Confidence Interval Quotes

I see at intervals the glance of a curious sort of bird through the close set bars of a cage: a vivid, restless, resolute captive is there; were it but free, it would soar cloud-high.

My calculations - allowing for a 12 percent margin of error, based on the radius of the corresponding confidence interval and the surgeon general's warning - concluded that they probably didn't stay behind for the tacos.

Even from the abyss of horror in which we try to feel our way today, half-blind, our hearts distraught and shattered, I look up again and again to the ancient constellations that shone on my childhood, comforting myself with the inherited confidence that, some day, this relapse will appear only an interval in the eternal rhythm of progress onward and upward.

The word hope first appeared in English about a thousand years ago, denoting some combination of confidence and desire. But what I desired—life—was not what I was confident about—death. When I talked about hope, then, did I really mean “Leave some room for unfounded desire?” No. Medical statistics not only describe numbers such as mean survival, they measure our confidence in our numbers, with tools like confidence levels, confidence intervals, and confidence bounds. So did I mean “Leave some room for a statistically improbable but still plausible outcome—a survival just above the measured 95 percent confidence interval?” Is that what hope was? Could we divide the curve into existential sections, from “defeated” to “pessimistic” to “realistic” to “hopeful” to “delusional”? Weren’t the numbers just the numbers? Had we all just given in to the “hope” that every patient was above average? It occurred to me that my relationship with statistics changed as soon as I became one.

Doubt is the only force capable of disturbing the seed or impression; to avoid a miscarriage of so wonderful a child, walk in secrecy through the necessary interval of time that it will take the impression to become an expression. Tell no man of your spiritual romance. Lock your secret within you in joy, confident and happy that some day you will bear the son of your lover by expressing and possessing the nature of your impression. Then will you know the mystery of “God said, Let us make man in our image.

Perhaps in Vanity Fair there are no better satires than letters. Take a bundle of your dear friend’s of ten years back—your dear friend whom you hate now. Look at a file of your sister’s! How you clung to each other till you quarreled about the twenty-pound legacy! Get down the round-hand scrawls of your son who has half broken your heart with selfish undutifulness since; or a parcel of your own, breathing endless ardour and love eternal, which were sent back by your mistress when she married the Nabob—your mistress for whom you now care no more than for Queen Elizabeth. Vows, love, promises, confidences, gratitude; how queerly they read after a while! There ought to be a law in Vanity Fair ordering the destruction of every written document (except receipted tradesmen’s bills) after a certain brief and proper interval. Those quacks and misanthropes who advertise indelible Japan ink should be made to perish along with their wicked discoveries. The best ink for Vanity Fair use would be one that faded utterly in a couple of days, and left the paper clean and blank, so that you might write on it to somebody else

It is worse, much worse, than you think. The slowness of climate change is a fairy tale, perhaps as pernicious as the one that says it isn’t happening at all, and comes to us bundled with several others in an anthology of comforting delusions: that global warming is an Arctic saga, unfolding remotely; that it is strictly a matter of sea level and coastlines, not an enveloping crisis sparing no place and leaving no life undeformed; that it is a crisis of the “natural” world, not the human one; that those two are distinct, and that we live today somehow outside or beyond or at the very least defended against nature, not inescapably within and literally overwhelmed by it; that wealth can be a shield against the ravages of warming; that the burning of fossil fuels is the price of continued economic growth; that growth, and the technology it produces, will allow us to engineer our way out of environmental disaster; that there is any analogue to the scale or scope of this threat, in the long span of human history, that might give us confidence in staring it down. None of this is true. But let’s begin with the speed of change. The earth has experienced five mass extinctions before the one we are living through now, each so complete a wiping of the fossil record that it functioned as an evolutionary reset, the planet’s phylogenetic tree first expanding, then collapsing, at intervals, like a lung: 86 percent of all species dead, 450 million years ago; 70 million years later, 75 percent; 125 million years later, 96 percent; 50 million years later, 80 percent; 135 million years after that, 75 percent again. Unless you are a teenager, you probably read in your high school textbooks that these extinctions were the result of asteroids. In fact, all but the one that killed the dinosaurs involved climate change produced by greenhouse gas. The most notorious was 250 million years ago; it began when carbon dioxide warmed the planet by five degrees Celsius, accelerated when that warming triggered the release of methane, another greenhouse gas, and ended with all but a sliver of life on Earth dead. We are currently adding carbon to the atmosphere at a considerably faster rate; by most estimates, at least ten times faster. The rate is one hundred times faster than at any point in human history before the beginning of industrialization. And there is already, right now, fully a third more carbon in the atmosphere than at any point in the last 800,000 years—perhaps in as long as 15 million years. There were no humans then. The oceans were more than a hundred feet higher.

The wide confidence interval is a confession of ignorance, which is not socially acceptable for someone who is paid to be knowledgeable in financial matters. Even if they knew how little they know, the executives would be penalized for admitting it.

My thoughts on the descent of our moral prejudices – for that is what this polemic is about – were first set out in a sketchy and provisional way in the collection of aphorisms entitled Human, All Too Human. A Book for Free Spirits, which I began to write in Sorrento during a winter that enabled me to pause, like a wanderer pauses, to take in the vast and dangerous land through which my mind had hitherto travelled. This was in the winter of 1876–7; the thoughts themselves go back further. They were mainly the same thoughts which I shall be taking up again in the present essays – let us hope that the long interval has done them good, that they have become riper, brighter, stronger and more perfect! The fact that I still stick to them today, and that they themselves in the meantime have stuck together increasingly firmly, even growing into one another and growing into one, makes me all the more blithely confident that from the first, they did not arise in me individually, randomly or sporadically but as stemming from a single root, from a fundamental will to knowledge deep inside me which took control, speaking more and more clearly and making ever clearer demands. And this is the only thing proper for a philosopher. We have no right to stand out individually: we must not either make mistakes or hit on the truth individually. Instead, our thoughts, values, every ‘yes’, ‘no’, ‘if ’ and ‘but’ grow from us with the same inevitability as fruits borne on the tree – all related and referring to one another and a testimonial to one will, one health, one earth, one sun. – Do you like the taste of our fruit? – But of what concern is that to the trees? And of what concern is it to us philosophers? . . .

The wide confidence interval is a confession of ignorance, which is not socially acceptable for someone who is paid to be knowledgeable in financial matters. Even if they knew how little they know, the executives would be penalized for admitting it. President Truman famously asked for a “one-armed economist” who would take a clear stand; he was sick and tired of economists who kept saying, “On the other hand…

Social psychology comes into the picture here, because the answer that a truthful CFO would offer is plainly ridiculous. A CFO who informs his colleagues that “there is a good chance that the S&P returns will be between –10% and +30%” can expect to be laughed out of the room. The wide confidence interval is a confession of ignorance, which is not socially acceptable for someone who is paid to be knowledgeable in financial matters.

Perhaps in Vanity Fair there are no better satires than letters. Take a bundle of your dear friend's of ten years back--your dear friend whom you hate now. Look at a file of your sister's: how you clung to each other till you quarrelled about the twenty-pound legacy! Get down the roundhand scrawls of your son who has half broken your heart with selfish undutifulness since; or a parcel of your own, breathing endless ardour and love eternal, which were sent back by your mistress when she married the nabob--your mistress for whom you now care no more than for Queen Elizabeth. Vows, love, promises, confidences, gratitude, how queerly they read after a while! There ought to be a law in Vanity Fair ordering the destruction of every written document (except receipted tradesmen's bills) after a certain brief and proper interval. Those quacks and misanthropes who advertise indelible Japan ink, should be made to perish along with their wicked discoveries. The best ink for Vanity Fair use would be one that faded utterly in a couple of days, and left the paper clean and blank, so that you might write on it to somebody else.

Time is ever conditioned by man's conception of himself. Confidence in yourself as determined by conditioned consciousness always shortens the interval of time. If you were accustomed to great accomplishments, you would give yourself a much shorter interval in which to accomplish your desire than the man schooled in defeat.

For two years he had lain beside Irene feeling her disease growing like a child of theirs. He had stayed awake in the shadow of her silence, marvelling at the stark untouchable beauty of her stoicism. In the dark her pain had seemed an incandescence. Toward the end, in the intervals when the haze of painkillers lifted, she spoke to him as she never had, lightly, as to another child whom she did not know well but with whom she had been fated to spend a long afternoon. “I think they might have been just kidding us,” she confided one time. “Suppose you don’t get to take a trip up to Heaven?” Or again, “I knew I was boring to you, but I didn’t know how else to be.” In her puzzlement at his tears she would touch his hair, not quite daring to touch his face.

The word hope first appeared in English about a thousand years ago, denoting some combination of confidence and desire. But what I desired—life—was not what I was confident about—death. When I talked about hope, then, did I really mean “Leave some room for unfounded desire?” No. Medical statistics not only describe numbers such as mean survival, they measure our confidence in our numbers, with tools like confidence levels, confidence intervals, and confidence bounds. So did I mean “Leave some room for a statistically improbable but still plausible outcome—a survival just above the measured 95 percent confidence interval?” Is that what hope was? Could we divide the curve into existential sections, from “defeated” to “pessimistic” to “realistic” to “hopeful” to “delusional”? Weren’t the numbers just the numbers? Had we all just given in to the “hope” that every patient was above average?

…yet, listen, there was rain, then the swift interval before evaporation, & the stillness of brimming, & the wet rainbowing where oil from exhaust picks up light, sheds glow, then echoes in the drains where deep inside the drops fall individually, plink, & the places where birds interject, & the coming-on of heat, & the girl looking sideways carrying the large bouquet of blue hydrangeas, shaking the water off, & the wondering if this is it, or are we in for another round, a glance up, a quick step over the puddle carrying speedy clouds, birdcall now confident again, heat drying…

As Graedon scrutinized the FDA’s standards for bioequivalence and the data that companies had to submit, he found that generics were much less equivalent than commonly assumed. The FDA’s statistical formula that defined bioequivalence as a range—a generic drug’s concentration in the blood could not fall below 80 percent or rise above 125 percent of the brand name’s concentration, using a 90 percent confidence interval—still allowed for a potential outside range of 45 percent among generics labeled as being the same. Patients getting switched from one generic to another might be on the low end one day, the high end the next. The FDA allowed drug companies to use different additional ingredients, known as excipients, that could be of lower quality. Those differences could affect a drug’s bioavailability, the amount of drug potentially absorbed into the bloodstream. But there was another problem that really drew Graedon’s attention. Generic drug companies submitted the results of patients’ blood tests in the form of bioequivalence curves. The graphs consisted of a vertical axis called Cmax, which mapped the maximum concentration of drug in the blood, and a horizontal axis called Tmax, the time to maximum concentration. The resulting curve looked like an upside-down U. The FDA was using the highest point on that curve, peak drug concentration, to assess the rate of absorption into the blood. But peak drug concentration, the point at which the blood had absorbed the largest amount of drug, was a single number at one point in time. The FDA was using that point as a stand-in for “rate of absorption.” So long as the generic hit a similar peak of drug concentration in the blood as the brand name, it could be deemed bioequivalent, even if the two curves reflecting the time to that peak looked totally different. Two different curves indicated two entirely different experiences in the body, Graedon realized. The measurement of time to maximum concentration, the horizontal axis, was crucial for time-release drugs, which had not been widely available when the FDA first created its bioequivalence standard in 1992. That standard had not been meaningfully updated since then. “The time to Tmax can vary all over the place and they don’t give a damn,” Graedon emailed a reporter. That “seems pretty bizarre to us.” Though the FDA asserted that it wouldn’t approve generics with “clinically significant” differences in release rates, the agency didn’t disclose data filed by the companies, so it was impossible to know how dramatic the differences were.

Hamilton argued that the security of liberty and property were inseparable and that governments should honor their debts because contracts formed the basis of public and private morality: “States, like individuals, who observe their engagements are respected and trusted, while the reverse is the fate of those who pursue an opposite conduct.”The proper handling of government debt would permit America to borrow at affordable interest rates and would also act as a tonic to the economy. Used as loan collateral, government bonds could function as money—and it was the scarcity of money, Hamilton observed, that had crippled the economy and resulted in severe deflation in the value of land. America was a young country rich in opportunity. It lacked only liquid capital, and government debt could supply that gaping deficiency. The secret of managing government debt was to fund it properly by setting aside revenues at regular intervals to service interest and pay off principal. Hamilton refuted charges that his funding scheme would feed speculation. Quite the contrary: if investors knew for sure that government bonds would be paid off, the prices would not fluctuate wildly, depriving speculators of opportunities to exploit. What mattered was that people trusted the government to make good on repayment: “In nothing are appearances of greater moment than in whatever regards credit. Opinion is the soul of it and this is affected by appearances as well as realities.” Hamilton intuited that public relations and confidence building were to be the special burdens of every future treasury secretary.

The reason for which a work of genius is not easily admired from the first is that the man who has created it is extraordinary, that few other men resemble him. It was Beethoven’s Quartets themselves (the Twelfth, Thirteenth, Fourteenth and Fifteenth) that devoted half a century to forming, fashioning and enlarging a public for Beethoven’s Quartets, marking in this way, like every great work of art, an advance if not in artistic merit at least in intellectual society, largely composed to-day of what was not to be found when the work first appeared, that is to say of persons capable of enjoying it. What artists call posterity is the posterity of the work of art. It is essential that the work (leaving out of account, for brevity’s sake, the contingency that several men of genius may at the same time be working along parallel lines to create a more instructed public in the future, a public from which other men of genius shall reap the benefit) shall create its own posterity. For if the work were held in reserve, were revealed only to posterity, that audience, for that particular work, would be not posterity but a group of contemporaries who were merely living half-a-century later in time. And so it is essential that the artist (and this is what Vinteuil had done), if he wishes his work to be free to follow its own course, shall launch it, wherever he may find sufficient depth, confidently outward bound towards the future. And yet this interval of time, the true perspective in which to behold a work of art, if leaving it out of account is the mistake made by bad judges, taking it into account is at times a dangerous precaution of the good. No doubt one can easily imagine, by an illusion similar to that which makes everything on the horizon appear equidistant, that all the revolutions which have hitherto occurred in painting or in music did at least shew respect for certain rules, whereas that which immediately confronts us, be it impressionism, a striving after discord, an exclusive use of the Chinese scale, cubism, futurism or what you will, differs outrageously from all that have occurred before. Simply because those that have occurred before we are apt to regard as a whole, forgetting that a long process of assimilation has melted them into a continuous substance, varied of course but, taking it as a whole, homogeneous, in which Hugo blends with Molière. Let us try to imagine the shocking incoherence that we should find, if we did not take into account the future, and the changes that it must bring about, in a horoscope of our own riper years, drawn and presented to us in our youth. Only horoscopes are not always accurate, and the necessity, when judging a work of art, of including the temporal factor in the sum total of its beauty introduces, to our way of thinking, something as hazardous, and consequently as barren of interest, as every prophecy the non-fulfillment of which will not at all imply any inadequacy on the prophet’s part, for the power to summon possibilities into existence or to exclude them from it is not necessarily within the competence of genius; one may have had genius and yet not have believed in the future of railways or of flight, or, although a brilliant psychologist, in the infidelity of a mistress or of a friend whose treachery persons far less gifted would have foreseen.

Normal reference ranges use a 95 percent confidence interval, and that means that five percent of normal, healthy people will fall outside of that range. Calling these values abnormal is essentially a false positive, and because some of the companies that market tests to athletes use an even narrower reference range, that means they’re going to generate even more false positives. (They’re also, of course, incentivizing people to come back for retesting. Ka-ching!)

On the other hand, smaller samples obviously make for larger standard errors and therefore a larger confidence interval (or “margin of sampling error,” to use the polling lingo).

The “feeling of being stared at” is the focus of a subset of distant-mental-interaction studies. This is a particularly interesting belief to investigate because it is related to one of the oldest known superstitions in the Western world, the “evil eye,” and to one of the oldest known blessings in the Eastern world, the darshan, or gaze of an enlightened master. Most ancient peoples feared the evil eye and took measures to deflect the attraction of the eye, often by wearing shiny or attractive amulets around the neck. Today, most fears about the evil eye have subsided, at least among educated peoples. And yet many people still report the “feeling of being stared at” from a distance. Is this visceral feeling what it appears to be—a distant mental influence of the nervous system—or can it be better understood in more prosaic ways? In the laboratory today, the question is studied by separating two people and monitoring the first person’s nervous system (usually electrodermal activity) while the second person stares at the first at random times over a one-way closed-circuit video system. The stared-at person has no idea when the starer is looking at him or her. Figure 9.2. Effect sizes for studies testing the “feeling of being stared at,” where 50 percent is chance expectation. Confidence intervals are 95 percent. Figure 9.2 shows the results for staring studies conducted over eight decades.34 Similar to William Braud’s electrodermal studies but conducted in a context that more closely matched common descriptions of “feeling stared at,” these studies resulted in an overall effect of 63 percent where chance expectation is 50 percent. This is remarkably robust for a phenomenon that—according to conventional scientific models—is not supposed to exist. The combined studies result in odds against chance of 3.8 million to 1. Summary Given the evidence for psi perception and mind-matter interaction effects discussed so far, we could have expected that experiments involving living systems would also be successful. The studies discussed here show that our expectations are confirmed. The implications for distant healing are clear. All the experiments discussed so far have been replicated in the laboratory dozens to hundreds of times. They demonstrate that some of the “psychic” experiences people report probably do involve genuine psi. Now we move outside the laboratory to examine a new type of experiment, one that explores mind-matter interaction effects apparently associated with the collective attention of groups.

Die-Face Analysis In the 1930s, J. B. Rhine and his colleagues recognized and took into account the possibility that some dice studies may have been flawed because the probabilities of die faces are not equal. With some dice, it is slightly more likely that one will roll a 6 face than a 1 face because the die faces are marked by scooping out bits of material. The 6 face, for example, has six scoops removed from the surface of that side of the die, so it has slightly less mass than the other die faces. On any random toss, that tiny difference in mass will make the 6 slightly more likely to land face up, followed in decreasing probability by the 5, 4, 3, 2, and 1 faces. Thus, an experiment that relied exclusively upon the 6 face as the target may have been flawed because, unless there were also control tosses with no mental intention applied, we could not tell whether above-chance results were due to a mind-matter interaction or to the slightly higher probability of rolling a 6. To see whether this bias was present in these dice studies, we sifted out all reports for which the published data allowed us to calculate the effective hit rate separately for each of the six die faces used under experimental and control conditions. In fact, the suspected biases were found, as shown in figure 8.3. The hit rates for both experimental and control tosses tended to increase from die faces 1 to 6. However, most of the experimental hit rates were also larger than the corresponding control hit rates, suggested some thing interesting beyond the artifacts caused by die-face biases. For example, for die face 6 the experimental condition was significantly larger than the control with odds against chance of five thousand to one. Figure 8.3. Relationship between die face and hit rates for experimental and control conditions. The error bars are 65 percent confidence intervals. Because of the evidence that the die faces were slightly biased, we examined a subset of studies that controlled for these dice biases—studies using design protocols where die faces were equally distributed among the six targets. We referred to such studies as the “balanced-protocol subset.” Sixty-nine experiments met the balanced-protocol criteria. Our examination of those experiments resulted in three notable points: there was still highly significant evidence for mind-matter interaction, with odds against chance of greater than a trillion to one; the effects were constant across different measures of experimental quality; and the selective-reporting “file drawer” required a twenty-to-one ratio of unretrieved, nonsignificant studies for each observed study. Thus chance, quality, and selective reporting could not explain away the results. Dice Conclusions Our meta-analysis findings led us to conclude that a genuine mind-matter interaction did exist with experiments testing tossed dice. The effect had been successfully replicated in more than a hundred experiments by more than fifty investigators for more than a half-century.

We can see this with technologies like the Kalman filter, which was used for steering the spaceship used in the moon landing. You can see the full technical details here, but roughly speaking the Kalman filter uses past measurements x[t​−​1],​x[t​−​2],​x[t​−​3] to inform the estimate of a system’s current state x[t], the action that should be taken u[t], and the corresponding prediction of the future state x[t​+​1] should that action be taken. For example, it uses past velocity, direction headings, fuel levels, and the like to recommend how a space shuttle should be steered at the current timestep. Crucially, if the microhistory is not accurate enough, if the confidence intervals around each measurement are too wide, or if (say) the velocity estimate is wrong altogether, then the Kalman Filter does not work and Apollo doesn’t happen.

value at risk, a technique used to estimate the probability of portfolio losses based on the statistical analysis of historical price trends and volatilities. It measures the worst expected loss under normal market conditions over a specific time interval at a given confidence level. Which means it measures both fear and optimism.

Statistical significance is often a crutch, a catchier-sounding but less informative substitute for a good confidence interval.

By comparing the confidence intervals of different means (or other parameters) we can get some idea about whether the means came from the same or different populations. FIGURE

specified confidence intervals (for example, the statement that 40 per cent of the balls in the jar are white, at a confidence interval of 95 per cent, implies that the precise value lies somewhere between 35 and 45 per cent - 40 plus or minus 5 per cent).

Even in the abyss of despair in which today, half-blinded, we grope about with distorted and broken souls, I look up again and again to those old star-patterns that shone over my childhood, and comfort myself with the inherited confidence that this collapse will appear, in days to come, as a mere interval in the eternal rhythm of the onward and onward.

At the other extreme, if you are at the end of the middle 95 percent, you are situated just 2.5 percent from the end. In that case, 39/40ths of the interval are in the past and 1/40th of the interval remains in the future, making the future only 1/39th as long as the past. Thus, you can say with 95 percent confidence that you fall between these two extremes and that the future longevity of whatever you are observing lies between 1/39th and 39 times its past longevity (see Figure 31).

If you’re not confident that the market is low or fairly low, you’ll be wise to use dollar-cost averaging by investing a fixed dollar amount at regular intervals to get gradually invested over time.

So, does one bad action make a person bad?” Quinn placed his palm against the five-point fingerprint screen; he then punched in the code to call the elevator. “No, a person is the sum of his or her choices, and therefore, is largely defined by his or her actions.” “No one makes all good choices, and everyone makes mistakes.” “Ah, ha! Yes, that’s why I also consider intentions as the defining denominator in my good-people, bad-people confidence interval.

duality between p-values and confidence intervals. For the Null hypothesis of no-difference commonly used in controlled experiments, a 95% confidence interval of the Treatment effect that does not cross zero implies that the p-value is < 0.05.

Confidence intervals incorporate the uncertainty and sample error to create a range of values the actual population value is likely to fall within.

a confidence interval of [176 186] indicates that we can be confident that the real population mean falls within this range.

So, if it’s not actually probable that the true value of a parameter is contained within a given confidence interval, why report it? If it’s not actually highly probable that the null hypothesis is false, why reject it?

whether the confidence interval overlaps with zero.

95% confidence interval [Δ − 1.96 σ, Δ + 1.96 σ] to assess statistical significance. If zero lies outside of the confidence interval, we declare significance

doubt Lucilla had a confidence that, whatever difficulties there might have been, she would have extricated herself from them with satisfaction and even éclat, but still it was better to avoid the necessity. Thus it was with a serene conviction that “whatever is, is best,” that Miss Marjoribanks betook herself to her peaceful slumbers. There are so many people in the world who hold, or are tempted to hold, an entirely different opinion, that it is pleasant to linger over the spectacle of a mind so perfectly well regulated. Very different were the sentiments of Mr Cavendish, who could not sleep for the ghosts that kept tugging at him on every side; and those of Barbara Lake, who felt that for her too the flower of her hero’s love had been nipped in the bud. But, to be sure, it is only natural that goodness and self-control should have the best of it sometimes even in this uncertain world. Chapter XXII THE ARCHDEACON RETURNED to Carlingford before Thursday, as he had anticipated; but in the interval Mr Cavendish had not recovered his courage so far as to renew his visit to Miss Marjoribanks, or to face the man who had alarmed him so much.

With your new .01 standard error, the 95 percent confidence intervals for the candidates are the following: Republican: 52 ± 2, or between 50 and 54 percent of the votes cast; Democrat: 45 ± 2, or between 43 and 47 percent of the votes cast. There is no longer any overlap between the two confidence intervals. You can predict on air that the Republican candidate is the winner; more than 95 times out of 100 you will be correct.*

We can say that 95 times out of 100, we expect our confidence interval, which is 4.5 ± .26, to contain the true population parameter.

Today was to be my tortoise moment. Slow and steady, cautious and smart. The plan hatched by Chris Hauth was to break the run into an extremely conservative interval workout. Run four miles. Then walk a full mile. Repeat. It was a strategy devised to prevent my core temperature from rising beyond the point of no return. No one wanted to fall prey to the dreaded “Ironman shuffle”—that arresting corpse-like crawl brought on by overwhelming fatigue. But it was also a plan that required me to check my ego at the door. Walk? I’d specifically trained to run the entire distance. And having completed a forty-five-mile run just weeks prior, I knew I could do it. My pride revolted at a strategy that seemed to bespeak a lack of confidence in my abilities.

Put on your lipstick and a nice pair of shoes, hold your head up high and act as if you did nothing wrong. Half the people you meet don’t care about the truth, they only care about how you carry yourself.

One of the first scientific papers to write about exercise-induced myokines labeled them “hope molecules.” Ultra-endurance athletes talk about the metaphor of putting one foot in front of the other—how learning that you can take one more step, even when it feels like you can’t possibly keep going, builds confidence and courage. The existence of hope molecules reveals that this is not merely a metaphor. Hope can begin in your muscles. Every time you take a single step, you contract over two hundred myokine-releasing muscles. The very same muscles that propel your body forward also send proteins to your brain that stimulate the neurochemistry of resilience. Importantly, you don’t need to run an ultramarathon across the Arctic to infuse your bloodstream with these chemicals. Any movement that involves muscular contraction—which is to say, all movement—releases beneficial myokines. It seems likely that some ultra-endurance athletes are drawn to the sport precisely because they have a natural capacity to endure. The extreme circumstances of these events allow them to both challenge and enjoy that part of their personality. Yet it’s also possible that the intense physical training contributes to the mental toughness that ultra-endurance athletes demonstrate. Endurance activities like walking, hiking, jogging, running, cycling, and swimming, as well as high-intensity exercise such as interval training, are especially likely to produce a myokinome that supports mental health. Among those who are already active, increasing training intensity or volume—going harder, faster, further, or longer—can jolt muscles to stimulate an even greater myokine release. In one study, running to exhaustion increased irisin levels for the duration of the run and well into a recovery period—an effect that could be viewed as an intravenous dose of hope. Many of the world’s top ultra-endurance athletes have a history of depression, anxiety, trauma, or addiction. Some, like ultrarunner Shawn Bearden, credit the sport with helping to save their lives. This, too, is part of what draws people to the ultra-endurance world. You can start off with seemingly superhuman abilities to endure, or you can build your capacity for resilience one step at a time. Months after I spoke with Bearden, an image from his Instagram account appeared in my feed. It was taken from the middle of a paved road that stretches toward a mountain range, with grassy fields on either side. The sky is blue, except for a huge dark cloud that appears to be hovering directly over the person taking the photo. I remembered how Bearden had described his depression as a black thundercloud rolling in. Under the Instagram photo, Bearden had written, “Tons of wind today, making an easy run far more challenging. So happy to be able to do this. Every day above ground is a good day.” Below, a single comment cheered him on, like a fellow runner on the trail: “Amen to this! Keep striving.

To successfully launch a product, generic drug companies must tread in reverse through this obstacle course. Once a generic company zeroes in on a molecule, and its scientists figure out how it operates in the body, its lawyers get to work to establish how well protected it is legally. The next step takes place in the laboratory: developing the active pharmaceutical ingredient by synthesizing it into ingredient form. That alone can take several years of trial and error. Once successful, the finished generic has to take the same form as the brand, whether that be pill, capsule, tablet, or injection. Formulating it requires additional ingredients known as excipients, which can be different, but might also be litigated. Then comes testing. In the lab, the in-vitro tests replicate conditions in the body. During dissolution tests, for example, the drug will be put in beakers whose contents mimic stomach conditions, to see how the drugs break down. But some of the most important tests are in-vivo—when the drug is tested on people. Brand-name companies must test new drugs on thousands of patients to prove that they are safe and effective. Generic companies have to prove only that their drug performs similarly in the body to the brand-name drug. To do this, they must test it on a few dozen healthy volunteers and map the concentration of the drug in their blood. The results yield a graph that contains the all-important bioequivalence curve. The horizontal line reflects the time to maximum concentration (Tmax) of drug in the blood. The vertical line reflects the peak concentration (Cmax) of drug in the blood. Between these two axes lies the area under the curve (AUC). The test results must fall in that area to be deemed bioequivalent. Every batch of drugs has variation. Even brand-name drugs made in the same laboratory under the exact same conditions will have some batch-to-batch differences. So, in 1992, the FDA created a complex statistical formula that defined bioequivalence as a range—a generic drug’s concentration in the blood could not fall below 80 percent or rise above 125 percent of the brand name’s concentration. But the formula also required companies to impose a 90 percent confidence interval on their testing, to ensure that less than 20 percent of samples would fall outside the designated range and far more would land within a closer range to the innovator product.

staring at me, her anxiety clearly evident as she said, “Why ninety-seven percent?” “A three percent confidence interval is standard.

Frequent consumption (more than once a day) of soy milk was associated with 70 per cent reduction of the risk of prostate cancer (relative risk=0.3, 95 percent confidence interval 0.1-1.0, p-value for linear trend=0.03). Jacobsen, B. K., Knutsen, S. F., & Fraser, G. E. (1998).

combined data pile up on the confidence interval, squeeze it closer to the mean. Foresight and hindsight begin to converge.

Doubt is the only force capable of disturbing the seed or impression; to avoid a miscarriage of so wonderful a child, walk in secrecy through the necessary interval of time that it will take the impression to become an expression. Tell no man of your spiritual romance. Lock your secret within you in joy, confident and happy that some day you will bear the son of your lover by expressing and possessing the nature of your impression. Then will you know the mystery of "God said, Let us make man in our image.

In like manner go to the end of that which you seek; witness the happy end of it by consciously feeling you express and possess that which you desire to express and possess; and you, through faith, already understanding the end, will have confidence born of this knowledge. This knowledge will sustain you through the necessary interval of time that it takes the picture to unfold. Ask no help of man; feel, "It is done," by consciously claiming yourself to be, now, that which as man you hope to be.

The “preliminary” step of locating possibilities worthy of explicit consideration includes steps like: weighing what you know and don’t know, what you can and can’t predict; making a deliberate effort to avoid absurdity bias and widen confidence intervals; pondering which questions are the important ones, trying to adjust for possible Black Swans

My second decision, to leave out statistical esoterica, was made with much less regret. I don’t mention confidence intervals, sample sizes, p values, and similar devices in Dataclysm because the book is above all a popularization of data and data science. Mathematical wonkiness wasn’t what I wanted to get across.

Bayesian x% credible interval that extends from the to the percentile of the posterior distribution. For the posterior distribution in Figure 1.1, a 95% Bayesian credible interval for extends from 0.59 to 0.98. In contrast to the orthodox confidence interval, this means that one can be 95% confident that the true value of lies in between 0.59 and 0.98.