"[…] wrong hypotheses, rightly worked from, have produced more useful results than unguided observation." (Augustus de Morgan, "A Budget of Paradoxes", 1872)
"A false hypothesis, if it serve as a guide for further enquiry, may, at the right stage of science, be as useful as, or more useful than, a truer one for which acceptable evidence is not yet at hand." (William C Dampier, "Science and the Human Mind, Science in the Ancient World", 1912)
"Rule 1. Original data should be presented in a way that will preserve the evidence in the original data for all the predictions assumed to be useful." (Walter A Shewhart, "Economic Control of Quality of Manufactured Product", 1931)
"Without an adequate understanding of the statistical methods, the investigator in the social sciences may be like the blind man groping in a dark room for a black cat that is not there. The methods of Statistics are useful in an over-widening range of human activities in any field of thought in which numerical data may be had." (Frederick E Croxton & Dudley J Cowden, "Practical Business Statistics", 1937)
"Starting from statistical observations, it is possible to arrive at conclusions which not less reliable or useful than those obtained in any other exact science. It is only necessary to apply a clear and precise concept of probability to such observations. (Richard von Mises, "Probability, Statistics, and Truth", 1939)
"Analogies are useful for analysis in unexplored fields. By means of analogies an unfamiliar system may be compared with one that is better known. The relations and actions are more easily visualized, the mathematics more readily applied, and the analytical solutions more readily obtained in the familiar system." (Harry F Olson, "Dynamical Analogies", 1943)
"The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is false. A natural consequence of doing so is that one then assumes that there is no virtue in the mere working out of consequences from data and general principles." (Alan Turing, "Computing Machinery and Intelligence", Mind Vol. 59, 1950)
"Undoubtedly one of the most elegant, powerful, and useful techniques in modern statistical method is that of the Analysis of Variation and Co-variation by which the total variation in a set of data may be reduced to components associated with possible sources of variability whose relative importance we wish to assess. The precise form which any given analysis will take is intimately connected with the structure of the investigation from which the data are obtained. A simple structure will lead to a simple analysis; a complex structure to a complex analysis." (Michael J Moroney, "Facts from Figures", 1951)
"Extrapolations are useful, particularly in the form of soothsaying called forecasting trends. But in looking at the figures or the charts made from them, it is necessary to remember one thing constantly: The trend to now may be a fact, but the future trend represents no more than an educated guess. Implicit in it is 'everything else being equal' and 'present trends continuing'. And somehow everything else refuses to remain equal." (Darell Huff, "How to Lie with Statistics", 1954)
"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)
"A model is a useful (and often indispensable) framework on which to organize our knowledge about a phenomenon. […] It must not be overlooked that the quantitative consequences of any model can be no more reliable than the a priori agreement between the assumptions of the model and the known facts about the real phenomenon. When the model is known to diverge significantly from the facts, it is self-deceiving to claim quantitative usefulness for it by appeal to agreement between a prediction of the model and observation." (John R Philip, 1966)
"An average is sometimes called a 'measure of central tendency' because individual values of the variable usually cluster around it. Averages are useful, however, for certain types of data in which there is little or no central tendency." (William A Spirr & Charles P Bonini, "Statistical Analysis for Business Decisions" 3rd Ed., 1967)
"[…] fitting lines to relationships between variables is often a useful and powerful method of summarizing a set of data. Regression analysis fits naturally with the development of causal explanations, simply because the research worker must, at a minimum, know what he or she is seeking to explain." (Edward R Tufte, 'Data Analysis for Politics and Policy", 1974)
"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)
"When a real situation involves chance we have to use probability mathematics to understand it quantitatively. Direct mathematical solutions sometimes exist […] but most real systems are too complicated for direct solutions. In these cases the computer, once taught to generate random numbers, can use simulation to get useful answers to otherwise impossible problems." (Robert Hooke, "How to Tell the Liars from the Statisticians", 1983)
"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)
"The heart of the scientific method is the problem-hypothesis-test process. And, necessarily, the scientific method involves predictions. And predictions, to be useful in scientific methodology, must be subject to test empirically." (Paul Davies, "The Cosmic Blueprint: New Discoveries in Nature's Creative Ability to, Order the Universe", 1988)
"Statistics is a tool. In experimental science you plan and carry out experiments, and then analyse and interpret the results. To do this you use statistical arguments and calculations. Like any other tool - an oscilloscope, for example, or a spectrometer, or even a humble spanner - you can use it delicately or clumsily, skillfully or ineptly. The more you know about it and understand how it works, the better you will be able to use it and the more useful it will be." (Roger Barlow, "Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences", 1989)
"Science is (or should be) a precise art. Precise, because data may be taken or theories formulated with a certain amount of accuracy; an art, because putting the information into the most useful form for investigation or for presentation requires a certain amount of creativity and insight." (Patricia H Reiff, "The Use and Misuse of Statistics in Space Physics", Journal of Geomagnetism and Geoelectricity 42, 1990)
"A useful description relates the systematic variation to one or more factors; if the residuals dwarf the effects for a factor, we may not be able to relate variation in the data to changes in the factor. Furthermore, changes in the factor may bring no important change in the response. Such comparisons of residuals and effects require a measure of the variation of overlays relative to each other." (Christopher H Schrnid, "Value Splitting: Taking the Data Apart", 1991)
"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)
"The point is that scientific descriptions of phenomena in all of these cases do not fully capture reality they are models. This is not a shortcoming but a strength of science much of the scientist's art lies in figuring out what to include and what to exclude in a model, and this ability allows science to make useful predictions without getting bogged down by intractable details." (Philip Ball, "The Self-Made Tapestry: Pattern Formation in Nature", 1998)
"We should push for de-emphasizing some topics, such as statistical significance tests - an unfortunate carry-over from the traditional elementary statistics course. We would suggest a greater focus on confidence intervals - these achieve the aim of formal hypothesis testing, often provide additional useful information, and are not as easily misinterpreted." (Gerry Hahn et al, "The Impact of Six Sigma Improvement: A Glimpse Into the Future of Statistics", The American Statistician, 1999)
"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)
"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)
"[…] 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)
"A model is a simplification or approximation of reality and hence will not reflect all of reality. […] Box noted that ‘all models are wrong, but some are useful’. While a model can never be ‘truth’, a model might be ranked from very useful, to useful, to somewhat useful to, finally, essentially useless.”" (Kenneth P Burnham & David R Anderson, 'Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach” 2nd Ed., 2005)
"First, we affirm that all models are wrong, some of them are useful. Since a model is an abstraction of reality, and that too only from a particular perspective, they are fundamentally wrong because they are not reality. That gives no license to models that are wrongly built - after all, two wrongs don’t make a right. So usefulness, or purpose, is what determines a model’s role, given that it is correctly formed. Models therefore have teleological value even though they are ontologically erroneous." (John Boardman & Brian Sauser, "Systems Thinking: Coping with 21st Century Problems", 2008)
"We face danger whenever information growth outpaces our understanding of how to process it. The last forty years of human history imply that it can still take a long time to translate information into useful knowledge, and that if we are not careful, we may take a step back in the meantime." (Nate Silver, "The Signal and the Noise", 2012)
"Complexity scientists concluded that there are just too many factors - both concordant and contrarian - to understand. And with so many potential gaps in information, almost nobody can see the whole picture. Complex systems have severe limits, not only to predictability but also to measurability. Some complexity theorists argue that modelling, while useful for thinking and for studying the complexities of the world, is a particularly poor tool for predicting what will happen." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)
"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)
"To find signals in data, we must learn to reduce the noise - not just the noise that resides in the data, but also the noise that resides in us. It is nearly impossible for noisy minds to perceive anything but noise in data. […] Signals always point to something. In this sense, a signal is not a thing but a relationship. Data becomes useful knowledge of something that matters when it builds a bridge between a question and an answer. This connection is the signal." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)
"Data visualization is marketed today as the miracle cure that will open the doors to success, whatever its shape. We have enough experience to realize that in reality it’s not always easy to distinguish between real usefulness and zealous marketing. After the initial excitement over the prospects of data visualization comes disillusionment, and after that the possibility of a balanced assessment. The key is to get to this point quickly, without disappointments and at a lower cost." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)
"Effects without an understanding of the causes behind them, on the other hand, are just bunches of data points floating in the ether, offering nothing useful by themselves. Big Data is information, equivalent to the patterns of light that fall onto the eye. Big Data is like the history of stimuli that our eyes have responded to. And as we discussed earlier, stimuli are themselves meaningless because they could mean anything. The same is true for Big Data, unless something transformative is brought to all those data sets… understanding." (Beau Lotto, "Deviate: The Science of Seeing Differently", 2017)
"The goal of data science is to improve decision making by basing decisions on insights extracted from large data sets. As a field of activity, data science encompasses a set of principles, problem definitions, algorithms, and processes for extracting nonobvious and useful patterns from large data sets. It is closely related to the fields of data mining and machine learning, but it is broader in scope." (John D Kelleher & Brendan Tierney, "Data Science", 2018)
"In machine learning, our data has biases as well as useful information for our task. The more exactly our machine learning model fits the data, the more it reflects these biases. This means that the predictions may be based on spurious relationships that incidentally occur in the training data." (Alex Thomas, "Natural Language Processing with Spark NLP", 2020)
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