"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 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.
"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.
"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).
"[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.
"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."
"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.
"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.
"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."
"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."
"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."
