🦋Science: On Samples (Quotes)

"Little experience is sufficient to show that the traditional machinery of statistical processes is wholly unsuited to the needs of practical research. Not only does it take a cannon to shoot a sparrow, but it misses the sparrow! The elaborate mechanism built on the theory of infinitely large samples is not accurate enough for simple laboratory data. Only by systematically tackling small sample problems on their metrics does it seem possible to apply accurate tests to practical data." (Ronald A Fisher, "Statistical Methods for Research Workers", 1925)

"The postulate of randomness thus resolves itself into the question, ‘of what population is this a random sample?’ which must frequently be asked by every practical statistician." (Ronald  A Fisher, "On the Mathematical Foundation of Theoretical Statistics", Philosophical Transactions of the Royal Society of London Vol. A222, 1922) 

"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)

"Assumptions that we make, such as those concerning the form of the population sampled, are always untrue." (David R Cox, "Some problems connected with statistical inference", Annals of Mathematical Statistics 29, 1958)

"[...] a priori reasons for believing that the null hypothesis is generally false anyway. One of the common experiences of research workers is the very high frequency with which significant results are obtained with large samples." (David Bakan, "The test of significance in psychological research", Psychological Bulletin 66, 1966)

"People have erroneous intuitions about the laws of chance. In particular, they regard a sample randomly drawn from a population as highly representative, that is, similar to the population in all essential characteristics. The prevalence of the belief and its unfortunate consequences for psychological research are illustrated by the responses of professional psychologists to a questionnaire concerning research decisions." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1971)

"[...] too many users of the analysis of variance seem to regard the reaching of a mediocre level of significance as more important than any descriptive specification of the underlying averages Our thesis is that people have strong intuitions about random sampling; that these intuitions are wrong in fundamental respects; that these intuitions are shared by naive subjects and by trained scientists; and that they are applied with unfortunate consequences in the course of scientific inquiry. We submit that people view a sample randomly drawn from a population as highly representative, that is, similar to the population in all essential characteristics. Consequently, they expect any two samples drawn from a particular population to be more similar to one another and to the population than sampling theory predicts, at least for small samples." (Amos Tversky & Daniel Kahneman, "Belief in the law of small numbers", Psychological Bulletin 76(2), 1971) 

"It would help if the standard statistical programs did not generate t statistics in such profusion. The programs might be written to ask, 'Do you really have a probability sample?', 'By what standard would you judge a fitted coefficient large or small?' Or perhaps they could merely say, printed in bold capitals beside each equation, 'So What Else Is New?'" (Donald M McCloskey, "The Loss Function Has Been Mislaid: The Rhetoric of Significance Tests", American Economic Review Vol. 75, 1985)

"Since a point hypothesis is not to be expected in practice to be exactly true, but only approximate, a proper test of significance should almost always show significance for large enough samples. So the whole game of testing point hypotheses, power analysis notwithstanding, is but a mathematical game without empirical importance." (Louis Guttman, "The illogic of statistical inference for cumulative science", Applied Stochastic Models and Data Analysis, 1985)

"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 45, 1990)

"Unfortunately, when applied in a cook-book fashion, such significance tests do not extract the maximum amount of information available from the data. Worse still, misleading conclusions can be drawn. There are at least three problems: (1) a conclusion that there is a significant difference can often be reached merely by collecting enough samples; (2) a statistically significant result is not necessarily practically significant; and (3) reports of the presence or absence of significant differences for multiple tests are not comparable unless identical sample sizes are used." (Graham B McBride et al, "What do significance tests really tell us about the environment?", Environmental Management 17, 1993)

"Statistical hypothesis testing is commonly used inappropriately to analyze data, determine causality, and make decisions about significance in ecological risk assessment,[...] It discourages good toxicity testing and field studies, it provides less protection to ecosystems or their components that are difficult to sample or replicate, and it provides less protection when more treatments or responses are used. It provides a poor basis for decision-making because it does not generate a conclusion of no effect, it does not indicate the nature or magnitude of effects, it does address effects at untested exposure levels, and it confounds effects and uncertainty[...]. Risk assessors should focus on analyzing the relationship between exposure and effects[...]."  (Glenn W Suter, "Abuse of hypothesis testing statistics in ecological risk assessment", Human and Ecological Risk Assessment 2, 1996)

"The standard error of most statistics is proportional to 1 over the square root of the sample size. God did this, and there is nothing we can do to change it." (Howard Wainer, "Improving Tabular Displays, With NAEP Tables as Examples and Inspirations", Journal of Educational and Behavioral Statistics Vol 22 (1), 1997)

"It is not always convenient to remember that the right model for a population can fit a sample of data worse than a wrong model - even a wrong model with fewer parameters. We cannot rely on statistical diagnostics to save us, especially with small samples. We must think about what our models mean, regardless of fit, or we will promulgate nonsense." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"It’s a commonplace among statisticians that a chi-squared test (and, really, any p-value) can be viewed as a crude measure of sample size: When sample size is small, it’s very difficult to get a rejection (that is, a p-value below 0.05), whereas when sample size is huge, just about anything will bag you a rejection. With large n, a smaller signal can be found amid the noise. In general: small n, unlikely to get small p-values. Large n, likely to find something. Huge n, almost certain to find lots of small p-values." (Andrew Gelman, "The sample size is huge, so a p-value of 0.007 is not that impressive", 2009)

"Why are you testing your data for normality? For large sample sizes the normality tests often give a meaningful answer to a meaningless question (for small samples they give a meaningless answer to a meaningful question)." (Greg Snow, "R-Help", 2014)

"The Dirty Data Theorem states that 'real world' data tends to come from bizarre and unspecifiable distributions of highly correlated variables and have unequal sample sizes, missing data points, non-independent observations, and an indeterminate number of inaccurately recorded values." (Anon, Statistically Speaking)

"The old rule of trusting the Central Limit Theorem if the sample size is larger than 30 is just that–old. Bootstrap and permutation testing let us more easily do inferences for a wider variety of statistics." (Tim Hesterberg)

"While the main emphasis in the development of power analysis has been to provide methods for assessing and increasing power, it should also be noted that it is possible to have too much power. If your sample is too large, nearly any difference, no matter how small or meaningless from a practical standpoint, will be ‘statistically significant’." (Clay Helberg) 

🦋Science: On Confidence Intervals (Quotes)

"Confidence intervals give a feeling of the uncertainty of experimental evidence, and (very important) give it in the same units [...] as the original observations." (Mary G Natrella, "The relation between confidence intervals and tests of significance", American Statistician 14, 1960)

"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)

"Whereas hypothesis testing emphasizes a very narrow question (‘Do the population means fail to conform to a specific pattern?’), the use of confidence intervals emphasizes a much broader question (‘What are the population means?’). Knowing what the means are, of course, implies knowing whether they fail to conform to a specific pattern, although the reverse is not true. In this sense, use of confidence intervals subsumes the process of hypothesis testing." (Geoffrey R Loftus, "On the tyranny of hypothesis testing in the social sciences", Contemporary Psychology 36, 1991)

"Probabilistic inference is the classical paradigm for data analysis in science and technology. It rests on a foundation of randomness; variation in data is ascribed to a random process in which nature generates data according to a probability distribution. This leads to a codification of uncertainly by confidence intervals and hypothesis tests." (William S Cleveland, "Visualizing Data", 1993)

"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)

"Precision does not vary linearly with increasing sample size. As is well known, the width of a confidence interval is a function of the square root of the number of observations. But it is more complicate than that. The basic elements determining a confidence interval are the sample size, an estimate of variability, and a pivotal variable associated with the estimate of variability." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"The important thing is to understand that frequentist and Bayesian methods are answering different questions. To combine prior beliefs with data in a principled way, use Bayesian inference. To construct procedures with guaranteed long run performance, such as confidence intervals, use frequentist methods. Generally, Bayesian methods run into problems when the parameter space is high dimensional." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004) 

"There is a tendency to use hypothesis testing methods even when they are not appropriate. Often, estimation and confidence intervals are better tools. Use hypothesis testing only when you want to test a well-defined hypothesis." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"Scholars feel the need to present tables of model parameters in academic articles (perhaps just as evidence that they ran the analysis they claimed to have run), but these tables are rarely interpreted other than for their sign and statistical significance. Most of the numbers in these tables are never even discussed in the text. From the perspective of the applied data analyst, R packages without procedures to compute quantities of scientific interest are woefully incomplete. A better approach focuses on quantities of direct scientific interest rather than uninterpretable model parameters. [...] For each quantity of interest, the user needs some summary that includes a point estimate and a measure of uncertainty such as a standard error, confidence interval, or a distribution. The methods of calculating these differ greatly across theories of inference and methods of analysis. However, from the user’s perspective, the result is almost always the same: the point estimate and uncertainty of some quantity of interest." (Kousuke Imai et al, "Toward a Common Framework for Statistical Analysis and Development", Journal of Computational and Graphical Statistics vol. 17, 2008)

"Given the important role that correlation plays in structural equation modeling, we need to understand the factors that affect establishing relationships among multivariable data points. The key factors are the level of measurement, restriction of range in data values (variability, skewness, kurtosis), missing data, nonlinearity, outliers, correction for attenuation, and issues related to sampling variation, confidence intervals, effect size, significance, sample size, and power." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"A complete data analysis will involve the following steps: (i) Finding a good model to fit the signal based on the data. (ii) Finding a good model to fit the noise, based on the residuals from the model. (iii) Adjusting variances, test statistics, confidence intervals, and predictions, based on the model for the noise." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"For a confidence interval, the central limit theorem plays a role in the reliability of the interval because the sample mean is often approximately normal even when the underlying data is not. A prediction interval has no such protection. The shape of the interval reflects the shape of the underlying distribution. It is more important to examine carefully the normality assumption by checking the residuals […]." (DeWayne R Derryberry, "Basic data analysis for time series with R", 2014)

"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)

"[...] a hypothesis test tells us whether the observed data are consistent with the null hypothesis, and a confidence interval tells us which hypotheses are consistent with the data." (William C Blackwelder)

🦋Science: On Statistical Models (Quotes)

"The most widely used mathematical tools in the social sciences are statistical, and the prevalence of statistical methods has given rise to theories so abstract and so hugely complicated that they seem a discipline in themselves, divorced from the world outside learned journals. Statistical theories usually assume that the behavior of large numbers of people is a smooth, average 'summing-up' of behavior over a long period of time. It is difficult for them to take into account the sudden, critical points of important qualitative change. The statistical approach leads to models that emphasize the quantitative conditions needed for equilibrium - a balance of wages and prices, say, or of imports and exports. These models are ill suited to describe qualitative change and social discontinuity, and it is here that catastrophe theory may be especially helpful." (Alexander Woodcock & Monte Davis, "Catastrophe Theory", 1978)

"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)

"[…] it does not seem helpful just to say that all models are wrong. The very word model implies simplification and idealization. The idea that complex physical, biological or sociological systems can be exactly described by a few formulae is patently absurd. The construction of idealized representations that capture important stable aspects of such systems is, however, a vital part of general scientific analysis and statistical models, especially substantive ones, do not seem essentially different from other kinds of model." (Sir David Cox, "Comment on ‘Model uncertainty, data mining and statistical inference’", Journal of the Royal Statistical Society, Series A 158, 1995)

"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)

"The role of graphs in probabilistic and statistical modeling is threefold: (1) to provide convenient means of expressing substantive assumptions; (2) to facilitate economical representation of joint probability functions; and (3) to facilitate efficient inferences from observations." (Judea Pearl, "Causality: Models, Reasoning, and Inference", 2000)

"It is impossible to construct a model that provides an entirely accurate picture of network behavior. Statistical models are almost always based on idealized assumptions, such as independent and identically distributed (i.i.d.) interarrival times, and it is often difficult to capture features such as machine breakdowns, disconnected links, scheduled repairs, or uncertainty in processing rates." (Sean Meyn, "Control Techniques for Complex Networks", 2008)

"Statistical cognition is concerned with obtaining cognitive evidence about various statistical techniques and ways to present data. It’s certainly important to choose an appropriate statistical model, use the correct formulas, and carry out accurate calculations. It’s also important, however, to focus on understanding, and to consider statistics as communication between researchers and readers." (Geoff Cumming, "Understanding the New Statistics", 2012)

"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)

"A statistical model is a relatively simple approximation to account for complex phenomena that generate data. A statistical model consists of one or more equations involving both random variables and parameters. The random variables have stated or assumed distributions. The parameters are unknown fixed quantities. The random components of statistical models account for the inherent variability in most observed phenomena." (Richard M Heiberger & Burt Holland, "Statistics Concepts", 2015)

"An oft-repeated rule of thumb in any sort of statistical model fitting is 'you can't fit a model with more parameters than data points'. This idea appears to be as wide-spread as it is incorrect. On the contrary, if you construct your models carefully, you can fit models with more parameters than datapoints [...]. A model with more parameters than datapoints is known as an under-determined system, and it's a common misperception that such a model cannot be solved in any circumstance. [...] this misconception, which I like to call the 'model complexity myth' [...] is not true in general, it is true in the specific case of simple linear models, which perhaps explains why the myth is so pervasive." (Jake Vanderplas, "The Model Complexity Myth", 2015) [source]

"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)

"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)

"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)

"The central limit conjecture states that most errors are the result of many small errors and, as such, have a normal distribution. The assumption of a normal distribution for error has many advantages and has often been made in applications of statistical models." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"When we use algebraic notation in statistical models, the problem becomes more complicated because we cannot 'observe' a probability and know its exact number. We can only estimate probabilities on the basis of observations." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Any fool can fit a statistical model, given the data and some software. The real challenge is to decide whether it actually fits the data adequately. It might be the best that can be obtained, but still not good enough to use." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

🦋Science: On Independence (Quotes)

"To apply the category of cause and effect means to find out which parts of nature stand in this relation. Similarly, to apply the gestalt category means to find out which parts of nature belong as parts to functional wholes, to discover their position in these wholes, their degree of relative independence, and the articulation of larger wholes into sub-wholes." (Kurt Koffka, 1931)

"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)

"A satisfactory prediction of the sequential properties of learning data from a single experiment is by no means a final test of a model. Numerous other criteria - and some more demanding - can be specified. For example, a model with specific numerical parameter values should be invariant to changes in independent variables that explicitly enter in the model." (Robert R Bush & Frederick Mosteller,"A Comparison of Eight Models?", Studies in Mathematical Learning Theory, 1959)

"[A] sequence is random if it has every property that is shared by all infinite sequences of independent samples of random variables from the uniform distribution." (Joel N Franklin, 1962)

"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)

"Bayesian networks provide a more flexible representation for encoding the conditional independence assumptions between the features in a domain. Ideally, the topology of a network should reflect the causal relationships between the entities in a domain. Properly constructed Bayesian networks are relatively powerful models that can capture the interactions between descriptive features in determining a prediction." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015) 

"Bayesian networks use a graph-based representation to encode the structural relationships - such as direct influence and conditional independence - between subsets of features in a domain. Consequently, a Bayesian network representation is generally more compact than a full joint distribution (because it can encode conditional independence relationships), yet it is not forced to assert a global conditional independence between all descriptive features. As such, Bayesian network models are an intermediary between full joint distributions and naive Bayes models and offer a useful compromise between model compactness and predictive accuracy." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015)

"The main differences between Bayesian networks and causal diagrams lie in how they are constructed and the uses to which they are put. A Bayesian network is literally nothing more than a compact representation of a huge probability table. The arrows mean only that the probabilities of child nodes are related to the values of parent nodes by a certain formula (the conditional probability tables) and that this relation is sufficient. That is, knowing additional ancestors of the child will not change the formula. Likewise, a missing arrow between any two nodes means that they are independent, once we know the values of their parents. [...] If, however, the same diagram has been constructed as a causal diagram, then both the thinking that goes into the construction and the interpretation of the final diagram change." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

🦋Science: On Outliers (Quotes)

"An observation with an abnormally large residual will be referred to as an outlier. Other terms in English are 'wild', 'straggler', 'sport' and 'maverick'; one may also speak of a 'discordant', 'anomalous' or 'aberrant' observation." (Francis J Anscombe, "Rejection of Outliers", Technometrics Vol. 2, 1960)

"One sufficiently erroneous reading can wreck the whole of a statistical analysis, however many observations there are." (Francis J Anscombe, "Rejection of Outliers", Technometrics Vol. 2, 1960)

"The fact that something is far-fetched is no reason why it should not be true; it cannot be as far-fetched as the fact that something exists." (Celia Green, "The Decline and Fall of Science", 1976)

"A good description of the data summarizes the systematic variation and leaves residuals that look structureless. That is, the residuals exhibit no patterns and have no exceptionally large values, or outliers. Any structure present in the residuals indicates an inadequate fit. Looking at the residuals laid out in an overlay helps to spot patterns and outliers and to associate them with their source in the data." (Christopher H Schrnid, "Value Splitting: Taking the Data Apart", 1991)

"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)

"The inability to predict outliers implies the inability to predict the course of history.” (Nassim N Taleb, “The Black Swan”, 2007)

"Given the important role that correlation plays in structural equation modeling, we need to understand the factors that affect establishing relationships among multivariable data points. The key factors are the level of measurement, restriction of range in data values (variability, skewness, kurtosis), missing data, nonlinearity, outliers, correction for attenuation, and issues related to sampling variation, confidence intervals, effect size, significance, sample size, and power." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"Need to consider outliers as they can affect statistics such as means, standard deviations, and correlations. They can either be explained, deleted, or accommodated (using either robust statistics or obtaining additional data to fill-in). Can be detected by methods such as box plots, scatterplots, histograms or frequency distributions." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"Outliers or influential data points can be defined as data values that are extreme or atypical on either the independent (X variables) or dependent (Y variables) variables or both. Outliers can occur as a result of observation errors, data entry errors, instrument errors based on layout or instructions, or actual extreme values from self-report data. Because outliers affect the mean, the standard deviation, and correlation coefficient values, they must be explained, deleted, or accommodated by using robust statistics." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"There are several key issues in the field of statistics that impact our analyses once data have been imported into a software program. These data issues are commonly referred to as the measurement scale of variables, restriction in the range of data, missing data values, outliers, linearity, and nonnormality." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"After you visualize your data, there are certain things to look for […]: increasing, decreasing, outliers, or some mix, and of course, be sure you’re not mixing up noise for patterns. Also note how much of a change there is and how prominent the patterns are. How does the difference compare to the randomness in the data? Observations can stand out because of human or mechanical error, because of the uncertainty of estimated values, or because there was a person or thing that stood out from the rest. You should know which it is." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"What is good visualization? It is a representation of data that helps you see what you otherwise would have been blind to if you looked only at the naked source. It enables you to see trends, patterns, and outliers that tell you about yourself and what surrounds you. The best visualization evokes that moment of bliss when seeing something for the first time, knowing that what you see has been right in front of you, just slightly hidden. Sometimes it is a simple bar graph, and other times the visualization is complex because the data requires it." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"When we find data quality issues due to valid data during data exploration, we should note these issues in a data quality plan for potential handling later in the project. The most common issues in this regard are missing values and outliers, which are both examples of noise in the data." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015)

"I don’t see the logic of rejecting data just because they seem incredible." (Fred Hoyle)

"In almost every true series of observations, some are found, which differ so much from the others as to indicate some abnormal source of error not contemplated in the theoretical discussions, and the introduction of which into the investigations can only serve, in the present state of science, to perplex and mislead the inquirer." (Benjamin Peirce, The Astronomical Journal)

🦋Science: On Correlation (Quotes)

"It had appeared from observation, and it was fully confirmed by this theory, that such a thing existed as an 'Index of Correlation', that is to say, a fraction, now commonly written T, that connects with close approximation every value of the deviation on the part of the subject, with the average of all the associated deviations of the Relative [...]" (Francis Galton, "Memories of My Life", 1908)

"One of the main duties of science is the correlation of phenomena, apparently disconnected and even contradictory." (Frederick Soddy, "The Interpretation of Radium and the Structure of the Atom", 1909)

"To speak of the cause of an event is therefore misleading. Any set of antecedents from which the event can theoretically be inferred by means of correlations might be called a cause of the event. But to speak of the cause is to imply a uniqueness [...]." (Bertrand Russell, "Mysticism and Logic: And Other Essays", 1910)

"'Causation' has been popularly used to express the condition of association, when applied to natural phenomena. There is no philosophical basis for giving it a wider meaning than partial or absolute association. In no case has it been proved that there is an inherent necessity in the laws of nature. Causation is correlation. [...] perfect correlation, when based upon sufficient experience, is causation in the scientific sense." (Henry E. Niles, "Correlation, Causation and Wright's Theory of 'Path Coefficients'", Genetics, 1922)

"The futile elaboration of innumerable measures of correlation, and the evasion of the real difficulties of sampling problems under cover of a contempt for small samples, were obviously beginning to make its pretensions ridiculous. These procedures were not only ill-aimed, but for all their elaboration, not sufficiently accurate." (Sir Ronald A Fisher, "Statistical Methods for Research Workers", 1925)

"Graphic methods are very commonly used in business correlation problems. On the whole, carefully handled and skillfully interpreted graphs have certain advantages over mathematical methods of determining correlation in the usual business problems. The elements of judgment and special knowledge of conditions can be more easily introduced in studying correlation graphically. Mathematical correlation is often much too rigid for the data at hand." (John R Riggleman & Ira N Frisbee, "Business Statistics", 1938)

"[…] statistical literacy. That is, the ability to read diagrams and maps; a 'consumer' understanding of common statistical terms, as average, percent, dispersion, correlation, and index number."  (Douglas Scates, "Statistics: The Mathematics for Social Problems", 1943)

"Another thing to watch out for is a conclusion in which a correlation has been inferred to continue beyond the data with which it has been demonstrated." (Darell Huff, "How to Lie with Statistics", 1954)

"Keep in mind that a correlation may be real and based on real cause and effect, and still be almost worthless in determining action in any single case." (Darell Huff, "How to Lie with Statistics", 1954)

"When you find somebody - usually an interested party - making a fuss about a correlation, look first of all to see if it is not one of this type, produced by the stream of events, the trend of the times." (Darell Huff, "How to Lie with Statistics", 1954)

"There is no correlation between the cause and the effect. The events reveal only an aleatory determination, connected not so much with the imperfection of our knowledge as with the structure of the human world." (Raymond Aron, "The Opium of the Intellectuals", 1955)

"The well-known virtue of the experimental method is that it brings situational variables under tight control. It thus permits rigorous tests of hypotheses and confidential statements about causation. The correlational method, for its part, can study what man has not learned to control. Nature has been experimenting since the beginning of time, with a boldness and complexity far beyond the resources of science. The correlator’s mission is to observe and organize the data of nature’s experiments." (Lee J Cronbach, "The Two Disciplines of Scientific Psychology", The American Psychologist Vol. 12, 1957)

"It has been said that data collection is like garbage collection: before you collect it you should have in mind what you are going to do with it." (Russell Fox & Max Gorbuny, "The Science of Science: Methods of Interpreting Physical Phenomena", 1964)

"Today we preach that science is not science unless it is quantitative. We substitute correlation for causal studies, and physical equations for organic reasoning. Measurements and equations are supposed to sharpen thinking, but [...] they more often tend to make the thinking non-causal and fuzzy." (John R Platt, "Strong Inference", Science Vol. 146 (3641), 1964)

"If we gather more and more data and establish more and more associations, however, we will not finally find that we know something. We will simply end up having more and more data and larger sets of correlations." (Kenneth N Waltz, "Theory of International Politics Source: Theory of International Politics", 1979)

"The invalid assumption that correlation implies cause is probably among the two or three most serious and common errors of human reasoning." (Stephen J Gould, "The Mismeasure of Man", 1980)

"Correlation and causation are two quite different words, and the innumerate are more prone to mistake them than most." (John A Paulos, "Innumeracy: Mathematical Illiteracy and its Consequences", 1988)

"Nature normally hates power laws. In ordinary systems all quantities follow bell curves, and correlations decay rapidly, obeying exponential laws. But all that changes if the system is forced to undergo a phase transition. Then power laws emerge-nature's unmistakable sign that chaos is departing in favor of order. The theory of phase transitions told us loud and clear that the road from disorder to order is maintained by the powerful forces of self-organization and is paved by power laws. It told us that power laws are not just another way of characterizing a system's behavior. They are the patent signatures of self-organization in complex systems." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"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)

"Nonetheless, the basic principles regarding correlations between variables are not that diffcult to understand. We must look for patterns that reveal potential relationships and for evidence that variables are actually related. But when we do spot those relationships, we should not jump to conclusions about causality. Instead, we need to weigh the strength of the relationship and the plausibility of our theory, and we must always try to discount the possibility of spuriousness." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)

"Given the important role that correlation plays in structural equation modeling, we need to understand the factors that affect establishing relationships among multivariable data points. The key factors are the level of measurement, restriction of range in data values (variability, skewness, kurtosis), missing data, nonlinearity, outliers, correction for attenuation, and issues related to sampling variation, confidence intervals, effect size, significance, sample size, and power." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"[...] if you want to show change through time, use a time-series chart; if you need to compare, use a bar chart; or to display correlation, use a scatter-plot - because some of these rules make good common sense." (Alberto Cairo, "The Functional Art", 2011)

"Economists should study financial markets as they actually operate, not as they assume them to operate - observing the way in which information is actually processed, observing the serial correlations, bonanzas, and sudden stops, not assuming these away as noise around the edges of efficient and rational markets." (Adair Turner, "Economics after the Crisis: Objectives and means", 2012)

"Without precise predictability, control is impotent and almost meaningless. In other words, the lesser the predictability, the harder the entity or system is to control, and vice versa. If our universe actually operated on linear causality, with no surprises, uncertainty, or abrupt changes, all future events would be absolutely predictable in a sort of waveless orderliness." (Lawrence K Samuels, "Defense of Chaos", 2013)

"The problem of complexity is at the heart of mankind’s inability to predict future events with any accuracy. Complexity science has demonstrated that the more factors found within a complex system, the more chances of unpredictable behavior. And without predictability, any meaningful control is nearly impossible. Obviously, this means that you cannot control what you cannot predict. The ability ever to predict long-term events is a pipedream. Mankind has little to do with changing climate; complexity does." (Lawrence K Samuels, "The Real Science Behind Changing Climate", LewRockwell.com, August 1, 2014)

"The correlational technique known as multiple regression is used frequently in medical and social science research. This technique essentially correlates many independent (or predictor) variables simultaneously with a given dependent variable (outcome or output). It asks, 'Net of the effects of all the other variables, what is the effect of variable A on the dependent variable?' Despite its popularity, the technique is inherently weak and often yields misleading results. The problem is due to self-selection. If we don’t assign cases to a particular treatment, the cases may differ in any number of ways that could be causing them to differ along some dimension related to the dependent variable. We can know that the answer given by a multiple regression analysis is wrong because randomized control experiments, frequently referred to as the gold standard of research techniques, may give answers that are quite different from those obtained by multiple regression analysis." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

"The theory behind multiple regression analysis is that if you control for everything that is related to the independent variable and the dependent variable by pulling their correlations out of the mix, you can get at the true causal relation between the predictor variable and the outcome variable. That’s the theory. In practice, many things prevent this ideal case from being the norm." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

"Correlation is not equivalent to cause for one major reason. Correlation is well defined in terms of a mathematical formula. Cause is not well defined." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"The degree to which one variable can be predicted from another can be calculated as the correlation between them. The square of the correlation (R^2) is the proportion of the variance of one that can be 'explained' by knowledge of the other." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Correlation quantifies the relationship between features. The purpose of correlation analysis is to understand the dependencies between features, so that observed effects can be explained or desired effects can be achieved." (Thomas A Runkler, "Data Analytics: Models and Algorithms for Intelligent Data Analysis" 3rd Ed., 2020)

🦋Science: On Sampling (Quotes)

"By a small sample we may judge of the whole piece." (Miguel de Cervantes, "Don Quixote de la Mancha", 1605–1615)

"If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty: (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals." (William S Gosset, "The Probable Error of a Mean", Biometrika, 1908)

"The postulate of randomness thus resolves itself into the question, 'of what population is this a random sample?' which must frequently be asked by every practical statistician." (Ronald Fisher, "On the Mathematical Foundation of Theoretical Statistics", Philosophical Transactions of the Royal Society of London Vol. A222, 1922)

"If the chance of error alone were the sole basis for evaluating methods of inference, we would never reach a decision, but would merely keep increasing the sample size indefinitely." (C West Churchman, "Theory of Experimental Inference", 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)

"A good sample-design is lost if it is not carried out according to plans." (W Edwards Deming, "Some Theory of Sampling", 1950)

"Sampling is the science and art of controlling and measuring the reliability of useful statistical information through the theory of probability." (William E Deming, "Some Theory of Sampling", 1950)

"Almost any sort of inquiry that is general and not particular involves both sampling and measurement […]. Further, both the measurement and the sampling will be imperfect in almost every case. We can define away either imperfection in certain cases. But the resulting appearance of perfection is usually only an illusion." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"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)

"In many cases general probability samples can be thought of in terms of (1) a subdivision of the population into strata, (2) a self-weighting probability sample in each stratum, and (3) combination of the stratum sample means weighted by the size of the stratum." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"Precision is expressed by an international standard, viz., the standard error. It measures the average of the difference between a complete coverage and a long series of estimates formed from samples drawn from this complete coverage by a particular procedure or drawing, and processed by a particular estimating formula." (W Edwards Deming, "On the Presentation of the Results of Sample Surveys as Legal Evidence", Journal of the American Statistical Association Vol 49 (268), 1954)

"The purely random sample is the only kind that can be examined with entire confidence by means of statistical theory, but there is one thing wrong with it. It is so difficult and expensive to obtain for many uses that sheer cost eliminates it." (Darell Huff, "How to Lie with Statistics", 1954)

"To be worth much, a report based on sampling must use a representative sample, which is one from which every source of bias has been removed." (Darell Huff, "How to Lie with Statistics", 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)

"[A] sequence is random if it has every property that is shared by all infinite sequences of independent samples of random variables from the uniform distribution." (Joel N Franklin, 1962)

"Weighing a sample appropriately is no more fudging the data than is correcting a gas volume for barometric pressure." (Frederick Mosteller, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1964)

"Entropy theory is indeed a first attempt to deal with global form; but it has not been dealing with structure. All it says is that a large sum of elements may have properties not found in a smaller sample of them." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1974) 

"The fact must be expressed as data, but there is a problem in that the correct data is difficult to catch. So that I always say 'When you see the data, doubt it!' 'When you see the measurement instrument, doubt it!' [...] For example, if the methods such as sampling, measurement, testing and chemical analysis methods were incorrect, data. […] to measure true characteristics and in an unavoidable case, using statistical sensory test and express them as data." (Kaoru Ishikawa, Annual Quality Congress Transactions, 1981)

"The law of truly large numbers states: With a large enough sample, any outrageous thing is likely to happen." (Frederick Mosteller, "Methods for Studying Coincidences", Journal of the American Statistical Association Vol. 84, 1989)

"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)

"When looking at the end result of any statistical analysis, one must be very cautious not to over interpret the data. Care must be taken to know the size of the sample, and to be certain the method forg athering information is consistent with other samples gathered. […] No one should ever base conclusions without knowing the size of the sample and how random a sample it was. But all too often such data is not mentioned when the statistics are given - perhaps it is overlooked or even intentionally omitted." (Theoni Pappas, "More Joy of Mathematics: Exploring mathematical insights & concepts", 1991)

"When the sample size is small or the study is of one organization, descriptive use of the thematic coding is desirable." (Richard Boyatzis, "Transforming qualitative information", 1998)

"Statisticians can calculate the probability that such random samples represent the population; this is usually expressed in terms of sampling error [...]. The real problem is that few samples are random. Even when researchers know the nature of the population, it can be time-consuming and expensive to draw a random sample; all too often, it is impossible to draw a true random sample because the population cannot be defined. This is particularly true for studies of social problems.[...] The best samples are those that come as close as possible to being random." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"There are two problems with sampling - one obvious, and  the other more subtle. The obvious problem is sample size. Samples tend to be much smaller than their populations. [...] Obviously, it is possible to question results based on small samples. The smaller the sample, the less confidence we have that the sample accurately reflects the population. However, large samples aren't necessarily good samples. This leads to the second issue: the representativeness of a sample is actually far more important than sample size. A good sample accurately reflects (or 'represents') the population." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Traditional statistics is strong in devising ways of describing data and inferring distributional parameters from sample. Causal inference requires two additional ingredients: a science-friendly language for articulating causal knowledge, and a mathematical machinery for processing that knowledge, combining it with data and drawing new causal conclusions about a phenomenon." (Judea Pearl, "Causal inference in statistics: An overview", Statistics Surveys 3, 2009)

"The closer that sample-selection procedures approach the gold standard of random selection - for which the definition is that every individual in the population has an equal chance of appearing in the sample - the more we should trust them. If we don’t know whether a sample is random, any statistical measure we conduct may be biased in some unknown way." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

"A popular misconception holds that the era of Big Data means the end of a need for sampling. In fact, the proliferation of data of varying quality and relevance reinforces the need for sampling as a tool to work efficiently with a variety of data, and minimize bias. Even in a Big Data project, predictive models are typically developed and piloted with samples." (Peter C Bruce & Andrew G Bruce, "Statistics for Data Scientists: 50 Essential Concepts", 2016)

"Repeated observations of the same phenomenon do not always produce the same results, due to random noise or error. Sampling errors result when our observations capture unrepresentative circumstances, like measuring rush hour traffic on weekends as well as during the work week. Measurement errors reflect the limits of precision inherent in any sensing device. The notion of signal to noise ratio captures the degree to which a series of observations reflects a quantity of interest as opposed to data variance. As data scientists, we care about changes in the signal instead of the noise, and such variance often makes this problem surprisingly difficult." (Steven S Skiena, "The Data Science Design Manual", 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)

"To be any good, a sample has to be representative. A sample is representative if every person or thing in the group you’re studying has an equally likely chance of being chosen. If not, your sample is biased. […] The job of the statistician is to formulate an inventory of all those things that matter in order to obtain a representative sample. Researchers have to avoid the tendency to capture variables that are easy to identify or collect data on - sometimes the things that matter are not obvious or are difficult to measure." (Daniel J Levitin, "Weaponized Lies", 2017)

🦋Science: On Regression (Quotes)

"One feature [...] which requires much more justification than is usually given, is the setting up of unplausible null hypotheses. For example, a statistician may set out a test to see whether two drugs have exactly the same effect, or whether a regression line is exactly straight. These hypotheses can scarcely be taken literally." (Cedric A B Smith, "Book review of Norman T. J. Bailey: Statistical Methods in Biology", Applied Statistics 9, 1960)

"The method of least squares is used in the analysis of data from planned experiments and also in the analysis of data from unplanned happenings. The word 'regression' is most often used to describe analysis of unplanned data. It is the tacit assumption that the requirements for the validity of least squares analysis are satisfied for unplanned data that produces a great deal of trouble." (George E P Box, "Use and Abuse of Regression", 1966)

"Stepwise regression is probably the most abused computerized statistical technique ever devised. If you think you need stepwise regression to solve a particular problem you have, it is almost certain that you do not. Professional statisticians rarely use automated stepwise regression." (Leland Wilkinson, "SYSTAT", 1984)

"Someone has characterized the user of stepwise regression as a person who checks his or her brain at the entrance of the computer center." (Dick R Wittink, "The application of regression analysis", 1988)

"Linear regression assumes that in the population a normal distribution of error values around the predicted Y is associated with each X value, and that the dispersion of the error values for each X value is the same. The assumptions imply normal and similarly dispersed error distributions." (Fred C Pampel, "Linear Regression: A primer", 2000)

"Regression toward the mean. That is, in any series of random events an extraordinary event is most likely to be followed, due purely to chance, by a more ordinary one." (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"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)

"Regression analysis, like all forms of statistical inference, is designed to offer us insights into the world around us. We seek patterns that will hold true for the larger population. However, our results are valid only for a population that is similar to the sample on which the analysis has been done." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Multiple regression, like all statistical techniques based on correlation, has a severe limitation due to the fact that correlation doesn't prove causation. And no amount of measuring of 'control' variables can untangle the web of causality. What nature hath joined together, multiple regression cannot put asunder." (Richard Nisbett, "2014 : What scientific idea is ready for retirement?", 2013)

"What nature hath joined together, multiple regression cannot put asunder."  (Richard Nisbett, "2014 : What scientific idea is ready for retirement?", 2013)

"Regression does not describe changes in ability that happen as time passes […]. Regression is caused by performances fluctuating about ability, so that performances far from the mean reflect abilities that are closer to the mean." (Gary Smith, "Standard Deviations", 2014)

"Regression toward the mean does not imply that everyone will soon be the same height any more than it implies that everyone will soon get the same score on history tests. What regression toward the mean does say is that observed heights are an imperfect measure of the genetic influences that we inherit from our parents and pass on to our children. […] Regression works in both directions since it reflects nothing more than random fluctuations. Tall parents tend to have somewhat shorter children, and tall children tend to have somewhat shorter parents." (Gary Smith, "Standard Deviations", 2014)

"We encounter regression in many contexts - pretty much whenever we see an imperfect measure of what we are trying to measure. Standardized tests are obviously an imperfect measure of ability. [...] Each experimental score is an imperfect measure of 'ability', the benefits from the layout. To the extent there is randomness in this experiment - and there surely is - the prospective benefits from the layout that has the highest score are probably closer to the mean than was the score." (Gary Smith, "Standard Deviations", 2014)

"When a trait, such as academic or athletic ability, is measured imperfectly, the observed differences in performance exaggerate the actual differences in ability. Those who perform the best are probably not as far above average as they seem. Nor are those who perform the worst as far below average as they seem. Their subsequent performances will consequently regress to the mean." (Gary Smith, "Standard Deviations", 2014)

"Working an integral or performing a linear regression is something a computer can do quite effectively. Understanding whether the result makes sense - or deciding whether the method is the right one to use in the first place - requires a guiding human hand. When we teach mathematics we are supposed to be explaining how to be that guide. A math course that fails to do so is essentially training the student to be a very slow, buggy version of Microsoft Excel." (Jordan Ellenberg, "How Not to Be Wrong: The Power of Mathematical Thinking", 2014)

"A basic problem with MRA is that it typically assumes that the independent variables can be regarded as building blocks, with each variable taken by itself being logically independent of all the others. This is usually not the case, at least for behavioral data. […] Just as correlation doesn’t prove causation, absence of correlation fails to prove absence of causation. False-negative findings can occur using MRA just as false-positive findings do—because of the hidden web of causation that we’ve failed to identify." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

"One technique employing correlational analysis is multiple regression analysis (MRA), in which a number of independent variables are correlated simultaneously (or sometimes sequentially, but we won’t talk about that variant of MRA) with some dependent variable. The predictor variable of interest is examined along with other independent variables that are referred to as control variables. The goal is to show that variable A influences variable B 'net of' the effects of all the other variables. That is to say, the relationship holds even when the effects of the control variables on the dependent variable are taken into account." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

"The fundamental problem with MRA, as with all correlational methods, is self-selection. The investigator doesn’t choose the value for the independent variable for each subject (or case). This means that any number of variables correlated with the independent variable of interest have been dragged along with it. In most cases, we will fail to identify all these variables. In the case of behavioral research, it’s normally certain that we can’t be confident that we’ve identified all the plausibly relevant variables." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

"The theory behind multiple regression analysis is that if you control for everything that is related to the independent variable and the dependent variable by pulling their correlations out of the mix, you can get at the true causal relation between the predictor variable and the outcome variable. That’s the theory. In practice, many things prevent this ideal case from being the norm." (Richard E Nisbett, "Mindware: Tools for Smart Thinking", 2015)

🦋Science: On Statistics (Quotes)

"There are two aspects of statistics that are continually mixed, the method and the science. Statistics are used as a method, whenever we measure something, for example, the size of a district, the number of inhabitants of a country, the quantity or price of certain commodities, etc. […] There is, moreover, a science of statistics. It consists of knowing how to gather numbers, combine them and calculate them, in the best way to lead to certain results. But this is, strictly speaking, a branch of mathematics." (Alphonse P de Candolle, "Considerations on Crime Statistics", 1833)

"Statistics has then for its object that of presenting a faithful representation of a state at a determined epoch." (Adolphe Quetelet, 1849)

"[Statistics] are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man." (Sir Francis Galton, "Natural Inheritance", 1889)

"[…] statistics is the science of the measurement of the social organism, regarded as a whole, in all its manifestations." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"Statistics may rightly be called the science of averages. […] Great numbers and the averages resulting from them, such as we always obtain in measuring social phenomena, have great inertia. […] It is this constancy of great numbers that makes statistical measurement possible. It is to great numbers that statistical measurement chiefly applies." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"Statistics may, for instance, be called the science of counting. Counting appears at first sight to be a very simple operation, which any one can perform or which can be done automatically; but, as a matter of fact, when we come to large numbers, e.g., the population of the United Kingdom, counting is by no means easy, or within the power of an individual; limits of time and place alone prevent it being so carried out, and in no way can absolute accuracy be obtained when the numbers surpass certain limits." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"Statistics may be defined as numerical statements of facts by means of which large aggregates are analyzed, the relations of individual units to their groups are ascertained, comparisons are made between groups, and continuous records are maintained for comparative purposes." (Melvin T Copeland. "Statistical Methods" [in: Harvard Business Studies, Vol. III, Ed. by Melvin T Copeland, 1917])

"Statistics may be regarded as (i) the study of populations, (ii) as the study of variation, and (iii) as the study of methods of the reduction of data." (Sir Ronald A Fisher, "Statistical Methods for Research Worker", 1925)

"Statistics is a scientific discipline concerned with collection, analysis, and interpretation of data obtained from observation or experiment. The subject has a coherent structure based on the theory of Probability and includes many different procedures which contribute to research and development throughout the whole of Science and Technology." (Egon Pearson, 1936)

"All statistical analysis in business must aim at the control of action. The possible conclusions are: 1. Certain action must be taken. 2. No action is required. 3. Certain tendencies must be watched. 4. The analysis is not significant and either (a) certain further facts are required, or (b) there are no indications that further facts should be obtained." (John R Riggleman & Ira N Frisbee, "Business Statistics", 1938)

"[Statistics] is both a science and an art. It is a science in that its methods are basically systematic and have general application; and an art in that their successful application depends to a considerable degree on the skill and special experience of the statistician, and on his knowledge of the field of application, e.g. economics." (Leonard H C Tippett, "Statistics", 1943)

"Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of populations of natural phenomena. In this definition 'natural phenomena' includes all the happenings of the external world, whether human or not " (Sir Maurice G Kendall, "Advanced Theory of Statistics", Vol. 1, 1943)

"To some people, statistics is ‘quartered pies, cute little battleships and tapering rows of sturdy soldiers in diversified uniforms’. To others, it is columns and columns of numerical facts. Many regard it as a branch of economics. The beginning student of the subject considers it to be largely mathematics." (The Editors, "Statistics, The Physical Sciences and Engineering", The American Statistician, Vol. 2, No. 4, 1948)

"[...] the whole of modern statistics, philosophy and methods alike, is based on the principle of interpreting what did happen in terms of what might have happened." (John W Tukey, "Standard Methods of Analyzing Data, 1951)

"Statistics is the name for that science and art which deals with uncertain inferences - which uses numbers to find out something about nature and experience." (Warren Weaver, 1952)

"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)

"Just remember that not all statistics has been mathematized - and that we may not have to wait for its mathematization in order to use it." (John W Tukey, "The Growth of Experimental Design in a Research Laboratory, 1953)

"Today one of statistics' great needs is a body of able investigators who make it clear to the intellectual world that they are scientific statisticians, and they are proud of that fact that to them mathematics is incidental, though perhaps indispensable." (John W Tukey, "Statistical and Quantitative Methodology, 1961)

"[Statistics] is concerned with things we can count. In so far as things, persons, are unique or ill-defined, statistics are meaningless and statisticians silenced; in so far as things are similar and definite - so many workers over 25, so many nuts and bolts made during December - they can be counted and new statistical facts are born." (Maurice S Bartlett, "Essays on Probability and Statistics", 1962)

"Statistics is the branch of scientific method which deals with the data obtained by counting or measuring the properties of populations of natural phenomena." (Sir Maurice G Kendall & Alan Stuart, "The Advanced Theory of Statistics", 1963)

"The typical statistician has learned from bitter experience that negative results are just as important as positive ones, sometimes more so." (John W Tukey, "A Statistician's Comment", 1967)

"It is fair to say that statistics has made its greatest progress by having to move away from certainty [...] If we really want to make progress, we need to identify our next step away from certainty." 

(John W Tukey, "What Have Statisticians Been Forgetting", 1967)

"Statistics may be defined as the discipline concerned with the treatment of numerical data derived from groups of individuals." (Peter Armitage, "Statistical Methods in Medical Research", 1971)

"We provisionally define statistics as the study of how information should be employed to reflect on, and give guidance for action in, a practical situation involving uncertainty." (Vic Barnett, "Comparative Statistical Inference" 2nd Ed., 1982)

"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)

"The science of statistics may be described as exploring, analyzing and summarizing data; designing or choosing appropriate ways of collecting data and extracting information from them; and communicating that information. Statistics also involves constructing and testing models for describing chance phenomena. These models can be used as a basis for making inferences and drawing conclusions and, finally, perhaps for making decisions." (Fergus Daly et al, "Elements of Statistics", 1995)

"Statistics is a general intellectual method that applies wherever data, variation, and chance appear. It is a fundamental method because data, variation and chance are omnipresent in modern life. It is an independent discipline with its own core ideas rather than, for example, a branch of mathematics. […] Statistics offers general, fundamental, and independent ways of thinking." (David S Moore, "Statistics among the Liberal Arts", Journal of the American Statistical Association, 1998)

"Statistics is the branch of mathematics that uses observations and measurements called data to analyze, summarize, make inferences, and draw conclusions based on the data gathered." (Allan G Bluman, "Probability Demystified", 2005)

"Put simply, statistics is a range of procedures for gathering, organizing, analyzing and presenting quantitative data. […] Essentially […], statistics is a scientific approach to analyzing numerical data in order to enable us to maximize our interpretation, understanding and use. This means that statistics helps us turn data into information; that is, data that have been interpreted, understood and are useful to the recipient. Put formally, for your project, statistics is the systematic collection and analysis of numerical data, in order to investigate or discover relationships among phenomena so as to explain, predict and control their occurrence." (Reva B Brown & Mark Saunders, "Dealing with Statistics: What You Need to Know", 2008)

"Statistics is the art of learning from data. It is concerned with the collection of data, their subsequent description, and their analysis, which often leads to the drawing of conclusions." (Sheldon M Ross, "Introductory Statistics" 3rd Ed., 2009)

"Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions." (Ron Larson & Betsy Farber, "Elementary Statistics: Picturing the World" 5th Ed., 2011)

"Statistics is the discipline of using data samples to support claims about populations." (Allen B Downey, "Think Stats: Probability and Statistics for Programmers", 2011)

"Statistics is the scientific discipline that provides methods to help us make sense of data. […] The field of statistics teaches us how to make intelligent judgments and informed decisions in the presence of uncertainty and variation." (Roxy Peck & Jay L Devore, "Statistics: The Exploration and Analysis of Data" 7th Ed, 2012)

"[…] statistics is a method of pursuing truth. At a minimum, statistics can tell you the likelihood that your hunch is true in this time and place and with these sorts of people. This type of pursuit of truth, especially in the form of an event’s future likelihood, is the essence of psychology, of science, and of human evolution." (Arthhur Aron et al, "Statistics for Phsychology" 6th Ed., 2012)

"The four questions of data analysis are the questions of description, probability, inference, and homogeneity. [...] Descriptive statistics are built on the assumption that we can use a single value to characterize a single property for a single universe. […] Probability theory is focused on what happens to samples drawn from a known universe. If the data happen to come from different sources, then there are multiple universes with different probability models.  [...] Statistical inference assumes that you have a sample that is known to have come from one universe." (Donald J Wheeler," Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)

"Statistics is the art and science of designing studies and analyzing the data that those studies produce. Its ultimate goal is translating data into knowledge and understanding of the world around us. In short, statistics is the art and science of learning from data." (Alan Agresti & Christine Franklin, "Statistics: The Art and Science of Learning from Data" 3rd Ed., 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)

"Statistics is an integral part of the quantitative approach to knowledge. The field of statistics is concerned with the scientific study of collecting, organizing, analyzing, and drawing conclusions from data." (Kandethody M Ramachandran & Chris P Tsokos, "Mathematical Statistics with Applications in R" 2nd Ed., 2015)

"Statistics can be defined as a collection of techniques used when planning a data collection, and when subsequently analyzing and presenting data." (Birger S Madsen, "Statistics for Non-Statisticians", 2016)

"Statistics is the science of collecting, organizing, and interpreting numerical facts, which we call data. […] Statistics is the science of learning from data." (Moore McCabe & Alwan Craig, "The Practice of Statistics for Business and Economics" 4th Ed., 2016)

"Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions. In addition, statistics is about providing a measure of confidence in any conclusions." (Michael Sullivan, "Statistics: Informed Decisions Using Data", 5th Ed., 2017)

"Estimates based on data are often uncertain. If the data were intended to tell us something about a wider population (like a poll of voting intentions before an election), or about the future, then we need to acknowledge that uncertainty. This is a double challenge for data visualization: it has to be calculated in some meaningful way and then shown on top of the data or statistics without making it all too cluttered." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Good statistics are not a trick, although they are a kind of magic. Good statistics are not smoke and mirrors; in fact, they help us see more clearly. Good statistics are like a telescope for an astronomer, a microscope for a bacteriologist, or an X-ray for a radiologist. If we are willing to let them, good statistics help us see things about the world around us and about ourselves - both large and small - that we would not be able to see in any other way." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Ideally, a decision maker or a forecaster will combine the outside view and the inside view - or, similarly, statistics plus personal experience. But it’s much better to start with the statistical view, the outside view, and then modify it in the light of personal experience than it is to go the other way around. If you start with the inside view you have no real frame of reference, no sense of scale - and can easily come up with a probability that is ten times too large, or ten times too small." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"If we don’t understand the statistics, we’re likely to be badly mistaken about the way the world is. It is all too easy to convince ourselves that whatever we’ve seen with our own eyes is the whole truth; it isn’t. Understanding causation is tough even with good statistics, but hopeless without them. [...] And yet, if we understand only the statistics, we understand little. We need to be curious about the world that we see, hear, touch, and smell, as well as the world we can examine through a spreadsheet." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"The contradiction between what we see with our own eyes and what the statistics claim can be very real. […] The truth is more complicated. Our personal experiences should not be dismissed along with our feelings, at least not without further thought. Sometimes the statistics give us a vastly better way to understand the world; sometimes they mislead us. We need to be wise enough to figure out when the statistics are in conflict with everyday experience - and in those cases, which to believe." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"The whole discipline of statistics is built on measuring or counting things. […] it is important to understand what is being measured or counted, and how. It is surprising how rarely we do this. Over the years, as I found myself trying to lead people out of statistical mazes week after week, I came to realize that many of the problems I encountered were because people had taken a wrong turn right at the start. They had dived into the mathematics of a statistical claim - asking about sampling errors and margins of error, debating if the number is rising or falling, believing, doubting, analyzing, dissecting - without taking the ti- me to understand the first and most obvious fact: What is being measured, or counted? What definition is being used?" (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

🦋Science: On Errors in Statistics (Quotes)

"[It] may be laid down as a general rule that, if the result of a long series of precise observations approximates a simple relation so closely that the remaining difference is undetectable by observation and may be attributed to the errors to which they are liable, then this relation is probably that of nature." (Pierre-Simon Laplace, "Mémoire sur les Inégalites Séculaires des Planètes et des Satellites", 1787)

"It is surprising to learn the number of causes of error which enter into the simplest experiment, when we strive to attain rigid accuracy." (William S Jevons, "The Principles of Science: A Treatise on Logic and Scientific Method", 1874)

"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)

"If the number of experiments be very large, we may have precise information as to the value of the mean, but if our sample be small, we have two sources of uncertainty: (I) owing to the 'error of random sampling' the mean of our series of experiments deviates more or less widely from the mean of the population, and (2) the sample is not sufficiently large to determine what is the law of distribution of individuals." (William S Gosset, "The Probable Error of a Mean", Biometrika, 1908)

"We know not to what are due the accidental errors, and precisely because we do not know, we are aware they obey the law of Gauss. Such is the paradox." (Henri Poincaré, "The Foundations of Science", 1913)

"No observations are absolutely trustworthy. In no field of observation can we entirely rule out the possibility that an observation is vitiated by a large measurement or execution error. If a reading is found to lie a very long way from its fellows in a series of replicate observations, there must be a suspicion that the deviation is caused by a blunder or gross error of some kind. [...] One sufficiently erroneous reading can wreck the whole of a statistical analysis, however many observations there are." (Francis J Anscombe, "Rejection of Outliers", Technometrics Vol. 2 (2), 1960)

"It might be reasonable to expect that the more we know about any set of statistics, the greater the confidence we would have in using them, since we would know in which directions they were defective; and that the less we know about a set of figures, the more timid and hesitant we would be in using them. But, in fact, it is the exact opposite which is normally the case; in this field, as in many others, knowledge leads to caution and hesitation, it is ignorance that gives confidence and boldness. For knowledge about any set of statistics reveals the possibility of error at every stage of the statistical process; the difficulty of getting complete coverage in the returns, the difficulty of framing answers precisely and unequivocally, doubts about the reliability of the answers, arbitrary decisions about classification, the roughness of some of the estimates that are made before publishing the final results. Knowledge of all this, and much else, in detail, about any set of figures makes one hesitant and cautious, perhaps even timid, in using them." (Ely Devons, "Essays in Economics", 1961)

"The art of using the language of figures correctly is not to be over-impressed by the apparent ai

"Measurement, we have seen, always has an element of error in it. The most exact description or prediction that a scientist can make is still only approximate." (Abraham Kaplan, "The Conduct of Inquiry: Methodology for Behavioral Science", 1964)

"A mature science, with respect to the matter of errors in variables, is not one that measures its variables without error, for this is impossible. It is, rather, a science which properly manages its errors, controlling their magnitudes and correctly calculating their implications for substantive conclusions." (Otis D Duncan, "Introduction to Structural Equation Models", 1975)

"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)

"Linear regression assumes that in the population a normal distribution of error values around the predicted Y is associated with each X value, and that the dispersion of the error values for each X value is the same. The assumptions imply normal and similarly dispersed error distributions." (Fred C Pampel, "Linear Regression: A primer", 2000)

"Compound errors can begin with any of the standard sorts of bad statistics - a guess, a poor sample, an inadvertent transformation, perhaps confusion over the meaning of a complex statistic. People inevitably want to put statistics to use, to explore a number's implications. [...] The strengths and weaknesses of those original numbers should affect our confidence in the second-generation statistics." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Trimming potentially theoretically meaningful variables is not advisable unless one is quite certain that the coefficient for the variable is near zero, that the variable is inconsequential, and that trimming will not introduce misspecification error." (James Jaccard, "Interaction Effects in Logistic Regression", 2001)

"The central limit theorem says that, under conditions almost always satisfied in the real world of experimentation, the distribution of such a linear function of errors will tend to normality as the number of its components becomes large. The tendency to normality occurs almost regardless of the individual distributions of the component errors. An important proviso is that several sources of error must make important contributions to the overall error and that no particular source of error dominate the rest." (George E P Box et al, "Statistics for Experimenters: Design, discovery, and innovation" 2^nd Ed., 2005)

"Two things explain the importance of the normal distribution: (1) The central limit effect that produces a tendency for real error distributions to be 'normal like'. (2) The robustness to nonnormality of some common statistical procedures, where 'robustness' means insensitivity to deviations from theoretical normality." (George E P Box et al, "Statistics for Experimenters: Design, discovery, and innovation" 2^nd Ed., 2005)

"Always expect to find at least one error when you proofread your own statistics. If you don’t, you are probably making the same mistake twice." (Cheryl Russell)

[Murphy’s Laws of Analysis:] "(1) In any collection of data, the figures that are obviously correct contain errors. (2) It is customary for a decimal to be misplaced. (3) An error that can creep into a calculation, will. Also, it will always be in the direction that will cause the most damage to the calculation." (G C Deakly)

🦋Science: On Numbers (Quotes)

"Figures are not always facts." (Aesop, "The Widow and the Hen", cca. 6th century BC)

"Things that matter most
Must never be at the mercy of things that matter least.
The first sign we don’t know what we are doing is an obsession with numbers." (Johann Wolfgang von Goethe)

"Round numbers are always false." (Samuel Johnson, [Letter to Thomas Boswell], 1778)

"There is no inquiry which is not finally reducible to a question of Numbers; for there is none which may not be conceived of as consisting in the determination of quantities by each other, according to certain relations." (Auguste Comte, “The Positive Philosophy”, 1830)

"There are two aspects of statistics that are continually mixed, the method and the science. Statistics are used as a method, whenever we measure something, for example, the size of a district, the number of inhabitants of a country, the quantity or price of certain commodities, etc. […] There is, moreover, a science of statistics. It consists of knowing how to gather numbers, combine them and calculate them, in the best way to lead to certain results. But this is, strictly speaking, a branch of mathematics." (Alphonse P de Candolle, "Considerations on Crime Statistics", 1833)

"If statistical graphics, although born just yesterday, extends its reach every day, it is because it replaces long tables of numbers and it allows one not only to embrace at glance the series of phenomena, but also to signal the correspondences or anomalies, to find the causes, to identify the laws." (Émile Cheysson, cca. 1877) 

"[…] when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meager and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely in your thoughts advanced to the state of science." (William T Kelvin, "Electrical Units of Measurement", 1883)

"Statistics may, for instance, be called the science of counting. Counting appears at first sight to be a very simple operation, which any one can perform or which can be done automatically; but, as a matter of fact, when we come to large numbers, e.g., the population of the United Kingdom, counting is by no means easy, or within the power of an individual; limits of time and place alone prevent it being so carried out, and in no way can absolute accuracy be obtained when the numbers surpass certain limits." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"Statistics may rightly be called the science of averages. […] Great numbers and the averages resulting from them, such as we always obtain in measuring social phenomena, have great inertia. […] It is this constancy of great numbers that makes statistical measurement possible. It is to great numbers that statistical measurement chiefly applies." (Sir Arthur L Bowley, "Elements of Statistics", 1901)

"Statistics is the name for that science and art which deals with uncertain inferences - which uses numbers to find out something about nature and experience." (Warren Weaver, 1952)

"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)

"Quantitative performance measurements - whether single, multiple, or composite - are seen to have undesirable consequences for over-all organizational performance. The complexity of large organizations requires better knowledge of organizational behavior for managers to make best use of the personnel available to them." (V F Ridgway, "Dysfunctional Consequences of Performance Measurements", Administrative Science Quarterly Vol. 1 (2), 1956)

"The purpose of computing is insight, not numbers […] sometimes […] the purpose of computing numbers is not yet in sight." (Richard Hamming, "Numerical Methods for Scientists and Engineers", 1962)

"A well constructed numerical estimate can be worth a thousand words." (Charles L Schultze, 1967)

"What goes wrong [in long-range planning] is that sensible anticipation gets converted into foolish numbers: and their validity always hinges on large loose assumptions." (Robert Heller, "The Naked Manager: Games Executives Play", 1972)

"[...] be wary of analysts that try to quantify the unquantifiable." (Ralph Keeney & Raiffa Howard, "Decisions with Multiple Objectives: Preferences and Value Trade-offs", 1976)

"Our mistake is not that we take our theories too seriously, but that we do not take them seriously enough. It is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world." (Steven Weinberg, "The First Three Minutes", 1977)

"Numbers are the product of counting. Quantities are the product of measurement. This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three there is a jump. In the case of quantity there is no such jump, and because jump is missing in the world of quantity it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate." (Gregory Bateson, "Number is Different from Quantity", CoEvolution Quarterly, 1978)

"People often feel inept when faced with numerical data. Many of us think that we lack numeracy, the ability to cope with numbers. […] The fault is not in ourselves, but in our data. Most data are badly presented and so the cure lies with the producers of the data. To draw an analogy with literacy, we do not need to learn to read better, but writers need to be taught to write better." (Andrew Ehrenberg, "The problem of numeracy", American Statistician 35(2), 1981)

“Data in isolation are meaningless, a collection of numbers. Only in context of a theory do they assume significance […]” (George Greenstein, “Frozen Star”, 1983)

"Inept graphics also flourish because many graphic artists believe that statistics are boring and tedious. It then follows that decorated graphics must pep up, animate, and all too often exaggerate what evidence there is in the data. […] If the statistics are boring, then you've got the wrong numbers." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"A final goal of any scientific theory must be the derivation of numbers. Theories stand or fall, ultimately, upon numbers." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)

"The drudgery of the numbers will make you free." (Harold Geneen, "Managing", 1984)

"The professional's grasp of the numbers is a measure of the control he has over the events that the figures represent." (Harold Geneen, Managing, 1984)

"When you have mastered the numbers, you will in fact no longer be reading numbers, any more than you read words when reading a book. You will be reading meanings." (Harold Geneen & Alvin Moscow, "Managing", 1984)

"Numbers have undoubted powers to beguile and benumb, but critics must probe behind numbers to the character of arguments and the biases that motivate them." (Stephen J Gould, "An Urchin in the Storm: Essays About Books and Ideas", 1987)

"Whenever decisions are made strictly on the basis of bottom-line arithmetic, human beings get crunched along with the numbers." (Thomas R Horton, Management Review, 1987)

"When you are drowning in numbers you need a system to separate the wheat from the chaff." (Anthony Adams, The New York Times, 1988)

"Torture numbers, and they will confess to anything." (Gregg Easterbrook, New Republic, 1989)

"[…] you simply cannot make sense of any number without a contextual basis. Yet the traditional attempts to provide this contextual basis are often flawed in their execution. [...] Data have no meaning apart from their context. Data presented without a context are effectively rendered meaningless." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Big numbers warn us that the problem is a common one, compelling our attention, concern, and action. The media like to report statistics because numbers seem to be 'hard facts' - little nuggets of indisputable truth. [...] One common innumerate error involves not distinguishing among large numbers. [...] Because many people have trouble appreciating the differences among big numbers, they tend to uncritically accept social statistics (which often, of course, feature big numbers)." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Big numbers warn us that the problem is a common one, compelling our attention, concern, and action. The media like to report statistics because numbers seem to be 'hard facts' - little nuggets of indisputable truth. [...] One common innumerate error involves not distinguishing among large numbers. [...] Because many people have trouble appreciating the differences among big numbers, they tend to uncritically accept social statistics (which often, of course, feature big numbers)." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Not all statistics start out bad, but any statistic can be made worse. Numbers - even good numbers - can be misunderstood or misinterpreted. Their meanings can be stretched, twisted, distorted, or mangled. These alterations create what we can call mutant statistics - distorted versions of the original figures." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Every number has its limitations; every number is a product of choices that inevitably involve compromise. Statistics are intended to help us summarize, to get an overview of part of the world’s complexity. But some information is always sacrificed in the process of choosing what will be counted and how. Something is, in short, always missing. In evaluating statistics, we should not forget what has been lost, if only because this helps us understand what we still have." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)

"In much the same way, people create statistics: they choose what to count, how to go about counting, which of the resulting numbers they share with others, and which words they use to describe and interpret those figures. Numbers do not exist independent of people; understanding numbers requires knowing who counted what, why they bothered counting, and how they went about it." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)

"Data, reason, and calculation can only produce conclusions; they do not inspire action. Good numbers are not the result of managing numbers." (Ronald J Baker, "Measure what Matters to Customers: Using Key Predictive Indicators", 2006)

"Statistics can certainly pronounce a fact, but they cannot explain it without an underlying context, or theory. Numbers have an unfortunate tendency to supersede other types of knowing. […] Numbers give the illusion of presenting more truth and precision than they are capable of providing." (Ronald J Baker, "Measure what Matters to Customers: Using Key Predictive Indicators", 2006)

"Our culture, obsessed with numbers, has given us the idea that what we can measure is more important than what we can't measure. Think about that for a minute. It means that we make quantity more important than quality." (Donella Meadows, "Thinking in Systems: A Primer", 2008)

"What gets measured gets managed - even when it’s pointless to measure and manage it, and even if it harms the purpose of the organisation to do so." (Simon Caulkin, "The rule is simple: be careful what you measure", 2008) [source]

"What gets measured gets managed - so be sure you have the right measures, because the wrong ones kill." (Simon Caulkin, "The rule is simple: be careful what you measure", 2008) [source]

"By giving numbers a proper shape, by visually encoding them, the graphic has saved you time and energy that you would otherwise waste if you had to use a table that was not designed to aid your mind." (Alberto Cairo, "The Functional Art", 2011) 

"The value of having numbers - data - is that they aren't subject to someone else's interpretation. They are just the numbers. You can decide what they mean for you." (Emily Oster, "Expecting Better", 2013)

"One very common problem in data visualization is that encoding numerical variables to area is incredibly popular, but readers can’t translate it back very well." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"As long as measurements are abused as a tool of control, measuring will remain the weakest area in a manager’s performance." (Peter Drucker)

"If the statistics are boring, you've got the wrong numbers." (Edward Tufte)

"Nothing is so fallacious as facts, except figures." (George Canning) [attributed]

"Sometimes the numbers don’t explain everything. The numbers are not the business - they are symbols of the business." (Gerald Deitchle)

"Strategic planning is not strategic thinking. Indeed, strategic planning often spoils strategic thinking, causing managers to confuse real vision with the manipulation of numbers." (Henry Mintzberg)