rooted in frequentist methods. A work-around is to perform MAP inference, which is optimization based. Most users of Bayesian estimation methods, in practice, are likely to use a mix of Bayesian and frequentist tools. The reverse is also true—frequentist data analysts, even if they stay formally within the frequentist framework, are often influenced by “Bayesian thinking,” referring to “priors” and “posteriors.” The most advisable position is probably to know both paradigms well, in order to make informed judgments about which tools to apply in which situations.

Fast-forward nearly a hundred years, and Prufrock’s protest is enshrined in high school syllabi, where it’s dutifully memorized, then quickly forgotten, by teens increasingly skilled at shaping their own online and offline personae. These students inhabit a world in which status, income, and self-esteem depend more than ever on the ability to meet the demands of the Culture of Personality. The pressure to entertain, to sell ourselves, and never to be visibly anxious keeps ratcheting up. The number of Americans who considered themselves shy increased from 40 percent in the 1970s to 50 percent in the 1990s, probably because we measured ourselves against ever higher standards of fearless self-presentation. “Social anxiety disorder”—which essentially means pathological shyness—is now thought to afflict nearly one in five of us. The most recent version of the Diagnostic and Statistical Manual (DSM-IV), the psychiatrist’s bible of mental disorders, considers the fear of public speaking to be a pathology—not an annoyance, not a disadvantage, but a disease—if it interferes with the sufferer’s job performance. “It’s not enough,” one senior manager at Eastman Kodak told the author Daniel Goleman, “to be able to sit at your computer excited about a fantastic regression analysis if you’re squeamish about presenting those results to an executive group.” (Apparently it’s OK to be squeamish about doing a regression analysis if you’re excited about giving speeches.)

College students were instructed to sit by themselves for up to fifteen minutes in a sparsely furnished, unadorned room and “entertain themselves with their thoughts.” They were allowed to think about whatever they liked, the only rules being that they should remain in their seat and stay awake. Before they entered the room they were obliged to surrender any means of distraction they had about their person, such as cell phones, books, or writing materials. Afterward, they were asked to rate the experience on various scales. Unsurprisingly, a majority reported that they found it difficult to concentrate and their minds had wandered, with around half saying they didn’t enjoy the experience. A subsequent experiment, however, revealed that many found being left alone in an empty room with nothing to occupy their minds so unpleasant (this is, after all, what makes solitary confinement such a harsh punishment in prisons) that they would rather give themselves electric shocks. In the first part of this experiment, the volunteers were asked to rate the unpleasantness of a shock delivered via electrodes attached to their ankle and say whether they would pay a small amount of money to avoid having to experience it again. In the second part, during which they were left alone with their thoughts for fifteen minutes, they were presented with the opportunity to zap themselves once again. Amazingly, among those who had said they would pay to avoid a repeat experience, 67 percent of the men (12 out of 18) and 25 percent of the women (6 out of 24) opted to shock themselves at least once. One of the women gave herself nine electric shocks. One of the men subjected himself to no fewer than 190 shocks, though he was considered exceptional—a statistical “outlier”—and his results were excluded from the final analysis. In their report for the journal Science, the researchers write, “What is striking is that simply being alone with their own thoughts for 15 minutes was apparently so aversive that it drove many participants to self-administer an electric shock that they had earlier said they would pay to avoid.” This goes a long way toward explaining why many people initially find it so hard to meditate, because to sit quietly with your eyes closed is to invite the mind to wander here, there, and everywhere. In a sense, that is the whole point: we are simply learning to notice when this has happened. So the frustrating realization that your thoughts have been straying—yet again—is a sign of progress rather than failure. Only by noticing the way thoughts ricochet about inside our heads like ball bearings in a pinball machine can we learn to observe them dispassionately and simply let them come to rest, resisting the urge to pull back the mental plunger and fire off more of them. One of the benefits of meditation is that one develops the ability to quiet the mind at will. “Without such training,” the psychologists conclude drily in their paper, “people prefer doing to thinking, even if what they are doing is so unpleasant they would normally pay to avoid it. The untutored mind does not like to be alone with itself.

Crime statistics are the first refuge of the reporters and public officials in denial about racial violence. But here is what they do not know or do not say: Violent crime is often not reported. A 2012 study from the Department of Justice says more than half the victims of violent crime do not call the police. And if they do, police often do not file crime reports. “More than half of the nation’s violent crimes, or nearly 3.4 million violent victimizations per year, went unreported to the police between 2006 and 2010,” said a Justice Department analysis.1

The important point here is that with hindsight it is always possible to spot the most anomalous features of the data and build a favorable statistical analysis around them. However, a properly-trained scientist (or simply a wise person) avoids doing so because he or she recognizes that constructing a statistical analysis retrospectively capitalizes too much on chance and renders the analysis meaningless. To the scientist, such apparent anomalies merely suggest hypotheses that are subsequently tested on other, independent sets of data. Only if the anomaly persists is the hypothesis to be taken seriously. Unfortunately, the intuitive assessments of the average person are not bound by these constraints. Hypotheses that are formed on the basis of one set of results are considered to have been proven by those very same results. By retrospectively and selectively perusing the data in this way, people tend to make too much of apparent anomalies and too often end up detecting order where none exists.

Statistical analysis also revealed a high correlation between deployment pain and key outcomes: the more painful code deployments are, the poorer the IT performance, organizational performance, and organizational culture

According to one statistical analysis, each additional happy friend we have in our social circle boosts our cheeriness by 9 percent, while each additional unhappy friend drags it down by 7 percent.

Systems Analysis and Design, Fourth Edition 5th Edition - Tilley and Rosenblatt Sams teach yourself C++ in 21 days Introduction to Probability and Statistics: Principles and Applications for Engineering and the Computing Sciences 4th Edition Milton and Arnold

Intelligence Gathering and Crime Analysis,

Understand the requirements for a “clean” database that is “tidy” and ready for use in statistical analysis. Understand the steps of cleaning raw data, integrating data, reducing and reshaping

The Center for American Progress had published a report in the fall of 2014 with some astounding statistics. As it wrote in an analysis of the 2007–9 recession, “Ninety-five percent of all income gains since the start of the recovery have accrued to the top 1 percent of US households.” This was only part of a longer trend. From 1983 to 2010, the top fifth of US families by net worth had increased their wealth by 120 percent and the middle fifth by only 13 percent; the net worth of the bottom fifth had decreased in that period. Looking at the theoretical household at the perfect center of American earnings—50 percent of American families earning more, and 50 percent earning less—they wrote, “The median family saw its income fall by 8 percent between 2000 and 2012.

it’s claimed that they can tell us most things about life. This trend isn’t just found in popular science books. At universities, economists analyse ever greater parts of existence as if it were a market. From suicide (the value of a life can be calculated like the value of a company, and now it’s time to shut the doors) to faked orgasms (he doesn’t have to study how her eyes roll back, her mouth opens, her neck reddens and her back arches – he can calculate whether she really means it). The question is what Keynes would think about an American economist like David Galenson. Galenson has developed a statistical method to calculate which works of art are meaningful. If you ask him what the most renowned work of the last century is, he’ll say ‘Les Demoiselles d’Avignon’. He has calculated it. Things put into numbers immediately become certainties. Five naked female prostitutes on Carrer d’Avinyó in Barcelona. Threatening, square, disconnected bodies, two with faces like African masks. The large oil painting that Picasso completed in 1907 is, according to Galenson, the most important artwork of the twentieth century, because it appears most often as an illustration in books. That’s the measure he uses. The same type of economic analysis that explains the price of leeks or green fuel is supposed to be able to explain our experience of art.

Lorenz was the charismatic, flamboyant thinker—he didn’t conduct a single statistical analysis in his life—while Tinbergen did the nitty-gritty of actual data collection.

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Galton, by comparison, was more a polymath, and made not insignificant contributions to a whole range of fields. His myriad gifts to the world included the first newspaper weather map,† the scientific basis of fingerprint analysis for forensics, a dizzying number of statistical techniques, many the underpinnings of all statistics used today, foundational work on the psychology of synesthesia, a vented hat to help cool the head while thinking hard,* and much else over his long and distinguished career.

So often, I see people bury themselves in mounds of data coming off their computers, hoping that some stream or other will yield an interesting correlation. There’s nothing wrong with using statistical analysis as a tool, and with this ability to crunch big data, the cost of this continues to drop. However, recognize that relying on this is just guessing.

Chapters 11 and 12 deal with the essential task of data preparation and pre-processing, which is mandatory before any data can be fed into a statistical analysis tool.

In the midst of World War II, Quincy Wright, a leader in the quantitative study of war, noted that people view war from contrasting perspectives: “To some it is a plague to be eliminated; to others, a crime which ought to be punished; to still others, it is an anachronism which no longer serves any purpose. On the other hand, there are some who take a more receptive attitude toward war, and regard it as an adventure which may be interesting, an instrument which may be legitimate and appropriate, or a condition of existence for which one must be prepared” Despite the millions of people who died in that most deadly war, and despite widespread avowals for peace, war remains as a mechanism of conflict resolution. Given the prevalence of war, the importance of war, and the enormous costs it entails, one would assume that substantial efforts would have been made to comprehensively study war. However, the systematic study of war is a relatively recent phenomenon. Generally, wars have been studied as historically unique events, which are generally utilized only as analogies or examples of failed or successful policies. There has been resistance to conceptualizing wars as events that can be studied in the aggregate in ways that might reveal patterns in war or its causes. For instance, in the United States there is no governmental department of peace with funding to scientifically study ways to prevent war, unlike the millions of dollars that the government allocates to the scientific study of disease prevention. This reluctance has even been common within the peace community, where it is more common to deplore war than to systematically figure out what to do to prevent it. Consequently, many government officials and citizens have supported decisions to go to war without having done their due diligence in studying war, without fully understanding its causes and consequences. The COW Project has produced a number of interesting observations about wars. For instance, an important early finding concerned the process of starting wars. A country’s goal in going to war is usually to win. Conventional wisdom was that the probability of success could be increased by striking first. However, a study found that the rate of victory for initiators of inter-state wars (or wars between two countries) was declining: “Until 1910 about 80 percent of all interstate wars were won by the states that had initiated them. . . . In the wars from 1911 through 1965, however, only about 40 percent of the war initiators won.” A recent update of this analysis found that “pre-1900, war initiators won 73% of wars. Since 1945 the win rate is 33%.”. In civil war the probability of success for the initiators is even lower. Most rebel groups, which are generally the initiators in these wars, lose. The government wins 57 percent of the civil wars that last less than a year and 78 percent of the civil wars lasting one to five years. So, it would seem that those initiating civil and inter-state wars were not able to consistently anticipate victory. Instead, the decision to go to war frequently appears less than rational. Leaders have brought on great carnage with no guarantee of success, frequently with no clear goals, and often with no real appreciation of the war’s ultimate costs. This conclusion is not new. Studying the outbreak of the first carefully documented war, which occurred some 2,500 years ago in Greece, historian Donald Kagan concluded: “The Peloponnesian War was not caused by impersonal forces, unless anger, fear, undue optimism, stubbornness, jealousy, bad judgment and lack of foresight are impersonal forces. It was caused by men who made bad decisions in difficult circumstances.” Of course, wars may also serve leaders’ individual goals, such as gaining or retaining power. Nonetheless, the very government officials who start a war are sometimes not even sure how or why a war started.

Clustering analysis developed originally from anthropology in 1932, before it was introduced to psychology in 1938 and was later adopted by personality psychology in 1943 for trait theory classification. Today, clustering analysis is used in data mining, information retrieval, machine learning, text mining, web analysis, marketing, medical diagnosis, and numerous other fields.

One of those 48 studies is the Danish analysis published in November 2020 in the world-renowned journal Annals of Internal Medicine, which concluded: „The trial found no statistically significant benefit of wearing a face mask.“1416 Shortly before, U.S. researcher Yinon Weiss updated his charts on cloth face masks mandates in various countries and U.S. states—and they also showed that mask mandates have made no difference or may even have been counterproductive.1417 The aforementioned website „Ärzte klären auf“ showed a graph with data going until December 4, 2020, which also refutes the effectiveness of the mask obligation.

In statistics, correlation is a quantitative assessment that measures both the direction and the strength of this tendency to vary together.

Pearson’s correlation takes all of the data points on this graph and represents them with a single summary statistic. In this case, the statistical output below indicates that the correlation is 0.705.

Pearson’s correlation coefficient is represented by the Greek letter rho (ρ) for the population parameter and r for a sample statistic. This coefficient is a single number that measures both the strength and direction of the linear relationship between two continuous variables. Values can range from -1 to +1.

Pearson’s correlation coefficient is unaffected by scaling issues. Consequently, a statistical assessment is better for determining the precise strength of the relationship.

What is a good correlation? How high should it be? These are commonly asked questions. I have seen several schemes that attempt to classify correlations as strong, medium, and weak. However, there is only one correct answer. The correlation coefficient should accurately reflect the strength of the relationship. Take a look at the correlation between the height and weight data, 0.705. It’s not a very strong relationship, but it accurately represents our data. An accurate representation is the best-case scenario for using a statistic to describe an entire dataset.

squared is a primary measure of how well a regression model fits the data. This statistic represents the percentage of variation in one variable that other variables explain. For a pair of variables, R-squared is simply the square of the Pearson’s correlation coefficient. For example, squaring the height-weight correlation coefficient of 0.705 produces an R-squared of 0.497, or 49.7%. In other words, height explains about half the variability of weight in preteen girls.

values and coefficients are they key regression output. Collectively, these statistics indicate whether the variables are statistically significant and describe the relationships between the independent variables and the dependent variable. Low p-values (typically < 0.05) indicate that the independent variable is statistically significant. Regression analysis is a form of inferential statistics. Consequently, the p-values help determine whether the relationships that you observe in your sample also exist in the larger population. The coefficients for the independent variables represent the average change in the dependent variable given a one-unit change in the independent variable (IV) while controlling the other IVs.

The low p-values indicate that both education and IQ are statistically significant. The coefficient for IQ (4.796) indicates that each additional IQ point increases your income by an average of approximately $4.80 while controlling everything else in the model. Furthermore, the education coefficient (24.215) indicates that an additional year of education increases average earnings by $24.22 while holding the other variables constant.

For a good model, the residuals should be relatively small and unbiased. In statistics, bias indicates that estimates are systematically too high or too low. Unbiased estimates are correct on average.

Additionally, if you take RSS / TSS, you’ll obtain the percentage of the variability of the dependent variable around its mean that your model explains. This statistic is R-squared!

From a time even before then, from before James was born, there's a list of frequently requested items in English and Chinese: Egg rolls Wontons Pot stickers Crab rangoons (What are these? Winnie, their mother, annotated in Chinese. Their father wrote underneath, Wontons filled with cream cheese.) Beef with broccoli Following a scattershot statistical analysis, Winnie also compiled a list of things Americans liked: Large chunks of meat Wontons and noodles together in the same soup Pea pods and green beans, carrots, broccoli, baby corn (no other vegetables) Ribs or chicken wings Beef with broccoli Chicken with peanuts Peanuts in everything Chop suey (What is this? Leo wrote. I don't know, Winnie wrote.) Anything with shrimp (The rest of them can't eat shrimp, she annotated. Be careful.) Anything from the deep fryer Anything with sweet and sour sauce Anything with a thick, brown sauce And there is, of course, the list of things the Americans didn't like: Meat on the bone (except ribs or chicken wings) Rice porridge Fermented soybeans

His greatest academic achievement was the discovery of the theory of statistical decision functions. Today, Wald is known as the founder of sequential analysis. He also published some of the first papers on game theory.2 The methods of sequential analysis he developed were widely applied to the US WWII effort.3 Wald was known

The credit card companies are at the forefront of this kind of analysis, both because they are privy to so much data on our spending habits and because their business model depends so heavily on finding customers who are just barely a good credit risk.

And, as recounted in the book Moneyball, statistical analysis can sometimes discover that clearly measureable but neglected characteristics are more significant than is recognized by intuitive understanding based on accumulated experience.

Measuring replication rates across different experiments requires that research be reviewed in some fashion. Research reviews can be classified into four types. A type 1 review simply identifies and discusses recent developments in a field, usually focusing on a few exemplar experiments. Such reviews are often found in popular-science magazines such as Scientific American. They are also commonly used in skeptical reviews of psi research because one or two carefully selected exemplars can provide easy targets to pick apart. The type 2 review uses a few research results to highlight or illustrate a new theory or to propose a new theoretical framework for understanding a phenomenon. Again, the review is not designed to be comprehensive but only to illustrate a general theme. Type 3 reviews organize and synthesize knowledge from various areas of research. Such narrative reviews are not comprehensive, because the entire pool of combined studies from many disciplines is typically too large to consider individually. So again, a few exemplars of the “best” studies are used to illustrate the point of the synthesis. Type 4 is the integrative review, or meta-analysis, which is a structured technique for exhaustively analyzing a complete body of experiments. It draws generalizations from a set of observations about each experiment.1 Integration Meta-analysis has been described as “a method of statistical analysis wherein the units of analysis are the results of independent studies, rather than the responses of individual subjects.”2 In a single experiment, the raw data points are typically the participants’ individual responses. In meta-analysis, the raw data points are the results of separate experiments.

I came up with three classifications of potential gain and added that information to all the previously entered data. The classifications were: Meaningless Synchronicity, Synchronicity of Need, and Synchronicity of Want. I had some three thousand predictions already in the database when I re-ran the analysis. "That analysis showed me I was predicting Meaningless Synchronicities with a really high degree of statistical certainty.

A statistical analysis appeared to affirm that there was a systemic disparity.7 The article ran with the logline “There’s software used across the country to predict future criminals. And it’s biased against blacks.

In the US, not only did the rise of postwar Neoclassicism represent the consolidation of a particular ‘triumvirate’ in economics—mathematics, formalism, and physics envy (Bateman 1998), but it also replaced an important interwar pluralism[26] that allowed for more than one single approach in economics to co-exist with certain prestige and influence.[27] Amongst the reasons for such a shift, historians of economic thought expose a complex story that involves changes in the epistemology, methodology, and sociology of the economics discipline (Morgan & Rutherford 1998). For the US, it involved inter alia a change in how mathematics began to dominate economics scholarship, and particularly how mathematical formalism began to be closely associated with the concept of scientific neutrality, objectivity, and universal applicability (Furner 1975). This led to an expansion of method-oriented analyses, reinforced by the adoption of econometrics and statistical analysis in economics.