'degree of certainty statistics' is an ongoing research project by David Addison stemming from the initial question: which two pieces of music would you like played at your funeral?
Submissions will be compiled and aim to inform a visual art project in 2018. Possible outcomes include a public exhibition, critical text(s), digital archive, printed publication or presentation within an audio format.
Please share with anyone you feel may be interested or benefit in somehow from tackling the question. A varied dataset of ages, locations, gender and cultural identities will help realise a more fully formed response and critical understanding. If you would like to discuss any aspects of the project in further detail then please get in touch at firstname.lastname@example.org
All submissions can be made anonymously, if contact details are provided then any personal data will be stored securely and if presented publically you will be consulted for consent before any distinguising information is released in a public facing format.
A 'song' here is defined as any piece of recorded music or other composition of sound, instrumental or otherwise. Please supply the performer(s) of your chosen version of the piece rather than original writer if different.
There is no physical force that means the odds of each side showing an equal occurrence rate is mandatory. I might have to go all the way to the 9th toss to have a 99.9% chance that, finally, heads came out! 19 examples: Provided one is consistent in application of these parameters, at least… The certainty and uncertainty a researcher has in his or her results presents another critical area to probe. It means that it takes 1 event (coin toss, that is) in order to have a 50-50 chance (or degree of certainty of 50%) that either heads or tails will come out. Plus, you can also calculate the very important binomial distribution formula (BDF) and binomial standard deviation (BSD), plus dozens of statistics and probability functions. Let's try to make sense of those numbers. How certain should you be after how many samples? We often expect randomness to mean no pattern. Being unforeseeable in advance makes them challenging to account for. Goals of this chapter – 1. By contrast, what they call theory of games is a form of vague mathematics: The formulae are barely vaguely correlated with real life. Rudolph Carnap viewed certainty as a matter of degree (degrees of certainty) which could be objectively measured, with degree one being certainty. Context always matters and later chapters continue to explore how to reliably sample to answer specific questions. It is the sum of the probability of each “right” value. He is calm and precise. These probabilities are the average chance. It is extremely popular and supposedly easy to win. Actually, it could be even worse: It might take 10 or 11 tosses until heads appear! In numerous other cases it's even worse. And that the point of this chapter, and book. This means the chance of seeing a high serial number sample were increased, more of the range of numbers explored, and the computed average interval will be more accurate. Below the lowest seen, between the lowest and the middle sample, between the middle and the highest, or above the highest sample. How certain? The Internet search on Degree of Certainty, DC yielded one and only one result in 1998: This very Web page (zero results in 1997, for DC was introduced in December of that glorious year, with some beautiful snowy days just before the Global Warming debate started ) For we shall always be mindful that nothing comes in absolute certainty; everything comes in degrees of certainty Never zero, Never absolutely. Vital Statistics Reporting Guidance U.S. Department of Health and Human Services • Centers for Disease Control and Prevention • National Center for Health Statistics • National Vital Statistics System 2 Certifying deaths due to COVID–19 If COVID–19 played a role in the death, this condition should be specified on the death certificate. This is often a surprise, its assumed hundreds or thousands of samples are required to have any significance. Or a 6. 2. Decision-making under Certainty: A condition of certainty exists when the decision-maker knows with reasonable certainty what the alternatives are, what conditions are associated with each alternative, and the outcome of each alternative. Certainty By Graham MacAree on Feb 9, 2008, 1:45pm PST 255. Born on 21 February 1875 to Nicolas (1837–1931) and Marguerite (neé Gilles 1838–1924), Jeanne died at a nursing home in Arles, southern France on 4 August 1997. (2020) It also displays the probability that a parameter will fall between a pair of values around the mean and it is most often constructed using confidence levels of 95% or 99%. Probability values In statistics, the established threshold for determining whether a given value occurs by chance. Heads, tails and un-observable are all possibilities. VI. If private organizations, such as the casinos, would conduct such forms of gambling, they would surely be outlawed on the grounds of extortion! Probability A measure of the degree of certainty of the occurrence of an event. With a third sample, there are now four possible intervals the next sample could fall. The following scenario is for samples taken from a non-repeating set of possible values. The upper and lower bounds of this range are based on the desired degree of certainty (for example, a 60 percent or 90 percent degree of certainty). But nothing is 100% certain, not even... 99.99%! The higher the probability of an event, the more certain we are that the event will occur. Pastel purple, pink or blue? This is the idea of probability : a higher probability expresses a higher degree of certainty that something will happen. If we need to know than chance on average whether the next sample serial number is higher than the highest we have seen, the answer would be 25%. That's almost 10 times worse than the American roulette -- considered by many a suckers' game! The width of the distribution represents our degree of certainty in our estimate. There is a reason the estimates were so close to the eventual actual determined through post-war records. We revisit observable and un-observable possibilities throughout this book to make sure they are considered, and only dismissed when properly accounted for. How many possibilities are there when tossing a traditional coin? Probability vs. When calculating probabilities from sample observations of an unknown range of values, there can be no way of knowing in advance all of the possibilities. Therefore, I needed $512 to make sure that I am very, very close to certainty (99.9%) that heads will show up and I win . There is no way of knowing for certain, but the odds are in their favor. Probability A measure of the degree of certainty of the occurrence of an event. This chapter continues to explore statistical sampling. Calculating probabilities for range problems requires knowing how many possible interval positions a value could fall between. Her wording of the question would be “What is the chance of rolling a head?” Strictly speaking the answer is 1 in 3. Many of you are now shaking your head and saying, what is the chance of un-observable happening? (2003) suggested summarising the knowledge in the group. Absence matters. The chance of a living swan being seen in Europe that is white in color is still almost 100%, then and now, except in zoos and apparently a few escapees in the wild. Let's say I pick the number 2-1-4 and play it every drawing. Now the odds are 50% heads, 50% tails. I look at the historical age of death for people similar to me (male, white, no cigarettes or recent skydiving activity) to give a probability of what my age and method of departure could be based on historical frequency. Yes, I am telling you that if samples are reliably taken, there is diminishing return in how much is learnt after nine samples or so. 1. Only by considering all of the possibilities can true answers emerge, no matter how many samples we can observe. Define probability and certainty 2. We mention (again) that when using sampling you can NEVER be “certain,” but we can be sure enough to tip the balance that a decision we make is more informed than one made with no data at all. After nine samples, each additional sample only reduces the uncertainty of any one interval by less than 1%. If the state lotteries want to treat their customers (players like you and me) more fairly, they should pay $690 or $700 for a $1 winning ticket. Journalists can ask researchers what they are certain of, the degree of certainty they have with their results and how they have established this certainty. From one up-to the lowest sample, between the two samples, or above the highest sample. Read more on my Web pages: Theory of Probability: Best introduction, formulae, algorithms, software and Mathematics of Fundamental Formula of Gambling. My chance is 50% that heads will appear in the 1st coin toss. None of these colors are out of the question now we know that not all swans are white. Death and Taxes Benjamin Franklin said that death is a certainty of life. It may not be certain enough for medical decisions about me, but it’s often enough to shine a bright light on a bias or an errant gut instinct. Certainty of Major by Credits Earned Credits Earned Very Uncertain Somewhat Certain Very Certain Row Total 0 - 9 12 8 3 23 10-59 8 6 10 24 60 or more 5 5 11 21 Col Total 25 19 24 68 The Difficulties of Statistics. The game has a total of 1,000 combinations. So, I would spend $692 and maybe I win $500! They are largely a matter of probability alone. Four equal possibilities each with a 25% chance. They also account for breaking many banks, economies and civilizations. These books are comical in places, alarming in others, but always eye opening about how to apply uncertainty in the real world. The value rolled on the previous dice roll plays no influence in the odds of the next roll. Less data than thought can help make informed decisions. How many observable six-sided values can be less than 4? The story goes that in Europe it was common knowledge and even formalized in a Latin proverb, that through observation all Swans are white. But people rarely consult the statistics of similar cases, seeing their case as special, into which they have special insight. Many of you said two, the possibilities are heads or tails. Sure, this problem of tank production doesn’t come up every day. Generating possibilities takes imagination, and sometimes experience or a sinister mind (as in my wife’s case, hi darling!). Look at the above chart. Rolling six ones in a row has the same odds as rolling, a sequence 1, 2, 3, 4, 5 and 6 or any other set of numbers. But, probability was on their side. I named this relation: Ion Saliu Paradox of N Trials. How to use certainty in a sentence. By the way, it is almost certain (99.5% to 99.9%) that the number 2-1-4 will come out within the next 400-500 drawings in Pennsylvania lottery. While on the subject of death, here is my prediction: I will die one day. The probability and statistical program allows you to calculate the number of trials N for any degree of certainty DC. If it was easy, I’d suspect people who perform prediction on stage (or on Wall Street) would all be retired and own small islands; And all faith healers would be doctors. If you are curious, simply multiply the numbers in the last column by 10,000 to get a general idea. A “black swan” was used as a metaphor for something that doesn’t exist, so certain are we that an alternative colored swan was thought ridiculous. Each dice roll is independent. I only have a 10% chance (DC) that my pick will come out winner within the next 105 drawings! There is no absolute statistical certainty since statistics often deals with human norms which are based on vague definitions not subject to mathematical calculation. Let’s look at the tank serial number problem again. The column illustrates the well-known3-digit lottery game. For now, all swans are white unless you are in Perth. I bet on it... even if I live 100 years after 2060, when Isaac Newton calculated that the world would end based on his mathematical interpretation of the Bible! Just like tank serial numbers! A standard six-sided dice has the numbers 1 to 6 printed on the six sides of a cube. The inverse relationship between the confidence interval width and the certainty of prediction should be noted. In other words, you need to show the degree of certainty. The correct answer is 3. ", My question dealt with three elements: The possibilities are black, white and another color we haven’t seen yet. Count the number of possible outcomes that match the desirable criteria. Table 3 shows the results of Equation 5 and Equation 6 for 1 to 30 prior samples. Therefore, lotteries are a form of taxation - the governments must tell the truth to their constituents... Let's go all the way to the last column: p=1/1,000. Divide the count of desired outcomes by the total possible outcomes. Instead, other lotto combinations, with a more natural standard devi(l)ation (yes, deviation), will repeat in the same frame of time. The exact point at which one ceases to be certain is the degree of certainty as opposed to the degree of belief measured as a probability function. Especially the color of them. We should read Nassim Taleb’s work on the limits of traditional probability and statistics in the face of massive impact, low probability, unforeseeable events. In the digit lotteries, the state commissions enjoy typically an extraordinary 50% house edge!!! Probability is primarily a branch of mathematics, which studies the consequences of mathematical definitions and real-life entities. If head or tails is played on a flat surface with lots of space, there is very low chance of un-observed. What is the chance of rolling any one of the numbers? Except, that’s not the case or at least guaranteed. This is gives a good enough outcome that insurance companies have worked out what my life insurance premiums should be to make insuring people similar to me a profitable activity on average. These partitions are called intervals. Hayes, A. When building a set of possibilities, you need to consider even the rare ones, so you can determine if context or location might increase or decrease the odds of occurring. Also, the casinos set limits on maximum bets: the players are not allowed to double up indefinitely. Back in 1982 professor Lazlo used degrees of certainty testing our knowledge in chemistry. Certainty to reasonable intent is necessary, and the meaning of that language ... as are incapable of being ascertained by the usual rules of evidence to a reasonable degree of certainty." This dangerous form of betting is called a Martingale system. When returning planes were analyzed for holes (remember in the previous chapter), it was the un-observable planes and “no” holes that were important. - Confidence level is known as confidence coefficient as well and represents the level of certainty expressed in percentage, that you assume when you calculate the required population sample size. We don't need to analyze the lotto games. And your right. A lot of assumptions are made that may not be true for all circumstances. Key points and tips discussed in this chapter:  In statistics, a percentage isn’t represented as 0% and 100%, its represented as 0 and 1 by the coolest kids. Look at how the number of samples relate… I also mention that all combinations have an equal probability of appearance. In normal statistical analysis, the confidence interval tells us the reliability of the sample mean as compared to the whole mean. With sampling you can never be sure, but you can’t be any surer without sampling. Research question: At α = .05, is the degree of certainty independent of credits earned? If you are asked to take a bet on what color a swan is in Europe, bet on white. They need what is known as house edge or percentage advantage. The second sample gives us a lot more information, we get a range, and any future sample has three distinct possibilities. The general problem though is estimating the likely range of values and how likely another sample might be above or below the extremes. degree of certainty that an event will appear, symbolized by DC Standard dice are designed to give an equal chance for each side. Assuming the samples are reliably taken and the actual serial numbers are non-repeating and sequential, the interval average will emerge quickly. If the probability is 1/N and we repeat the event N times, the degree of certainty is 1 (1/e), when N tends to infinity. Alpha is likelihood of being wrong we’re willing to accept. The post-Brexit trade agreement between the UK and EU offers travel retailers ‘a degree of certainty’ regarding new rules, says the UK Travel Retail Forum (UKTRF). You could also consider elapsed time as a non-repeating sequence of values, and I often use these same formulas when dealing with lead-time and cycle-time values as you will learn. “Uncertainty indicates we have limited knowledge about the future and can only represent our understanding with possibilities, and the probability of those possibilities” (Spetzler, Winter, & Meyer, 2016). Additionally to the use of certainty data to classify individual knowledge Bruttomesso et al. A … In fact, after nine samples, each sample only improves a probability of each interval by less than one percent. For many decisions, a few well taken reliable samples may prove better than a gut instinct or an unintentional cognitive bias. The certainty and uncertainty a researcher has in his or her results presents another critical area to probe. Subtract the minimum estimate from the highest to estimate, divide by how many of that component are used on each tank, and you have how many total tanks produced. The most used confidence levels are: 90%, 95%, 98% and 99%. We just know the sample values we have seen so far. For most practical surveys, the results are reported based on a 95% confidence interval. If there was one black swan, how many other colors are there? Enrich your vocabulary with the English Definition dictionary The certainty of a single measurement, of course, is zero. Even this easiest of the games of chance can lead to sizable losses. Problem is, you are just running the calculation once. Observable possibilities of coin toss: Heads — 50%, Tails — 50%. We don’t know when your project will finish, but we do know how other similar to it have delivered and can use that to make a more informed guess. V. Practical Dimension of Fundamental Formula of Gambling However, some rare event might disrupt your plans such as an earthquake. number of trials (events), symbolized by N. I was able to answer such a question and quantify it in a mathematical expression (logarithmic) I named the Fundamental Formula of Gambling (FFG): The Fundamental Formula of Gambling is an historic discovery in theory of probability, theory of games, and gambling mathematics. Uncertainty is limited knowledge about how a future event may play out. I’m going to stick my neck out and assume some of you who read the previous paragraph are thinking about swans. The degree of certainty DC rises exponentially with the increase in the number of trials N while the probability p is always the same or constant. Next try degree of certainty DC = 80, or whatever DC you want (greater than 0 but lower than 100). After that quasi-impossible event (for coin tossing has never been stopped after one flip by any authority), the degree of certainty, DC, rises with the increase in the number of trials, N, while the probability, p, always stays constant. A step in the Fundamental Formula of Gambling leads to this relation: I tested for N = 100,000,000 N = 500,000,000 N = 1,000,000,000 (one billion) trials. Knowing (even approximately) the highest and lowest serial number seen makes it pretty easy to estimate how many serial numbers were allocated by just subtracting the highest from the lowest. To compute a probability –. “Dinosaurs; if they still existed I think we would have seen one. With a 95% certainty, 19 of 20 survey samples drawn from the population of interest would lie within the confidence interval.) “Uncertainty indicates we have limited knowledge about the future and can only represent our understanding with possibilities, and the probability of those possibilities”. If the coin is tossed near a cliff edge and I don’t want any of you to go out and attempt to prove this, there is a lot higher chance of un-observable. For now, overly worrying about Black Swan events gets in the way of learning how probability applies on average and supersedes our gut instinct in decision making. Every roll could be a 1. Degrees of certainty in the present and past Grammar expert Betty Azar explains that these modals tell us how sure speakers are about what they are saying. That was until 1697 when Dutchman, Willem de Vlamingh, observed black swans frolicking happily off the coast of what is now known as Australia (New Holland at that time). Resources in Theory of Probability, Mathematics, Statistics, Combinatorics, Software See a comprehensive directory of the pages and materials on the subject of theory of probability, mathematics, statistics, combinatorics, plus software. You must know how to do it study this book thoroughly and grasp the new essential concepts: Number of trials N and especially the Degree of Certainty DC (in addition to the probability p). This gives three different methods to compare and contrast. The next one we see could be above or below or between the ones we have seen. In any event, the state lotteries defy all anti-trust laws: they do not allow the slightest form of competition! Expect to see me fall into 0 to 1 ranges later in this book, and expect to see most software that computes percentages to want a number from 0 to 1. Most people don't comprehend the concept of all-encompassing randomness because phenomena vary in the particular probability, p, and specific degree of certainty, DC, directly influenced by the number of trials, N. Please read an important article here: Combination 1 2 3 4 5 6: Probability and Reality. It analyzes the coin tossing game of chance. Yes, it is almost certain that my number will come out within 4,602 or within 6,904 drawings! This factor translates to longer losing streaks for the player, in addition to more wins for the house! ~ Discover profound philosophical implications of the Fundamental Formula of Gambling (FFG), including mathematics, probability, formula, gambling, lottery, software, degree of certainty, randomness. Sure, they were lucky. My wife is a lawyer, and she would say (and did) that there isn’t enough information to answer that question. To assess how likely one possibility is to all others, we divide the number of possibilities that match our desired outcome by the total number of possible outcomes. Since I bet $2 and doubling up to the 9th toss, two to the power of 9 is 512. Before pouring a stiff drink to calm your nerves, consider, does this really matter? Any casino would be a guaranteed loser in a matter of months! Very encouraging, isn't it? The first time I met degrees of certainty was in my first year as a veterinary student at Liege university. (.05 or 5% being wrong is the same as 95% certainty we’re correct.) See inductive logic, philosophy of probability, philosophy of statistics. Which also means that my pick will not come out before I play it for 692 drawings. We look into the probability the answer given by sampling likely matches reality. To calculate the probability of a single or set of possible values, we divide how many possibilities are in this group by the total number of possibilities. This Taxi Formula follows similar logic to estimating the probability of samples falling in different parts of an actual range. The easiest to understand are the numbers in the column under the heading p=1/2. Certainty grows the more samples we have, and the longer we reliably observe. (But they don't know there is more to the picture than meets the eye!). The researchers boosted their chances by using the serial numbers from the tank track rubber dolly wheels. Probability is the number of possibilities that match what we need divided by the total number of all possibilities. I introduced the DC concept in the year of grace 1997, or 1997+1 years after tribunicia potestas were granted to Octavianus Augustus (the point in time humans started the year count of Common Era, still in use). Most people still confuse probability for degree of certainty...or vice versa. Rather than calculating the probability of an exact value, the probability on average that the next sample falls into a possible interval range is computed. This book helps to understand the grey area between certain and never — where the outcome is uncertain at this time, but will be known at some future time. It takes the highest seen and adds a bit. Resources in Theory of Probability, Mathematics, Statistics, Software, And thusly we discovered here the much-feared mathematical concept of Degree of Certainty, DC. That would be the chance of a 1, 2 or 3 summed. Although we can’t rule out this possibility, I’ve seen enough obituary entries in the local newspapers to consider my death is so close to inevitable that semantic nuance won’t save me (if you are under the age of 18, google “newspaper”). Many of you said six. In reality, they now pay only $500 for a $1 winning bet!!! It’s 75% more likely that the next sample is lower than the highest we have seen. The serial numbers start from 1, are sequential, and ascend to an unknown maximum value. Nassim Taleb picked up the Black Swan theme in his books on life and uncertainty. | Home | Search | New Writings | Odds, Generator | Contents | Forums | Sitemap |, Theory of Probability Leading to Fundamental Formula of Gambling (FFG), Fundamental Formula of Gambling: Games Other Than Coin Tossing, Practical Dimension of Fundamental Formula of Gambling, Resources in Theory of Probability, Mathematics, Statistics, Software, The final version published in December 1997; first capture by the, Presenting the most astonishing formula in gambling mathematics, probability theory at large, widely known now as. Secured two tanks of chance can lead to sizable losses to accept games of can. At degree of certainty statistics tank track rubber dolly wheels thus, any particular pick-3 combination has a probability of side! 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