🔭Data Science: Models (Just the Quotes)

"A model, like a novel, may resonate with nature, but it is not a ‘real’ thing. Like a novel, a model may be convincing - it may ‘ring true’ if it is consistent with our experience of the natural world. But just as we may wonder how much the characters in a novel are drawn from real life and how much is artifice, we might ask the same of a model: How much is based on observation and measurement of accessible phenomena, how much is convenience? Fundamentally, the reason for modeling is a lack of full access, either in time or space, to the phenomena of interest." (Kenneth Belitz, Science, Vol. 263, 1944)

"The principle of complementarity states that no single model is possible which could provide a precise and rational analysis of the connections between these phenomena [before and after measurement]. In such a case, we are not supposed, for example, to attempt to describe in detail how future phenomena arise out of past phenomena. Instead, we should simply accept without further analysis the fact that future phenomena do in fact somehow manage to be produced, in a way that is, however, necessarily beyond the possibility of a detailed description. The only aim of a mathematical theory is then to predict the statistical relations, if any, connecting the phenomena." (David Bohm, "A Suggested Interpretation of the Quantum Theory in Terms of ‘Hidden’ Variables", 1952)

"Consistency and completeness can also be characterized in terms of models: a theory T is consistent if and only if it has at least one model; it is complete if and only if every sentence of T which is satified in one model is also satisfied in any other model of T. Two theories T1 and T2 are said to be compatible if they have a common consistent extension; this is equivalent to saying that the union of T1 and T2 is consistent." (Alfred Tarski et al, "Undecidable Theories", 1953)

"The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work" (John Von Neumann, "Method in the Physical Sciences", 1955)

"[…] no models are [true] = not even the Newtonian laws. When you construct a model you leave out all the details which you, with the knowledge at your disposal, consider inessential. […] Models should not be true, but it is important that they are applicable, and whether they are applicable for any given purpose must of course be investigated. This also means that a model is never accepted finally, only on trial." (Georg Rasch, "Probabilistic Models for Some Intelligence and Attainment Tests", 1960)

"[...] the null-hypothesis models [...] share a crippling flaw: in the real world the null hypothesis is almost never true, and it is usually nonsensical to perform an experiment with the sole aim of rejecting the null hypothesis." (Jum Nunnally, "The place of statistics in psychology", Educational and Psychological Measurement 20, 1960)

"If one technique of data analysis were to be exalted above all others for its ability to be revealing to the mind in connection with each of many different models, there is little doubt which one would be chosen. The simple graph has brought more information to the data analyst’s mind than any other device. It specializes in providing indications of unexpected phenomena." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics Vol. 33 (1), 1962)

"A model is essentially a calculating engine designed to produce some output for a given input." (Richard C Lewontin, "Models, Mathematics and Metaphors", Synthese, Vol. 15, No. 2, 1963)

"The usefulness of the models in constructing a testable theory of the process is severely limited by the quickly increasing number of parameters which must be estimated in order to compare the predictions of the models with empirical results" (Anatol Rapoport, "Prisoner's Dilemma: A study in conflict and cooperation", 1965)

"The validation of a model is not that it is 'true' but that it generates good testable hypotheses relevant to important problems." (Richard Levins, "The Strategy of Model Building in Population Biology", 1966)

"Models are to be used, but not to be believed." (Henri Theil, "Principles of Econometrics", 1971)

"A theory has only the alternative of being right or wrong. A model has a third possibility: it may be right, but irrelevant." (Manfred Eigen, 1973)

"A model is an abstract description of the real world. It is a simple representation of more complex forms, processes and functions of physical phenomena and ideas." (Moshe F Rubinstein & Iris R Firstenberg, "Patterns of Problem Solving", 1975)

"A model is an attempt to represent some segment of reality and explain, in a simplified manner, the way the segment operates." (E Frank Harrison, "The managerial decision-making process", 1975)

"The value of a model lies in its substitutability for the real system for achieving an intended purpose." (David I Cleland & William R King, "Systems analysis and project management" , 1975)

"For the theory-practice iteration to work, the scientist must be, as it were, mentally ambidextrous; fascinated equally on the one hand by possible meanings, theories, and tentative models to be induced from data and the practical reality of the real world, and on the other with the factual implications deducible from tentative theories, models and hypotheses." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)

"Mathematical models are more precise and less ambiguous than quantitative models and are therefore of greater value in obtaining specific answers to certain managerial questions." (Henry L Tosi & Stephen J Carrol, "Management", 1976)

"The aim of the model is of course not to reproduce reality in all its complexity. It is rather to capture in a vivid, often formal, way what is essential to understanding some aspect of its structure or behavior." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"Models, of course, are never true, but fortunately it is only necessary that they be useful. For this it is usually needful only that they not be grossly wrong. I think rather simple modifications of our present models will prove adequate to take account of most realities of the outside world. The difficulties of computation which would have been a barrier in the past need not deter us now." (George E P Box, "Some Problems of Statistics and Everyday Life", Journal of the American Statistical Association, Vol. 74 (365), 1979)

"The purpose of models is not to fit the data but to sharpen the questions." (Samuel Karlin, 1983)

"The connection between a model and a theory is that a model satisfies a theory; that is, a model obeys those laws of behavior that a corresponding theory explicity states or which may be derived from it. [...] Computers make possible an entirely new relationship between theories and models. [...] A theory written in the form of a computer program is [...] both a theory and, when placed on a computer and run, a model to which the theory applies." (Joseph Weizenbaum, "Computer Power and Human Reason", 1984)

“There are those who try to generalize, synthesize, and build models, and there are those who believe nothing and constantly call for more data. The tension between these two groups is a healthy one; science develops mainly because of the model builders, yet they need the second group to keep them honest.” (Andrew Miall, “Principles of Sedimentary Basin Analysis”, 1984)

"Competent scientists do not believe their own models or theories, but rather treat them as convenient fictions. [...] The issue to a scientist is not whether a model is true, but rather whether there is another whose predictive power is enough better to justify movement from today’s fiction to a new one." (Steve Vardeman, "Comment", Journal of the American Statistical Association 82, 1987)

"Models are often used to decide issues in situations marked by uncertainty. However statistical differences from data depend on assumptions about the process which generated these data. If the assumptions do not hold, the inferences may not be reliable either. This limitation is often ignored by applied workers who fail to identify crucial assumptions or subject them to any kind of empirical testing. In such circumstances, using statistical procedures may only compound the uncertainty." (David A Greedman & William C Navidi, "Regression Models for Adjusting the 1980 Census", Statistical Science Vol. 1 (1), 1986)

"The fact that [the model] is an approximation does not necessarily detract from its usefulness because models are approximations. All models are wrong, but some are useful." (George Box, 1987)

"A theory is a good theory if it satisfies two requirements: it must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations." (Stephen Hawking, "A Brief History of Time: From Big Bang To Black Holes", 1988) 

"[…] no good model ever accounted for all the facts, since some data was bound to be misleading if not plain wrong. A theory that did fit all the data would have been ‘carpentered’ to do this and would thus be open to suspicion." (Francis H C Crick, "What Mad Pursuit: A Personal View of Scientific Discovery", 1988)

"A model is generally more believable if it can predict what will happen, rather than 'explain' something that has already occurred. […] Model building is not so much the safe and cozy codification of what we are confident about as it is a means of orderly speculation." (James R Thompson, "Empirical Model Building", 1989)

"Model is used as a theory. It becomes theory when the purpose of building a model is to understand the mechanisms involved in the developmental process. Hence as theory, model does not carve up or change the world, but it explains how change takes place and in what way or manner. This leads to build change in the structures." (Laxmi K Patnaik, "Model Building in Political Science", The Indian Journal of Political Science Vol. 50 (2), 1989)

"When evaluating a model, at least two broad standards are relevant. One is whether the model is consistent with the data. The other is whether the model is consistent with the ‘real world’." (Kenneth A Bollen, "Structural Equations with Latent Variables", 1989)

"Statistical models are sometimes misunderstood in epidemiology. Statistical models for data are never true. The question whether a model is true is irrelevant. A more appropriate question is whether we obtain the correct scientific conclusion if we pretend that the process under study behaves according to a particular statistical model." (Scott Zeger, "Statistical reasoning in epidemiology", American Journal of Epidemiology, 1991)

"No one has ever shown that he or she had a free lunch. Here, of course, 'free lunch' means 'usefulness of a model that is locally easy to make inferences from'. (John Tukey, "Issues relevant to an honest account of data-based inference, partially in the light of Laurie Davies’ paper", 1993)

"Model building is the art of selecting those aspects of a process that are relevant to the question being asked. As with any art, this selection is guided by taste, elegance, and metaphor; it is a matter of induction, rather than deduction. High science depends on this art." (John H Holland, "Hidden Order: How Adaptation Builds Complexity", 1995)

"So we pour in data from the past to fuel the decision-making mechanisms created by our models, be they linear or nonlinear. But therein lies the logician's trap: past data from real life constitute a sequence of events rather than a set of independent observations, which is what the laws of probability demand. [...] It is in those outliers and imperfections that the wildness lurks." (Peter L Bernstein, "Against the Gods: The Remarkable Story of Risk", 1996)

"A good model makes the right strategic simplifications. In fact, a really good model is one that generates a lot of understanding from focusing on a very small number of causal arrows." (Robert M Solow, "How Did Economics Get That Way and What Way Did It Get?", Daedalus, Vol. 126, No. 1, 1997)

"A model is a deliberately simplified representation of a much more complicated situation. […] The idea is to focus on one or two causal or conditioning factors, exclude everything else, and hope to understand how just these aspects of reality work and interact." (Robert M Solow, "How Did Economics Get That Way and What Way Did It Get?", Daedalus, Vol. 126, No. 1, 1997)

"We do not learn much from looking at a model - we learn more from building the model and manipulating it. Just as one needs to use or observe the use of a hammer in order to really understand its function, similarly, models have to be used before they will give up their secrets. In this sense, they have the quality of a technology - the power of the model only becomes apparent in the context of its use." (Margaret Morrison & Mary S Morgan, "Models as mediating instruments", 1999)

"Building statistical models is just like this. You take a real situation with real data, messy as this is, and build a model that works to explain the behavior of real data." (Martha Stocking, New York Times, 2000)

"As I left consulting to go back to the university, these were the perceptions I had about working with data to find answers to problems: (a) Focus on finding a good solution–that’s what consultants get paid for. (b) Live with the data before you plunge into modelling. (c) Search for a model that gives a good solution, either algorithmic or data. (d) Predictive accuracy on test sets is the criterion for how good the model is. (e) Computers are an indispensable partner." (

Leo Breiman, "Statistical Modeling: The Two Cultures", Statistical Science Vol. 16(3), 2001)

"The goals in statistics are to use data to predict and to get information about the underlying data mechanism. Nowhere is it written on a stone tablet what kind of model should be used to solve problems involving data. To make my position clear, I am not against models per se. In some situations they are the most appropriate way to solve the problem. But the emphasis needs to be on the problem and on the data. Unfortunately, our field has a vested interest in models, come hell or high water." (Leo Breiman, "Statistical Modeling: The Two Cultures, Statistical Science" Vol. 16(3), 2001) 

"The point of a model is to get useful information about the relation between the response and predictor variables. Interpretability is a way of getting information. But a model does not have to be simple to provide reliable information about the relation between predictor and response variables; neither does it have to be a data model. The goal is not interpretability, but accurate information." (Leo Breiman, "Statistical Modeling: The Two Cultures, Statistical Science" Vol. 16(3), 2001)

"A good way to evaluate a model is to look at a visual representation of it. After all, what is easier to understand - a table full of mathematical relationships or a graphic displaying a decision tree with all of its splits and branches?" (Seth Paul et al. "Preparing and Mining Data with Microsoft SQL Server 2000 and Analysis", 2002)

"Models can be viewed and used at three levels. The first is a model that fits the data. A test of goodness-of-fit operates at this level. This level is the least useful but is frequently the one at which statisticians and researchers stop. For example, a test of a linear model is judged good when a quadratic term is not significant. A second level of usefulness is that the model predicts future observations. Such a model has been called a forecast model. This level is often required in screening studies or studies predicting outcomes such as growth rate. A third level is that a model reveals unexpected features of the situation being described, a structural model, [...] However, it does not explain the data." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"Ockham's Razor in statistical analysis is used implicitly when models are embedded in richer models -for example, when testing the adequacy of a linear model by incorporating a quadratic term. If the coefficient of the quadratic term is not significant, it is dropped and the linear model is assumed to summarize the data adequately." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"A smaller model with fewer covariates has two advantages: it might give better predictions than a big model and it is more parsimonious (simpler). Generally, as you add more variables to a regression, the bias of the predictions decreases and the variance increases. Too few covariates yields high bias; this called underfitting. Too many covariates yields high variance; this called overfitting. Good predictions result from achieving a good balance between bias and variance. […] finding a good model involves trading of fit and complexity." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"[…] studying methods for parametric models is useful for two reasons. First, there are some cases where background knowledge suggests that a parametric model provides a reasonable approximation. […] Second, the inferential concepts for parametric models provide background for understanding certain nonparametric methods." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"I have often thought that outliers contain more information than the model." (Arnold Goodman,  [Joint Statistical Meetings] 2005)

"Sometimes the most important fit statistic you can get is ‘convergence not met’ - it can tell you something is wrong with your model." (Oliver Schabenberger, "Applied Statistics in Agriculture Conference", 2006)

"Effective models require a real world that has enough structure so that some of the details can be ignored. This implies the existence of solid and stable building blocks that encapsulate key parts of the real system’s behavior. Such building blocks provide enough separation from details to allow modeling to proceed."(John H. Miller & Scott E. Page, "Complex Adaptive Systems: An Introduction to Computational Models of Social Life", 2007)

"In science we try to explain reality by using models (theories). This is necessary because reality itself is too complex. So we need to come up with a model for that aspect of reality we want to understand – usually with the help of mathematics. Of course, these models or theories can only be simplifications of that part of reality we are looking at. A model can never be a perfect description of reality, and there can never be a part of reality perfectly mirroring a model." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is also inevitable for any model or theory to have an uncertainty (a difference between model and reality). Such uncertainties apply both to the numerical parameters of the model and to the inadequacy of the model as well. Because it is much harder to get a grip on these types of uncertainties, they are disregarded, usually." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Outliers or flyers are those data points in a set that do not quite fit within the rest of the data, that agree with the model in use. The uncertainty of such an outlier is seemingly too small. The discrepancy between outliers and the model should be subject to thorough examination and should be given much thought. Isolated data points, i.e., data points that are at some distance from the bulk of the data are not outliers if their values are in agreement with the model in use." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"What should be the distribution of random effects in a mixed model? I think Gaussian is just fine, unless you are trying to write a journal paper." (Terry Therneau, "Speaking at useR", 2007)

"You might say that there’s no reason to bother with model checking since all models are false anyway. I do believe that all models are false, but for me the purpose of model checking is not to accept or reject a model, but to reveal aspects of the data that are not captured by the fitted model." (Andrew Gelman, "Some thoughts on the sociology of statistics", 2007)

"A model is a good model if it:1. Is elegant 2. Contains few arbitrary or adjustable elements 3. Agrees with and explains all existing observations 4. Makes detailed predictions about future observations that can disprove or falsify the model if they are not borne out." (Stephen Hawking & Leonard Mlodinow, "The Grand Design", 2010)

"In other words, the model is terrific in all ways other than the fact that it is totally useless. So why did we create it? In short, because we could: we have a data set, and a statistical package, and add the former to the latter, hit a few buttons and voila, we have another paper." (Andew J Vickers & Angel M Cronin, "Everything you always wanted to know about evaluating prediction models (but were too afraid to ask)", Urology 76(6), 2010)

"Darn right, graphs are not serious. Any untrained, unsophisticated, non-degree-holding civilian can display data. Relying on plots is like admitting you do not need a statistician. Show pictures of the numbers and let people make their own judgments? That can be no better than airing your statistical dirty laundry. People need guidance; they need to be shown what the data are supposed to say. Graphics cannot do that; models can." (William M Briggs, Comment, Journal of Computational and Graphical Statistics Vol. 20(1), 2011)

"Building exploratory scatterplots should precede the building of a model, if for no reason other than to check that the intuition gained from making the map makes sense. The relationships may be so obvious, or the confounders so unimportant, that the model is unnecessary. A lack of obvious relationships in pairwise scatterplots does not mean that a model of greater complexity would not be able to find signal, but if that’s what we’re up against, it is important to know it ahead of time. Similarly, building simple models before tackling more complex ones will save us time and energy." (Max Shron, "Thinking with Data: How to Turn Information into Insights", 2014)

"In general, when building statistical models, we must not forget that the aim is to understand something about the real world. Or predict, choose an action, make a decision, summarize evidence, and so on, but always about the real world, not an abstract mathematical world: our models are not the reality - a point well made by George Box in his oft-cited remark that "all models are wrong, but some are useful". (David Hand, "Wonderful examples, but let's not close our eyes", Statistical Science 29, 2014)

"Models that can be easily fit and interpreted (like a linear or logistic model), or models that have great predictive performance without much work (like random forests), serve as excellent places to start a predictive task. [...] It is important, though, to not get too deep into these exploratory steps and forget about the larger picture. Setting time limits (in hours or, at most, days) for these exploratory projects is a helpful way to avoid wasting time. To avoid losing the big picture, it also helps to write down the intended steps at the beginning. An explicitly written-down scaffolding plan can be a huge help to avoid getting sucked deeply into work that is ultimately of little value. A scaffolding plan lays out what our next few goals are, and what we expect to shift once we achieve them." (Max Shron, "Thinking with Data: How to Turn Information into Insights", 2014)

"Things which ought to be expected can seem quite extraordinary if you’ve got the wrong model." (David Hand, "Significance", 2014)

"It is important to remember that predictive data analytics models built using machine learning techniques are tools that we can use to help make better decisions within an organization and are not an end in themselves. It is paramount that, when tasked with creating a predictive model, we fully understand the business problem that this model is being constructed to address and ensure that it does address it." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015)

"The crucial concept that brings all of this together is one that is perhaps as rich and suggestive as that of a paradigm: the concept of a model. Some models are concrete, others are abstract. Certain models are fairly rigid; others are left somewhat unspecified. Some models are fully integrated into larger theories; others, or so the story goes, have a life of their own. Models of experiment, models of data, models in simulations, archeological modeling, diagrammatic reasoning, abductive inferences; it is difficult to imagine an area of scientific investigation, or established strategies of research, in which models are not present in some form or another. However, models are ultimately understood, there is no doubt that they play key roles in multiple areas of the sciences, engineering, and mathematics, just as models are central to our understanding of the practices of these fields, their history and the plethora of philosophical, conceptual, logical, and cognitive issues they raise." (Otávio Bueno, [in" Springer Handbook of Model-Based Science", Ed. by Lorenzo Magnani & Tommaso Bertolotti, 2017])

"The different classes of models have a lot to learn from each other, but the goal of full integration has proven counterproductive. No model can be all things to all people." (Olivier Blanchard, "On the future of macroeconomic models", Oxford Review of Economic Policy Vol. 34 (1–2), 2018)

"Bad data makes bad models. Bad models instruct people to make ineffective or harmful interventions. Those bad interventions produce more bad data, which is fed into more bad models." (Cory Doctorow, "Machine Learning’s Crumbling Foundations", 2021)

"On a final note, we would like to stress the importance of design, which often does not receive the attention it deserves. Sometimes, the large number of modeling options for spatial analysis may raise the false impression that design does not matter, and that a sophisticated analysis takes care of everything. Nothing could be further from the truth." (Hans-Peter Piepho et al, "Two-dimensional P-spline smoothing for spatial analysis of plant breeding trials", “Biometrical Journal”, 2022)

♟️Strategic Management: The Bad (Just the Quotes)

"To say a system is 'self-organizing' leaves open two quite different meanings. There is a first meaning that is simple and unobjectionable. This refers to the system that starts with its parts separate" (so that the behavior of each is independent of the others' states) and whose parts then act so that they change towards forming connections of some type. Such a system is 'self-organizing' in the sense that it changes from 'parts separated' to 'parts joined'. […] In general such systems can be more simply characterized as 'self-connecting', for the change from independence between the parts to conditionality can always be seen as some form of 'connection', even if it is as purely functional […]  'Organizing' […] may also mean 'changing from a bad organization to a good one' […] The system would be 'self-organizing' if a change were automatically made to the feedback, changing it from positive to negative; then the whole would have changed from a bad organization to a good." (W Ross Ashby, "Principles of the self-organizing system", 1962)

"The definition of a problem and the action taken to solve it largely depend on the view which the individuals or groups that discovered the problem have of the system to which it refers. A problem may thus find itself defined as a badly interpreted output, or as a faulty output of a faulty output device, or as a faulty output due to a malfunction in an otherwise faultless system, or as a correct but undesired output from a faultless and thus undesirable system. All definitions but the last suggest corrective action; only the last definition suggests change, and so presents an unsolvable problem to anyone opposed to change." (Herbert Brün, "Technology and the Composer", 1971)

"The dogma of delegation is simple - the Sixth Truth of Management again: either the delegatee is capable of running the operation successfully by himself or he isn't. This handy formula relieves the top executive of any responsibility except that of finding, supervising, and" (at the appropriate time) moving the men who are doing all the work. He Can then truly manage by exception: he does not get worked up over operations that are going well, but concentrates on the plague spots, where everything, including the management, is going badly." (Robert Heller, "The Naked Manager: Games Executives Play", 1972)

"Managers sometimes justify the stick by pointing to better results, with the assumption that the threats caused the improvements. Alas, this is unlikely. One event coming before another does not automatically mean that the first is the cause of the second; the rooster does not make the sun rise every morning, although it may think it does. Bad results are much more likely to improve than get worse due to the simple law of statistics known as regression: results average out over time. Poor performance will eventually improve even when left to itself." (Joseph O’Connor, "Leading With NLP: Essential Leadership Skills for Influencing and Managing People", 1998)

"Managers are incurably susceptible to panacea peddlers. They are rooted in the belief that there are simple, if not simple-minded, solutions to even the most complex of problems. And they do not learn from bad experiences. Managers fail to diagnose the failures of the fads they adopt; they do not understand them. […] Those at the top feel obliged to pretend to omniscience, and therefore refuse to learn anything new even if the cost of doing so is success." (Russell L Ackoff, "A Lifetime Of Systems Thinking", Systems Thinker, 1999)

"It’s tempting to view the multitude of monster projects gone bad as anomalies, excrescences of corporate and government bureaucracies run amok. But you will find similar tales of woe emerging from software projects big and small, public and private, old and new. Though details differ, the pattern is depressingly repetitive: Moving targets. Fluctuating goals. Unrealistic schedules. Missed deadlines. Ballooning costs. Despair. Chaos." (Scott Rosenberg, "Dreaming in Code", 2007)

"A bad strategy will fail no matter how good your information is and lame execution will stymie a good strategy. If you do enough things poorly, you will go out of business." (Bill Gates, "Business @ the Speed of Thought: Succeeding in the Digital Economy", 2009)

"A leader’s most important job is creating and constantly adjusting this strategic bridge between goals and objectives." (Richard Rumelt, "Good Strategy Bad Strategy", 2011)

"A strategy coordinates action to address a specific challenge. It is not defined by the pay grade of the person authorizing the action." (Richard Rumelt, "Good Strategy/Bad Strategy", 2011)

"Having conflicting goals, dedicating resources to unconnected targets, and accommodating incompatible interests are the luxuries of the rich and powerful, but they make for bad strategy. Despite this, most organizations will not create focused strategies. Instead, they will generate laundry lists of desirable outcomes and, at the same time, ignore the need for genuine competence in coordinating and focusing their resources. Good strategy requires leaders who are willing and able to say no to a wide variety of actions and interests. Strategy is at least as much about what an organization does not do as it is about what it does." (Richard Rumelt, "Good Strategy/Bad Strategy", 2011)

"Our minds, especially our intuitions, are not equipped to deal with a probabilistic world. Risk and prediction are widely misunderstood, […] All decision making in a probabilistic world involves estimating the likelihood of an event and how much we will value it" (affective forecasting). Humans are bad at both - ​​​​​ particularly at the former. […] In business, understanding the psychology of risk is more important than understanding the mathematics of risk." (Paul Gibbons, "The Science of Successful Organizational Change",  2015)

"The bad news is that companies tend to focus on three out of the four elements of the balanced scorecard and emphasis is skewed away from the customer component, which is the least understood and believed by many to be the least quantifiable." (Alan Pennington, "The Customer Experience Book", 2016)

🔭Data Science: Machine Learning (Just the Quotes)

"[…] an obvious difference between our best classifiers and human learning is the number of examples required in tasks such as object detection. […] the difficulty of a learning task depends on the size of the required hypothesis space. This complexity determines in turn how many training examples are needed to achieve a given level of generalization error. Thus the complexity of the hypothesis space sets the speed limit and the sample complexity for learning." (Tomaso Poggio & Steve Smale, "The Mathematics of Learning: Dealing with Data", Notices of the AMS, 2003)

"[…] learning techniques are similar to fitting a multivariate function to a certain number of measurement data. The key point, as we just mentioned, is that the fitting should be predictive in the same way that fitting experimental data from an experiment in physics can in principle uncover the underlying physical law, which is then used in a predictive way. In this sense, learning is also a principled method for distilling predictive and therefore scientific 'theories' from the data." (Tomaso Poggio & Steve Smale, "The Mathematics of Learning: Dealing with Data", Notices of the AMS, 2003)

"Much of machine learning is concerned with devising different models, and different algorithms to fit them. We can use methods such as cross validation to empirically choose the best method for our particular problem. However, there is no universally best model - this is sometimes called the no free lunch theorem. The reason for this is that a set of assumptions that works well in one domain may work poorly in another." (Kevin P Murphy, "Machine Learning: A Probabilistic Perspective", 2012)

"We have let ourselves become enchanted by big data only because we exoticize technology. We’re impressed with small feats accomplished by computers alone, but we ignore big achievements from complementarity because the human contribution makes them less uncanny. Watson, Deep Blue, and ever-better machine learning algorithms are cool. But the most valuable companies in the future won’t ask what problems can be solved with computers alone. Instead, they’ll ask: how can computers help humans solve hard problems?" (Peter Thiel & Blake Masters, "Zero to One: Notes on Startups, or How to Build the Future", 2014)

"A good proxy for complexity in a machine learning model is how fast it takes to train it." (Matthew Kirk, "Thoughtful Machine Learning", 2015)

"In machine learning, knowledge is often in the form of statistical models, because most knowledge is statistical [...] Machine learning is a kind of knowledge pump: we can use it to extract a lot of knowledge from data, but first we have to prime the pump." (Pedro Domingos, "The Master Algorithm", 2015)

"It is important to remember that predictive data analytics models built using machine learning techniques are tools that we can use to help make better decisions within an organization and are not an end in themselves. It is paramount that, when tasked with creating a predictive model, we fully understand the business problem that this model is being constructed to address and ensure that it does address it." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015)

"Learning theory claims that a machine learning algorithm can generalize well from a finite training set of examples. This seems to contradict some basic principles of logic. Inductive reasoning, or inferring general rules from a limited set of examples, is not logically valid. To logically infer a rule describing every member of a set, one must have information about every member of that set." (Ian Goodfellow et al, "Deep Learning", 2015)

"Machine learning is a science and requires an objective approach to problems. Just like the scientific method, test-driven development can aid in solving a problem. The reason that TDD and the scientific method are so similar is because of these three shared characteristics: Both propose that the solution is logical and valid. Both share results through documentation and work over time. Both work in feedback loops." (Matthew Kirk, "Thoughtful Machine Learning", 2015)

"Machine learning is the intersection between theoretically sound computer science and practically noisy data. Essentially, it’s about machines making sense out of data in much the same way that humans do." (Matthew Kirk, "Thoughtful Machine Learning", 2015)

"Machine learning is well suited for the unpredictable future, because most algorithms learn from new information. But as new information is found, it can also come in unstable forms, and new issues can arise that weren’t thought of before. We don’t know what we don’t know. When processing new information, it’s sometimes hard to tell whether our model is working." (Matthew Kirk, "Thoughtful Machine Learning", 2015)

"Machine learning takes many different forms and goes by many different names: pattern recognition, statistical modeling, data mining, knowledge discovery, predictive analytics, data science, adaptive systems, self-organizing systems, and more. Each of these is used by different communities and has different associations. Some have a long half-life, some less so." (Pedro Domingos, "The Master Algorithm", 2015)

"Precision and recall are ways of monitoring the power of the machine learning implementation. Precision is a metric that monitors the percentage of true positives. […] Recall is the ratio of true positives to true positive plus false negatives." (Matthew Kirk, "Thoughtful Machine Learning", 2015)

"Science’s predictions are more trustworthy, but they are limited to what we can systematically observe and tractably model. Big data and machine learning greatly expand that scope. Some everyday things can be predicted by the unaided mind, from catching a ball to carrying on a conversation. Some things, try as we might, are just unpredictable. For the vast middle ground between the two, there’s machine learning." (Pedro Domingos, "The Master Algorithm", 2015)

"The no free lunch theorem for machine learning states that, averaged over all possible data generating distributions, every classification algorithm has the same error rate when classifying previously unobserved points. In other words, in some sense, no machine learning algorithm is universally any better than any other. The most sophisticated algorithm we can conceive of has the same average performance (over all possible tasks) as merely predicting that every point belongs to the same class. [...] the goal of machine learning research is not to seek a universal learning algorithm or the absolute best learning algorithm. Instead, our goal is to understand what kinds of distributions are relevant to the 'real world' that an AI agent experiences, and what kinds of machine learning algorithms perform well on data drawn from the kinds of data generating distributions we care about." (Ian Goodfellow et al, "Deep Learning", 2015)

"The no free lunch theorem implies that we must design our machine learning algorithms to perform well on a specific task. We do so by building a set of preferences into the learning algorithm. When these preferences are aligned with the learning problems we ask the algorithm to solve, it performs better." (Ian Goodfellow et al, "Deep Learning", 2015)

"To make progress, every field of science needs to have data commensurate with the complexity of the phenomena it studies. [...] With big data and machine learning, you can understand much more complex phenomena than before. In most fields, scientists have traditionally used only very limited kinds of models, like linear regression, where the curve you fit to the data is always a straight line. Unfortunately, most phenomena in the world are nonlinear. [...] Machine learning opens up a vast new world of nonlinear models." (Pedro Domingos, "The Master Algorithm", 2015)

"Traditionally, the only way to get a computer to do something - from adding two numbers to flying an airplane - was to write down an algorithm explaining how, in painstaking detail. But machine-learning algorithms, also known as learners, are different: they figure it out on their own, by making inferences from data. And the more data they have, the better they get. Now we don’t have to program computers; they program themselves." (Pedro Domingos, "The Master Algorithm", 2015)

"In machine learning, a model is defined as a function, and we describe the learning function from the training data as inductive learning. Generalization refers to how well the concepts are learned by the model by applying them to data not seen before. The goal of a good machine-learning model is to reduce generalization errors and thus make good predictions on data that the model has never seen." (Umesh R Hodeghatta & Umesha Nayak, "Business Analytics Using R: A Practical Approach", 2017)

"Machine learning is about making computers learn and perform tasks better based on past historical data. Learning is always based on observations from the data available. The emphasis is on making computers build mathematical models based on that learning and perform tasks automatically without the intervention of humans." (Umesh R Hodeghatta & Umesha Nayak, "Business Analytics Using R: A Practical Approach", 2017)

"Graphs can embed complex semantic representations in a compact form. As such, modeling data as networks of related entities is a powerful mechanism for analytics, both for visual analyses and machine learning. Part of this power comes from performance advantages of using a graph data structure, and the other part comes from an inherent human ability to intuitively interact with small networks." (Benjamin Bengfort et al, "Applied Text Analysis with Python: Enabling Language-Aware Data Products with Machine Learning", 2018)

"However, because ML algorithms are biased to look for different types of patterns, and because there is no one learning bias across all situations, there is no one best ML algorithm. In fact, a theorem known as the 'no free lunch theorem' states that there is no one best ML algorithm that on average outperforms all other algorithms across all possible data sets." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"Just as they did thirty years ago, machine learning programs (including those with deep neural networks) operate almost entirely in an associational mode. They are driven by a stream of observations to which they attempt to fit a function, in much the same way that a statistician tries to fit a line to a collection of points. Deep neural networks have added many more layers to the complexity of the fitted function, but raw data still drives the fitting process. They continue to improve in accuracy as more data are fitted, but they do not benefit from the 'super-evolutionary speedup'."  (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Machine learning is often associated with the automation of decision making, but in practice, the process of constructing a predictive model generally requires a human in the loop. While computers are good at fast, accurate numerical computation, humans are instinctively and instantly able to identify patterns. The bridge between these two necessary skill sets lies in visualization - the precise and accurate rendering of data by a computer in visual terms and the immediate assignation of meaning to that data by humans." (Benjamin Bengfort et al, "Applied Text Analysis with Python: Enabling Language-Aware Data Products with Machine Learning", 2018)

"Quantum Machine Learning is defined as the branch of science and technology that is concerned with the application of quantum mechanical phenomena such as superposition, entanglement and tunneling for designing software and hardware to provide machines the ability to learn insights and patterns from data and the environment, and the ability to adapt automatically to changing situations with high precision, accuracy and speed." (Amit Ray, "Quantum Computing Algorithms for Artificial Intelligence", 2018)

"Quantum machine learning promises to discover the optimal network topologies and hyperparameters automatically without human intervention." (Amit Ray, "Quantum Computing Algorithms for Artificial Intelligence", 2018)

"The beauty of quantum machine learning is that we do not need to depend on an algorithm like gradient descent or convex objective function. The objective function can be nonconvex or something else." (Amit Ray, "Quantum Computing Algorithms for Artificial Intelligence", 2018)

"The premise of classification is simple: given a categorical target variable, learn patterns that exist between instances composed of independent variables and their relationship to the target. Because the target is given ahead of time, classification is said to be supervised machine learning because a model can be trained to minimize error between predicted and actual categories in the training data. Once a classification model is fit, it assigns categorical labels to new instances based on the patterns detected during training." (Benjamin Bengfort et al, "Applied Text Analysis with Python: Enabling Language-Aware Data Products with Machine Learning", 2018)

"A recurring theme in machine learning is combining predictions across multiple models. There are techniques called bagging and boosting which seek to tweak the data and fit many estimates to it. Averaging across these can give a better prediction than any one model on its own. But here a serious problem arises: it is then very hard to explain what the model is (often referred to as a 'black box'). It is now a mixture of many, perhaps a thousand or more, models." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Machines are not good at asking questions or even knowing what questions to ask. They are much better at answering them, provided the question is stated in a way that the computer can comprehend. Present-day machine learning algorithms partner with people much like a bloodhound works with its trainer: the dog's sense of smell may be many times stronger than its master's, but without being carefully directed, the hound may end up chasing its tail." (Brett Lantz, "Machine Learning with R", 2019)

"In an era of machine learning, where data is likely to be used to train AI, getting quality and governance under control is a business imperative. Failing to govern data surfaces problems late, often at the point closest to users (for example, by giving harmful guidance), and hinders explainability (garbage data in, machine-learned garbage out)." (Jesús Barrasa et al, "Knowledge Graphs: Data in Context for Responsive Businesses", 2021)

"Machine learning bias is typically understood as a source of learning error, a technical problem. […] Machine learning bias can introduce error simply because the system doesn’t 'look' for certain solutions in the first place. But bias is actually necessary in machine learning - it’s part of learning itself." (Erik J Larson, "The Myth of Artificial Intelligence: Why Computers Can’t Think the Way We Do", 2021)

"People who assume that extensions of modern machine learning methods like deep learning will somehow 'train up', or learn to be intelligent like humans, do not understand the fundamental limitations that are already known. Admitting the necessity of supplying a bias to learning systems is tantamount to Turing’s observing that insights about mathematics must be supplied by human minds from outside formal methods, since machine learning bias is determined, prior to learning, by human designers." (Erik J Larson, "The Myth of Artificial Intelligence: Why Computers Can’t Think the Way We Do", 2021)

"To accomplish their goals, what are now called machine learning systems must each learn something specific. Researchers call this giving the machine a 'bias'. […] A bias in machine learning means that the system is designed and tuned to learn something. But this is, of course, just the problem of producing narrow problem-solving applications." (Erik J Larson, "The Myth of Artificial Intelligence: Why Computers Can’t Think the Way We Do", 2021)

"[...] the focus on Big Data AI seems to be an excuse to put forth a number of vague and hand-waving theories, where the actual details and the ultimate success of neuroscience is handed over to quasi- mythological claims about the powers of large datasets and inductive computation. Where humans fail to illuminate a complicated domain with testable theory, machine learning and big data supposedly can step in and render traditional concerns about finding robust theories. This seems to be the logic of Data Brain efforts today. (Erik J Larson, "The Myth of Artificial Intelligence: Why Computers Can’t Think the Way We Do", 2021)

🔭Data Science: Significance (Just the Quotes)

"It is convenient to take this point as a limit in judging whether a deviation is to be considered significant or not. Deviations exceeding twice the standard deviation are thus formally regarded as significant." (Ronald A Fisher, "Statistical Methods for Research Workers", 1925)

"If one in twenty does not seem high enough odds, we may, if we prefer it, draw the line at one in fifty (the 2 per cent point), or one in a hundred (the 1 per centp oint). Personally, the writer prefers to set a low standard of significance at the 5 per cent point, and ignore entirely all results which fail to reach this level. A scientific fact should be regarded as experimentally established only if a properly designed experiment rarely fails to give this level of significance," (Ronald A Fisher, 1926)

"An observation is judged significant, if it would rarely have been produced, in the absence of a real cause of the kind we are seeking. It is a common practice to judge a result significant, if it is of such a magnitude that it would have been produced by chance not more frequently than once in twenty trials. This is an arbitrary, but convenient, level of significance for the practical investigator, but it does not mean that he allows himself to be deceived once in every twenty experiments. The test of significance only tells him what to ignore, namely all experiments in which significant results are not obtained. He should only claim that a phenomenon is experimentally demonstrable when he knows how to design an experiment so that it will rarely fail to give a significant result. Consequently, isolated significant results which he does not know how to reproduce are left in suspense pending further investigation." (Ronald A Fisher, "The Statistical Method in Psychical Research", Proceedings of the Society for Psychical Research 39, 1929)

"What the use of P [the significance level] implies, therefore, is that a hypothesis that may be true may be rejected because it has not predicted observable results that have not occurred." (Harold Jeffreys, "Theory of Probability", 1939)

"As usual we may make the errors of I) rejecting the null hypothesis when it is true, II) accepting the null hypothesis when it is false. But there is a third kind of error which is of interest because the present test of significance is tied up closely with the idea of making a correct decision about which distribution function has slipped furthest to the right. We may make the error of III) correctly rejecting the null hypothesis for the wrong reason." (Frederick Mosteller, "A k-Sample Slippage Test for an Extreme Population", The Annals of Mathematical Statistics 19, 1948)

"Errors of the third kind happen in conventional tests of differences of means, but they are usually not considered, although their existence is probably recognized. It seems to the author that there may be several reasons for this among which are 1) a preoccupation on the part of mathematical statisticians with the formal questions of acceptance and rejection of null hypotheses without adequate consideration of the implications of the error of the third kind for the practical experimenter, 2) the rarity with which an error of the third kind arises in the usual tests of significance." (Frederick Mosteller, "A k-Sample Slippage Test for an Extreme Population", The Annals of Mathematical Statistics 19, 1948)

"If significance tests are required for still larger samples, graphical accuracy is insufficient, and arithmetical methods are advised. A word to the wise is in order here, however. Almost never does it make sense to use exact binomial significance tests on such data - for the inevitable small deviations from the mathematical model of independence and constant split have piled up to such an extent that the binomial variability is deeply buried and unnoticeable. Graphical treatment of such large samples may still be worthwhile because it brings the results more vividly to the eye." (Frederick Mosteller & John W Tukey, "The Uses and Usefulness of Binomial Probability Paper?", Journal of the American Statistical Association 44, 1949)

"In the examples we have given [...] our judgment whether P was small enough to justify us in suspecting a significant difference [...] has been more or less intuitive. Most people would agree [...] that a probability of .0001 is so small that the evidence is very much in favour. . . . Suppose we had obtained P = 0.1. [...] Where, if anywhere, can we draw the line? The odds against the observed event which influence a decision one way or the other depend to some extent on the caution of the investigator. Some people (not necessarily statisticians) would regard odds of ten to one as sufficient. Others would be more conservative and reserve judgment until the odds were much greater. It is a matter of personal taste." (G U Yule & M G Kendall, "An introduction to the theoryof statistics" 14th ed., 1950)

"It will, of course, happen but rarely that the proportions will be identical, even if no real association exists. Evidently, therefore, we need a significance test to reassure ourselves that the observed difference of proportion is greater than could reasonably be attributed to chance. The significance test will test the reality of the association, without telling us anything about the intensity of association. It will be apparent that we need two distinct things: (a) a test of significance, to be used on the data first of all, and (b) some measure of the intensity of the association, which we shall only be justified in using if the significance test confirms that the association is real." (Michael J Moroney, "Facts from Figures", 1951)

"The main purpose of a significance test is to inhibit the natural enthusiasm of the investigator." (Frederick Mosteller, "Selected Quantitative Techniques", 1954)

"Null hypotheses of no difference are usually known to be false before the data are collected [...] when they are, their rejection or acceptance simply reflects the size of the sample and the power of the test, and is not a contribution to science." (I Richard Savage, "Nonparametric Statistics", Journal of the American Statistical Association 52, 1957)

"[...] to make measurements and then ignore their magnitude would ordinarily be pointless. Exclusive reliance on tests of significance obscures the fact that statistical significance does not imply substantive significance." (I Richard Savage, "Nonparametric Statistics", Journal of the American Statistical Association 52, 1957)

"[...] the tests of null hypotheses of zero differences, of no relationships, are frequently weak, perhaps trivial statements of the researcher’s aims [...] in many cases, instead of the tests of significance it would be more to the point to measure the magnitudes of the relationships, attaching proper statements of their sampling variation. The magnitudes of relationships cannot be measured in terms of levels of significance." (Leslie Kish, "Some statistical problems in research design", American Sociological Review 24, 1959)

"There are instances of research results presented in terms of probability values of ‘statistical significance’ alone, without noting the magnitude and importance of the relationships found. These attempts to use the probability levels of significance tests as measures of the strengths of relationships are very common and very mistaken." (Leslie Kish, "Some statistical problems in research design", American Sociological Review 24, 1959)

"The null-hypothesis significance test treats ‘acceptance’ or ‘rejection’ of a hypothesis as though these were decisions one makes. But a hypothesis is not something, like a piece of pie offered for dessert, which can be accepted or rejected by a voluntary physical action. Acceptance or rejection of a hypothesis is a cognitive process, a degree of believing or disbelieving which, if rational, is not a matter of choice but determined solely by how likely it is, given the evidence, that the hypothesis is true." (William W Rozeboom, "The fallacy of the null–hypothesis significance test", Psychological Bulletin 57, 1960)

"The null hypothesis of no difference has been judged to be no longer a sound or fruitful basis for statistical investigation. […] Significance tests do not provide the information that scientists need, and, furthermore, they are not the most effective method for analyzing and summarizing data." (Cherry A Clark, "Hypothesis Testing in Relation to Statistical Methodology", Review of Educational Research Vol. 33, 1963)

"[...] the test of significance has been carrying too much of the burden of scientific inference. It may well be the case that wise and ingenious investigators can find their way to reasonable conclusions from data because and in spite of their procedures. Too often, however, even wise and ingenious investigators [...] tend to credit the test of significance with properties it does not have." (David Bakan, "The test of significance in psychological research", Psychological Bulletin 66, 1966)

"[...] we need to get on with the business of generating [...] hypotheses and proceed to do investigations and make inferences which bear on them, instead of [...] testing the statistical null hypothesis in any number of contexts in which we have every reason to suppose that it is false in the first place." (David Bakan, "The test of significance in psychological research", Psychological Bulletin 66, 1966)

"Overemphasis on tests of significance at the expense especially of interval estimation has long been condemned." (David R Cox, "The role of significance tests", Scandanavian Journal of Statistics 4, 1977) 

"The central point is that statistical significance is quite different from scientific significance and that therefore estimation [...] of the magnitude of effects is in general essential regardless of whether statistically significant departure from the null hypothesis is achieved." (David R Cox, "The role of significance tests", Scandanavian Journal of Statistics 4, 1977) 

"Science usually amounts to a lot more than blind trial and error. Good statistics consists of much more than just significance tests; there are more sophisticated tools available for the analysis of results, such as confidence statements, multiple comparisons, and Bayesian analysis, to drop a few names. However, not all scientists are good statisticians, or want to be, and not all people who are called scientists by the media deserve to be so described." (Robert Hooke, "How to Tell the Liars from the Statisticians", 1983)

"The idea of statistical significance is valuable because it often keeps us from announcing results that later turn out to be nonresults. A significant result tells us that enough cases were observed to provide reasonable assurance of a real effect. It does not necessarily mean, though, that the effect is big enough to be important." (Robert Hooke, "How to Tell the Liars from the Statisticians", 1983)

"It is very bad practice to summarise an important investigation solely by a value of P." (David R Cox, "Statistical significance tests", British Journal of Clinical Pharmacology 14, 1982) 

"The criterion for publication should be the achievement of reasonable precision and not whether a significant effect has been found." (David R Cox, "Statistical significance tests", British Journal of Clinical Pharmacology 14, 1982) 

"The continued very extensive use of significance tests is alarming." (David R Cox, "Some general aspects of the theory of statistics", International Statistical Review 54, 1986) 

"It has been widely felt, probably for thirty years and more, that significance tests are overemphasized and often misused and that more emphasis should be put on estimation and prediction. While such a shift of emphasis does seem to be occurring, for example in medical statistics, the continued very extensive use of significance tests is on the one hand alarming and on the other evidence that they are aimed, even if imperfectly, at some widely felt need." (David R Cox, "Some general aspects of the theory of statistics", International Statistical Review 54, 1986) 

"A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence." (John A Paulos, "Innumeracy: Mathematical Illiteracy and its Consequences", 1988)

"Which I would like to stress are: (1) A significant effect is not necessarily the same thing as an interesting effect. (2) A non-significant effect is not necessarily the same thing as no difference." (Christopher Chatfield, "Problem solving: a statistician’s guide", 1988)

"A little thought reveals a fact widely understood among statisticians: The null hypothesis, taken literally (and that’s the only way you can take it in formal hypothesis testing), is always false in the real world. [...] If it is false, even to a tiny degree, it must be the case that a large enough sample will produce a significant result and lead to its rejection. So if the null hypothesis is always false, what’s the big deal about rejecting it?" (Jacob Cohen,"Things I Have Learned (So Far)", American Psychologist, 1990)

"I do not think that significance testing should be completely abandoned [...] and I don’t expect that it will be. But I urge researchers to provide estimates, with confidence intervals: scientific advance requires parameters with known reliability estimates. Classical confidence intervals are formally equivalent to a significance test, but they convey more information." (Nigel G Yoccoz, "Use, Overuse, and Misuse of Significance Tests in Evolutionary Biology and Ecology", Bulletin of the Ecological Society of America Vol. 72 (2), 1991)

"Rejection of a true null hypothesis at the 0.05 level will occur only one in 20 times. The overwhelming majority of these false rejections will be based on test statistics close to the borderline value. If the null hypothesis is false, the inter-ocular traumatic test ['hit between the eyes'] will often suffice to reject it; calculation will serve only to verify clear intuition." (Ward Edwards et al, "Bayesian Statistical Inference for Psychological Research", 1992) 

"Statistical significance testing can involve a tautological logic in which tired researchers, having collected data on hundreds of subjects, then conduct a statistical test to evaluate whether there were a lot of subjects, which the researchers already know, because they collected the data and know they are tired. This tautology has created considerable damage as regards the cumulation of knowledge." (Bruce Thompson, "Two and One-Half Decades of Leadership in Measurement and Evaluation", Journal of Counseling & Development 70 (3), 1992)

"[…] an honest exploratory study should indicate how many comparisons were made […] most experts agree that large numbers of comparisons will produce apparently statistically significant findings that are actually due to chance. The data torturer will act as if every positive result confirmed a major hypothesis. The honest investigator will limit the study to focused questions, all of which make biologic sense. The cautious reader should look at the number of ‘significant’ results in the context of how many comparisons were made." (James L Mills, "Data torturing", New England Journal of Medicine, 1993)

"Graphic misrepresentation is a frequent misuse in presentations to the nonprofessional. The granddaddy of all graphical offenses is to omit the zero on the vertical axis. As a consequence, the chart is often interpreted as if its bottom axis were zero, even though it may be far removed. This can lead to attention-getting headlines about 'a soar' or 'a dramatic rise (or fall)'. A modest, and possibly insignificant, change is amplified into a disastrous or inspirational trend." (Herbert F Spirer et al, "Misused Statistics" 2nd Ed, 1998)

"When significance tests are used and a null hypothesis is not rejected, a major problem often arises - namely, the result may be interpreted, without a logical basis, as providing evidence for the null hypothesis." (David F Parkhurst, "Statistical Significance Tests: Equivalence and Reverse Tests Should Reduce Misinterpretation", BioScience Vol. 51 (12), 2001)

"If you flip a coin three times and it lands on heads each time, it's probably chance. If you flip it a hundred times and it lands on heads each time, you can be pretty sure the coin has heads on both sides. That's the concept behind statistical significance - it's the odds that the correlation (or other finding) is real, that it isn't just random chance." (T Colin Campbell, "The China Study", 2004)

"Many statistics texts do not mention this and students often ask, ‘What if you get a probability of exactly 0.05?’ Here the result would be considered not significant, since significance has been defined as a probability of less than 0.05 (<0.05). Some texts define a significant result as one where the probability is less than or equal to 0.05 ( 0.05). In practice this will make very little difference, but since Fisher proposed the ‘less than 0.05’ definition, which is also used by most scientific publications, it will be used here." (Steve McKillup, "Statistics Explained: An Introductory Guide for Life Scientists", 2005)

"The dual meaning of the word significant brings into focus the distinction between drawing a mathematical inference and practical inference from statistical results." (Charles Livingston & Paul Voakes, "Working with Numbers and Statistics: A handbook for journalists", 2005)

"A common statistical error is to summarize comparisons by statistical significance and then draw a sharp distinction between significant and nonsignificant results. The approach of summarizing by statistical significance has a number of pitfalls, most of which are covered in standard statistics courses but one that we believe is less well known. We refer to the fact that changes in statistical significance are not themselves significant. A small change in a group mean, a regression coefficient, or any other statistical quantity can be neither statistically significant nor practically important, but such a change can lead to a large change in the significance level of that quantity relative to a null hypothesis." (Andrew Gelman & Hal Stern, "The Difference between 'Significant' and 'Not Significant' Is Not Itself Statistically Significant", The American Statistician Vol. 60 (4), 2006

"A type of error used in hypothesis testing that arises when incorrectly rejecting the null hypothesis, although it is actually true. Thus, based on the test statistic, the final conclusion rejects the Null hypothesis, but in truth it should be accepted. Type I error equates to the alpha (α) or significance level, whereby the generally accepted default is 5%." (Lynne Hambleton, "Treasure Chest of Six Sigma Growth Methods, Tools, and Best Practices", 2007)

"For the study of the topology of the interactions of a complex system it is of central importance to have proper random null models of networks, i.e., models of how a graph arises from a random process. Such models are needed for comparison with real world data. When analyzing the structure of real world networks, the null hypothesis shall always be that the link structure is due to chance alone. This null hypothesis may only be rejected if the link structure found differs significantly from an expectation value obtained from a random model. Any deviation from the random null model must be explained by non-random processes." (Jörg Reichardt, "Structure in Complex Networks", 2009)

"There are three possible reasons for [the] absence of predictive power. First, it is possible that the models are misspecified. Second, it is possible that the model’s explanatory factors are measured at too high a level of aggregation [...] Third, [...] the search for statistically significant relationships may not be the strategy best suited for evaluating our model’s ability to explain real world events [...] the lack of predictive power is the result of too much emphasis having been placed on finding statistically significant variables, which may be overdetermined. Statistical significance is generally a flawed way to prune variables in regression models [...] Statistically significant variables may actually degrade the predictive accuracy of a model [...] [By using] models that are constructed on the basis of pruning undertaken with the shears of statistical significance, it is quite possible that we are winnowing our models away from predictive accuracy." (Michael D Ward et al, "The perils of policy by p-value: predicting civil conflicts" Journal of Peace Research 47, 2010)

"If the group is large enough, even very small differences can become statistically significant." (Victor Cohn & Lewis Cope, "News & Numbers: A writer’s guide to statistics" 3rd Ed, 2012)

"Another way to secure statistical significance is to use the data to discover a theory. Statistical tests assume that the researcher starts with a theory, collects data to test the theory, and reports the results - whether statistically significant or not. Many people work in the other direction, scrutinizing the data until they find a pattern and then making up a theory that fits the pattern." (Gary Smith, "Standard Deviations", 2014)

"These practices - selective reporting and data pillaging - are known as data grubbing. The discovery of statistical significance by data grubbing shows little other than the researcher’s endurance. We cannot tell whether a data grubbing marathon demonstrates the validity of a useful theory or the perseverance of a determined researcher until independent tests confirm or refute the finding. But more often than not, the tests stop there. After all, you won’t become a star by confirming other people’s research, so why not spend your time discovering new theories? The data-grubbed theory consequently sits out there, untested and unchallenged." (Gary Smith, "Standard Deviations", 2014)

"With fast computers and plentiful data, finding statistical significance is trivial. If you look hard enough, it can even be found in tables of random numbers." (Gary Smith, "Standard Deviations", 2014)

"In short, statistical significance does not mean your result has any practical significance. As for statistical insignificance, it doesn’t tell you much. A statistically insignificant difference could be nothing but noise, or it could represent a real effect that can be pinned down only with more data." (Alex Reinhart, "Statistics Done Wrong: The Woefully Complete Guide", 2015)

"Statistical significance is a concept used by scientists and researchers to set an objective standard that can be used to determine whether or not a particular relationship 'statistically' exists in the data. Scientists test for statistical significance to distinguish between whether an observed effect is present in the data (given a high degree of probability), or just due to chance. It is important to note that finding a statistically significant relationship tells us nothing about whether a relationship is a simple correlation or a causal one, and it also can’t tell us anything about whether some omitted factor is driving the result." (John H Johnson & Mike Gluck, "Everydata: The misinformation hidden in the little data you consume every day", 2016)

"Statistical significance refers to the probability that something is true. It’s a measure of how probable it is that the effect we’re seeing is real (rather than due to chance occurrence), which is why it’s typically measured with a p-value. P, in this case, stands for probability. If you accept p-values as a measure of statistical significance, then the lower your p-value is, the less likely it is that the results you’re seeing are due to chance alone." (John H Johnson & Mike Gluck, "Everydata: The misinformation hidden in the little data you consume every day", 2016)

More quotes on "Significance" at the-web-of-knowledge.blogspot.com.

🔭Data Science: Variability (Just the Quotes)

"It is now beginning to be generally understood, even by merely practical statisticians, that there is truth in the theory that all variability is much the same kind." (Francis Galton, "Kinship and Correlation", North American Review Vol. 150 (11), 1890)

"It is clear that one who attempts to study precisely things that are changing must have a great deal to do with measures of change." (Charles Cooley, "Observations on the Measure of Change", Journal of the American Statistical Association (21), 1893)

"If significance tests are required for still larger samples, graphical accuracy is insufficient, and arithmetical methods are advised. A word to the wise is in order here, however. Almost never does it make sense to use exact binomial significance tests on such data - for the inevitable small deviations from the mathematical model of independence and constant split have piled up to such an extent that the binomial variability is deeply buried and unnoticeable. Graphical treatment of such large samples may still be worthwhile because it brings the results more vividly to the eye." (Frederick Mosteller & John W Tukey, "The Uses and Usefulness of Binomial Probability Paper?", Journal of the American Statistical Association 44, 1949)

"By sampling we can learn only about collective properties of populations, not about properties of individuals. We can study the average height, the percentage who wear hats, or the variability in weight of college juniors [...]. The population we study may be small or large, but there must be a population - and what we are studying must be a population characteristic. By sampling, we cannot study individuals as particular entities with unique idiosyncrasies; we can study regularities (including typical variabilities as well as typical levels) in a population as exemplified by the individuals in the sample." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"We realize that if someone just 'grabs a handful', the individuals in the handful almost always resemble one another (on the average) more than do the members of a simple random sample. Even if the 'grabs' [sampling] are randomly spread around so that every individual has an equal chance of entering the sample, there are difficulties. Since the individuals of grab samples resemble one another more than do individuals of random samples, it follows (by a simple mathematical argument) that the means of grab samples resemble one another less than the means of random samples of the same size. From a grab sample, therefore, we tend to underestimate the variability in the population, although we should have to overestimate it in order to obtain valid estimates of variability of grab sample means by substituting such an estimate into the formula for the variability of means of simple random samples. Thus using simple random sample formulas for grab sample means introduces a double bias, both parts of which lead to an unwarranted appearance of higher stability." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"To the author the main charm of probability theory lies in the enormous variability of its applications. Few mathematical disciplines have contributed to as wide a spectrum of subjects, a spectrum ranging from number theory to physics, and even fewer have penetrated so decisively the whole of our scientific thinking." (Mark Kac, "Lectures in Applied Mathematics" Vol. 1, 1959)

"[...] in a state of dynamic equilibrium with their environments. If they do not maintain this equilibrium they die; if they do maintain it they show a degree of spontaneity, variability, and purposiveness of response unknown in the non-living world. This is what is meant by ‘adaptation to environment’ […] [Its] essential feature […] is stability - that is, the ability to withstand disturbances." (Kenneth Craik, 'Living organisms', “The Nature of Psychology”, 1966)

"Adaptive system - whether on the biological, psychological, or sociocultural level - must manifest (1) some degree of 'plasticity' and 'irritability' vis-a-vis its environment such that it carries on a constant interchange with acting on and reacting to it; (2) some source or mechanism for variety, to act as a potential pool of adaptive variability to meet the problem of mapping new or more detailed variety and constraints in a changeable environment; (3) a set of selective criteria or mechanisms against which the 'variety pool' may be sifted into those variations in the organization or system that more closely map the environment and those that do not; and (4) an arrangement for preserving and/or propagating these 'successful' mappings." (Walter F Buckley," Sociology and modern systems theory", 1967)

"Statistical methods of analysis are intended to aid the interpretation of data that are subject to appreciable haphazard variability." (Sir David R Cox & David V Hinkley, "Theoretical Statistics", 1974)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"What is so unconventional about the statistical way of thinking? First, statisticians do not care much for the popular concept of the statistical average; instead, they fixate on any deviation from the average. They worry about how large these variations are, how frequently they occur, and why they exist. [...] Second, variability does not need to be explained by reasonable causes, despite our natural desire for a rational explanation of everything; statisticians are frequently just as happy to pore over patterns of correlation. [...] Third, statisticians are constantly looking out for missed nuances: a statistical average for all groups may well hide vital differences that exist between these groups. Ignoring group differences when they are present frequently portends inequitable treatment. [...] Fourth, decisions based on statistics can be calibrated to strike a balance between two types of errors. Predictably, decision makers have an incentive to focus exclusively on minimizing any mistake that could bring about public humiliation, but statisticians point out that because of this bias, their decisions will aggravate other errors, which are unnoticed but serious. [...] Finally, statisticians follow a specific protocol known as statistical testing when deciding whether the evidence fits the crime, so to speak. Unlike some of us, they don’t believe in miracles. In other words, if the most unusual coincidence must be contrived to explain the inexplicable, they prefer leaving the crime unsolved." (Kaiser Fung, "Numbers Rule the World", 2010) 

"The data is a simplification - an abstraction - of the real world. So when you visualize data, you visualize an abstraction of the world, or at least some tiny facet of it. Visualization is an abstraction of data, so in the end, you end up with an abstraction of an abstraction, which creates an interesting challenge. […] Just like what it represents, data can be complex with variability and uncertainty, but consider it all in the right context, and it starts to make sense." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"Statistics is a science that helps us make decisions and draw conclusions in the presence of variability." (Douglas C Montgomery & George C Runger, "Applied Statistics and Probability for Engineers" 6th Ed., 2014)

"Stochastic variability and tipping points in the catch are two different dynamical phenomena. Yet they are both compatible with real-world data [...]" (John D W Morecroft, "Strategic Modelling and Business Dynamics: A Feedback Systems Approach", 2015)

"The lack of variability is often a hallmark of faked data. […] The failure of faked data to have sufficient variability holds as long as the liar does not know this. If the liar knows this, his best approach is to start with real data and use it cleverly to adapt it to his needs." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Variability in data solely due to chance can be averaged out by increasing the sample size. Variability due to other causes cannot be." (William M Bolstad & James M Curran, "Introduction to Bayesian Statistics" 3^rd Ed., 2017)

🔭Data Science: Estimation (Just the Quotes)

"The scientific value of a theory of this kind, in which we make so many assumptions, and introduce so many adjustable constants, cannot be estimated merely by its numerical agreement with certain sets of experiments. If it has any value it is because it enables us to form a mental image of what takes place in a piece of iron during magnetization." (James C Maxwell, "Treatise on Electricity and Magnetism" Vol. II, 1873)

"It [probability] is the very guide of life, and hardly can we take a step or make a decision of any kind without correctly or incorrectly making an estimation of probabilities." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"A statistical estimate may be good or bad, accurate or the reverse; but in almost all cases it is likely to be more accurate than a casual observer’s impression, and the nature of things can only be disproved by statistical methods." (Arthur L Bowley, "Elements of Statistics", 1901)

"Great numbers are not counted correctly to a unit, they are estimated; and we might perhaps point to this as a division between arithmetic and statistics, that whereas arithmetic attains exactness, statistics deals with estimates, sometimes very accurate, and very often sufficiently so for their purpose, but never mathematically exact." (Arthur L Bowley, "Elements of Statistics", 1901)

“Some of the common ways of producing a false statistical argument are to quote figures without their context, omitting the cautions as to their incompleteness, or to apply them to a group of phenomena quite different to that to which they in reality relate; to take these estimates referring to only part of a group as complete; to enumerate the events favorable to an argument, omitting the other side; and to argue hastily from effect to cause, this last error being the one most often fathered on to statistics. For all these elementary mistakes in logic, statistics is held responsible.” (Sir Arthur L Bowley, “Elements of Statistics”, 1901)

"A good estimator will be unbiased and will converge more and more closely (in the long run) on the true value as the sample size increases. Such estimators are known as consistent. But consistency is not all we can ask of an estimator. In estimating the central tendency of a distribution, we are not confined to using the arithmetic mean; we might just as well use the median. Given a choice of possible estimators, all consistent in the sense just defined, we can see whether there is anything which recommends the choice of one rather than another. The thing which at once suggests itself is the sampling variance of the different estimators, since an estimator with a small sampling variance will be less likely to differ from the true value by a large amount than an estimator whose sampling variance is large." (Michael J Moroney, "Facts from Figures", 1951)

"The enthusiastic use of statistics to prove one side of a case is not open to criticism providing the work is honestly and accurately done, and providing the conclusions are not broader than indicated by the data. This type of work must not be confused with the unfair and dishonest use of both accurate and inaccurate data, which too commonly occurs in business. Dishonest statistical work usually takes the form of: (1) deliberate misinterpretation of data; (2) intentional making of overestimates or underestimates; and (3) biasing results by using partial data, making biased surveys, or using wrong statistical methods." (John R Riggleman & Ira N Frisbee, "Business Statistics", 1951)

"Statistics is the fundamental and most important part of inductive logic. It is both an art and a science, and it deals with the collection, the tabulation, the analysis and interpretation of quantitative and qualitative measurements. It is concerned with the classifying and determining of actual attributes as well as the making of estimates and the testing of various hypotheses by which probable, or expected, values are obtained. It is one of the means of carrying on scientific research in order to ascertain the laws of behavior of things - be they animate or inanimate. Statistics is the technique of the Scientific Method." (Bruce D Greenschields & Frank M Weida, "Statistics with Applications to Highway Traffic Analyses", 1952)

"We realize that if someone just 'grabs a handful', the individuals in the handful almost always resemble one another (on the average) more than do the members of a simple random sample. Even if the 'grabs' [sampling] are randomly spread around so that every individual has an equal chance of entering the sample, there are difficulties. Since the individuals of grab samples resemble one another more than do individuals of random samples, it follows (by a simple mathematical argument) that the means of grab samples resemble one another less than the means of random samples of the same size. From a grab sample, therefore, we tend to underestimate the variability in the population, although we should have to overestimate it in order to obtain valid estimates of variability of grab sample means by substituting such an estimate into the formula for the variability of means of simple random samples. Thus using simple random sample formulas for grab sample means introduces a double bias, both parts of which lead to an unwarranted appearance of higher stability." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"The central point is that statistical significance is quite different from scientific significance and that therefore estimation [...] of the magnitude of effects is in general essential regardless of whether statistically significant departure from the null hypothesis is achieved." (David R Cox, "The role of significance tests", Scandanavian Journal of Statistics 4, 1977)

"There are considerable dangers in overemphasizing the role of significance tests in the interpretation of data." (David R Cox, "The role of significance tests", Scandanavian Journal of Statistics 4, 1977)

"The usefulness of the models in constructing a testable theory of the process is severely limited by the quickly increasing number of parameters which must be estimated in order to compare the predictions of the models with empirical results" (Anatol Rapoport, "Prisoner's Dilemma: A study in conflict and cooperation", 1965)

"Pencil and paper for construction of distributions, scatter diagrams, and run-charts to compare small groups and to detect trends are more efficient methods of estimation than statistical inference that depends on variances and standard errors, as the simple techniques preserve the information in the original data." (William E Deming, "On Probability as Basis for Action" American Statistician Vol. 29 (4), 1975)

"In physics it is usual to give alternative theoretical treatments of the same phenomenon. We construct different models for different purposes, with different equations to describe them. Which is the right model, which the 'true' set of equations? The question is a mistake. One model brings out some aspects of the phenomenon; a different model brings out others. Some equations give a rougher estimate for a quantity of interest, but are easier to solve. No single model serves all purposes best." (Nancy Cartwright, "How the Laws of Physics Lie", 1983)

"Probability is the mathematics of uncertainty. Not only do we constantly face situations in which there is neither adequate data nor an adequate theory, but many modem theories have uncertainty built into their foundations. Thus learning to think in terms of probability is essential. Statistics is the reverse of probability (glibly speaking). In probability you go from the model of the situation to what you expect to see; in statistics you have the observations and you wish to estimate features of the underlying model." (Richard W Hamming, "Methods of Mathematics Applied to Calculus, Probability, and Statistics", 1985)

"A mechanistic model has the following advantages: 1. It contributes to our scientific understanding of the phenomenon under study. 2. It usually provides a better basis for extrapolation (at least to conditions worthy of further experimental investigation if not through the entire range of all input variables). 3. It tends to be parsimonious (i. e, frugal) in the use of parameters and to provide better estimates of the response." (George E P Box, "Empirical Model-Building and Response Surfaces", 1987)

"A tendency to drastically underestimate the frequency of coincidences is a prime characteristic of innumerates, who generally accord great significance to correspondences of all sorts while attributing too little significance to quite conclusive but less flashy statistical evidence." (John A Paulos, "Innumeracy: Mathematical Illiteracy and its Consequences", 1988)

"A model for simulating dynamic system behavior requires formal policy descriptions to specify how individual decisions are to be made. Flows of information are continuously converted into decisions and actions. No plea about the inadequacy of our understanding of the decision-making processes can excuse us from estimating decision-making criteria. To omit a decision point is to deny its presence - a mistake of far greater magnitude than any errors in our best estimate of the process." (Jay W Forrester, "Policies, decisions and information sources for modeling", 1994)

"In constructing a model, we always attempt to maximize its usefulness. This aim is closely connected with the relationship among three key characteristics of every systems model: complexity, credibility, and uncertainty. This relationship is not as yet fully understood. We only know that uncertainty (predictive, prescriptive, etc.) has a pivotal role in any efforts to maximize the usefulness of systems models. Although usually (but not always) undesirable when considered alone, uncertainty becomes very valuable when considered in connection to the other characteristics of systems models: in general, allowing more uncertainty tends to reduce complexity and increase credibility of the resulting model. Our challenge in systems modelling is to develop methods by which an optimal level of allowable uncertainty can be estimated for each modelling problem." (George J Klir & Bo Yuan, "Fuzzy Sets and Fuzzy Logic: Theory and Applications", 1995)

"Delay time, the time between causes and their impacts, can highly influence systems. Yet the concept of delayed effect is often missed in our impatient society, and when it is recognized, it’s almost always underestimated. Such oversight and devaluation can lead to poor decision making as well as poor problem solving, for decisions often have consequences that don’t show up until years later. Fortunately, mind mapping, fishbone diagrams, and creativity/brainstorming tools can be quite useful here." (Stephen G Haines, "The Manager's Pocket Guide to Strategic and Business Planning", 1998)

“Accurate estimates depend at least as much upon the mental model used in forming the picture as upon the number of pieces of the puzzle that have been collected.” (Richards J. Heuer Jr, “Psychology of Intelligence Analysis”, 1999)

“[…] we underestimate the share of randomness in about everything […]  The degree of resistance to randomness in one’s life is an abstract idea, part of its logic counterintuitive, and, to confuse matters, its realizations nonobservable.” (Nassim N Taleb, “Fooled by Randomness”, 2001)

"Most long-range forecasts of what is technically feasible in future time periods dramatically underestimate the power of future developments because they are based on what I call the 'intuitive linear' view of history rather than the 'historical exponential' view." (Ray Kurzweil, "The Singularity is Near", 2005)

"[myth:] Accuracy is more important than precision. For single best estimates, be it a mean value or a single data value, this question does not arise because in that case there is no difference between accuracy and precision. (Think of a single shot aimed at a target.) Generally, it is good practice to balance precision and accuracy. The actual requirements will differ from case to case." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"As uncertainties of scientific data values are nearly as important as the data values themselves, it is usually not acceptable that a best estimate is only accompanied by an estimated uncertainty. Therefore, only the size of nondominant uncertainties should be estimated. For estimating the size of a nondominant uncertainty we need to find its upper limit, i.e., we want to be as sure as possible that the uncertainty does not exceed a certain value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Before best estimates are extracted from data sets by way of a regression analysis, the uncertainties of the individual data values must be determined.In this case care must be taken to recognize which uncertainty components are common to all the values, i.e., those that are correlated (systematic)." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"[myth:] Counting can be done without error. Usually, the counted number is an integer and therefore without (rounding) error. However, the best estimate of a scientifically relevant value obtained by counting will always have an error. These errors can be very small in cases of consecutive counting, in particular of regular events, e.g., when measuring frequencies." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Due to the theory that underlies uncertainties an infinite number of data values would be necessary to determine the true value of any quantity. In reality the number of available data values will be relatively small and thus this requirement can never be fully met; all one can get is the best estimate of the true value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is the aim of all data analysis that a result is given in form of the best estimate of the true value. Only in simple cases is it possible to use the data value itself as result and thus as best estimate." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"It is the nature of an uncertainty that it is not known and can never be known, whether the best estimate is greater or less than the true value." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"The methodology of feedback design is borrowed from cybernetics (control theory). It is based upon methods of controlled system model’s building, methods of system states and parameters estimation (identification), and methods of feedback synthesis. The models of controlled system used in cybernetics differ from conventional models of physics and mechanics in that they have explicitly specified inputs and outputs. Unlike conventional physics results, often formulated as conservation laws, the results of cybernetical physics are formulated in the form of transformation laws, establishing the possibilities and limits of changing properties of a physical system by means of control." (Alexander L Fradkov, "Cybernetical Physics: From Control of Chaos to Quantum Control", 2007)

"A good estimator has to be more than just consistent. It also should be one whose variance is less than that of any other estimator. This property is called minimum variance. This means that if we run the experiment several times, the 'answers' we get will be closer to one another than 'answers' based on some other estimator." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"An estimate (the mathematical definition) is a number derived from observed values that is as close as we can get to the true parameter value. Useful estimators are those that are 'better' in some sense than any others." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Estimators are functions of the observed values that can be used to estimate specific parameters. Good estimators are those that are consistent and have minimum variance. These properties are guaranteed if the estimator maximizes the likelihood of the observations." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"GIGO is a famous saying coined by early computer scientists: garbage in, garbage out. At the time, people would blindly put their trust into anything a computer output indicated because the output had the illusion of precision and certainty. If a statistic is composed of a series of poorly defined measures, guesses, misunderstandings, oversimplifications, mismeasurements, or flawed estimates, the resulting conclusion will be flawed." (Daniel J Levitin, "Weaponized Lies", 2017)

"One final warning about the use of statistical models (whether linear or otherwise): The estimated model describes the structure of the data that have been observed. It is unwise to extend this model very far beyond the observed data." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"One kind of probability - classic probability - is based on the idea of symmetry and equal likelihood […] In the classic case, we know the parameters of the system and thus can calculate the probabilities for the events each system will generate. […] A second kind of probability arises because in daily life we often want to know something about the likelihood of other events occurring […]. In this second case, we need to estimate the parameters of the system because we don’t know what those parameters are. […] A third kind of probability differs from these first two because it’s not obtained from an experiment or a replicable event - rather, it expresses an opinion or degree of belief about how likely a particular event is to occur. This is called subjective probability […]." (Daniel J Levitin, "Weaponized Lies", 2017)

"Samples give us estimates of something, and they will almost always deviate from the true number by some amount, large or small, and that is the margin of error. […] The margin of error does not address underlying flaws in the research, only the degree of error in the sampling procedure. But ignoring those deeper possible flaws for the moment, there is another measurement or statistic that accompanies any rigorously defined sample: the confidence interval." (Daniel J Levitin, "Weaponized Lies", 2017)

"The margin of error is how accurate the results are, and the confidence interval is how confident you are that your estimate falls within the margin of error." (Daniel J Levitin, "Weaponized Lies", 2017)