On Data Analysis (1970-1979)

"Statistical methods are tools of scientific investigation. Scientific investigation is a controlled learning process in which various aspects of a problem are illuminated as the study proceeds. It can be thought of as a major iteration within which secondary iterations occur. The major iteration is that in which a tentative conjecture suggests an experiment, appropriate analysis of the data so generated leads to a modified conjecture, and this in turn leads to a new experiment, and so on." (George E P Box & George C Tjao, "Bayesian Inference in Statistical Analysis", 1973)

"Almost all efforts at data analysis seek, at some point, to generalize the results and extend the reach of the conclusions beyond a particular set of data. The inferential leap may be from past experiences to future ones, from a sample of a population to the whole population, or from a narrow range of a variable to a wider range. The real difficulty is in deciding when the extrapolation beyond the range of the variables is warranted and when it is merely naive. As usual, it is largely a matter of substantive judgment - or, as it is sometimes more delicately put, a matter of 'a priori nonstatistical considerations'." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"[…] it is not enough to say: 'There's error in the data and therefore the study must be terribly dubious'. A good critic and data analyst must do more: he or she must also show how the error in the measurement or the analysis affects the inferences made on the basis of that data and analysis." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"The use of statistical methods to analyze data does not make a study any more 'scientific', 'rigorous', or 'objective'. The purpose of quantitative analysis is not to sanctify a set of findings. Unfortunately, some studies, in the words of one critic, 'use statistics as a drunk uses a street lamp, for support rather than illumination'. Quantitative techniques will be more likely to illuminate if the data analyst is guided in methodological choices by a substantive understanding of the problem he or she is trying to learn about. Good procedures in data analysis involve techniques that help to (a) answer the substantive questions at hand, (b) squeeze all the relevant information out of the data, and (c) learn something new about the world." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Typically, data analysis is messy, and little details clutter it. Not only confounding factors, but also deviant cases, minor problems in measurement, and ambiguous results lead to frustration and discouragement, so that more data are collected than analyzed. Neglecting or hiding the messy details of the data reduces the researcher's chances of discovering something new." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

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

"[...] exploratory data analysis is an attitude, a state of flexibility, a willingness to look for those things that we believe are not there, as well as for those we believe might be there. Except for its emphasis on graphs, its tools are secondary to its purpose." (John W Tukey, [comment] 1979)

On Data Analysis (1990-1999)

"[…] data analysis in the context of basic mathematical concepts and skills. The ability to use and interpret simple graphical and numerical descriptions of data is the foundation of numeracy […] Meaningful data aid in replacing an emphasis on calculation by the exercise of judgement and a stress on interpreting and communicating results." (David S Moore, "Statistics for All: Why, What and How?", 1990)

"Data analysis is rarely as simple in practice as it appears in books. Like other statistical techniques, regression rests on certain assumptions and may produce unrealistic results if those assumptions are false. Furthermore it is not always obvious how to translate a research question into a regression model." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"Data analysis typically begins with straight-line models because they are simplest, not because we believe reality is inherently linear. Theory or data may suggest otherwise [...]" (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"90 percent of all problems can be solved by using the techniques of data stratification, histograms, and control charts. Among the causes of nonconformance, only one-fifth or less are attributable to the workers." (Kaoru Ishikawa, The Quality Management Journal Vol. 1, 1993)

"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)

"Visualization is an approach to data analysis that stresses a penetrating look at the structure of data. No other approach conveys as much information. […] Conclusions spring from data when this information is combined with the prior knowledge of the subject under investigation." (William S Cleveland, "Visualizing Data", 1993)

"When the distributions of two or more groups of univariate data are skewed, it is common to have the spread increase monotonically with location. This behavior is monotone spread. Strictly speaking, monotone spread includes the case where the spread decreases monotonically with location, but such a decrease is much less common for raw data. Monotone spread, as with skewness, adds to the difficulty of data analysis. For example, it means that we cannot fit just location estimates to produce homogeneous residuals; we must fit spread estimates as well. Furthermore, the distributions cannot be compared by a number of standard methods of probabilistic inference that are based on an assumption of equal spreads; the standard t-test is one example. Fortunately, remedies for skewness can cure monotone spread as well." (William S Cleveland, "Visualizing Data", 1993)

"A careful and sophisticated analysis of the data is often quite useless if the statistician cannot communicate the essential features of the data to a client for whom statistics is an entirely foreign language." (Christopher J Wild, "Embracing the ‘Wider view’ of Statistics", The American Statistician 48, 1994)

"Science is not impressed with a conglomeration of data. It likes carefully constructed analysis of each problem." (Daniel E Koshland Jr, Science Vol. 263 (5144), [editorial] 1994)

"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)

On Data Analysis (2010-2019)

"The discrepancy between our mental models and the real world may be a major problem of our times; especially in view of the difficulty of collecting, analyzing, and making sense of the unbelievable amount of data to which we have access today." (Ugo Bardi, "The Limits to Growth Revisited", 2011)

"Too often there is a disconnect between the people who run a study and those who do the data analysis. This is as predictable as it is unfortunate. If data are gathered with particular hypotheses in mind, too often they (the data) are passed on to someone who is tasked with testing those hypotheses and who has only marginal knowledge of the subject matter. Graphical displays, if prepared at all, are just summaries or tests of the assumptions underlying the tests being done. Broader displays, that have the potential of showing us things that we had not expected, are either not done at all, or their message is not able to be fully appreciated by the data analyst." (Howard Wainer, Comment, Journal of Computational and Graphical Statistics Vol. 20(1), 2011)

"Data analysis is not generally thought of as being simple or easy, but it can be. The first step is to understand that the purpose of data analysis is to separate any signals that may be contained within the data from the noise in the data. Once you have filtered out the noise, anything left over will be your potential signals. The rest is just details." (Donald J Wheeler," Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)

"The four questions of data analysis are the questions of description, probability, inference, and homogeneity. Any data analyst needs to know how to organize and use these four questions in order to obtain meaningful and correct results. [...] 

THE DESCRIPTION QUESTION: Given a collection of numbers, are there arithmetic values that will summarize the information contained in those numbers in some meaningful way?

THE PROBABILITY QUESTION: Given a known universe, what can we say about samples drawn from this universe? [...] 

THE INFERENCE QUESTION: Given an unknown universe, and given a sample that is known to have been drawn from that unknown universe, and given that we know everything about the sample, what can we say about the unknown universe? [...] 

THE HOMOGENEITY QUESTION: Given a collection of observations, is it reasonable to assume that they came from one universe, or do they show evidence of having come from multiple universes?" (Donald J Wheeler," Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)

"Each systems archetype embodies a particular theory about dynamic behavior that can serve as a starting point for selecting and formulating raw data into a coherent set of interrelationships. Once those relationships are made explicit and precise, the 'theory' of the archetype can then further guide us in our data-gathering process to test the causal relationships through direct observation, data analysis, or group deliberation." (Daniel H Kim, "Systems Archetypes as Dynamic Theories", The Systems Thinker Vol. 24 (1), 2013)

"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)

"The random element in most data analysis is assumed to be white noise - normal errors independent of each other. In a time series, the errors are often linked so that independence cannot be assumed (the last examples). Modeling the nature of this dependence is the key to time series." (DeWayne R Derryberry, "Basic data analysis for time series with R", 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)

"The dialectical interplay of experiment and theory is a key driving force of modern science. Experimental data do only have meaning in the light of a particular model or at least a theoretical background. Reversely theoretical considerations may be logically consistent as well as intellectually elegant: Without experimental evidence they are a mere exercise of thought no matter how difficult they are. Data analysis is a connector between experiment and theory: Its techniques advise possibilities of model extraction as well as model testing with experimental data." (Achim Zielesny, "From Curve Fitting to Machine Learning" 2^nd Ed., 2016)

"[…] the data itself can lead to new questions too. In exploratory data analysis (EDA), for example, the data analyst discovers new questions based on the data. The process of looking at the data to address some of these questions generates incidental visualizations - odd patterns, outliers, or surprising correlations that are worth looking into further." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical domain of interest. 'Structure' has long been understood as symmetry which can take many forms with respect to any transformation, including point, translational, rotational, and many others. Symmetries directly point to invariants, which pinpoint intrinsic properties of the data and of the background empirical domain of interest. As our data models change, so too do our perspectives on analysing data." (Fionn Murtagh, "Data Science Foundations: Geometry and Topology of Complex Hierarchic Systems and Big Data Analytics", 2018)

"Analysis is a two-step process that has an exploratory and an explanatory phase. In order to create a powerful data story, you must effectively transition from data discovery (when you’re finding insights) to data communication (when you’re explaining them to an audience). If you don’t properly traverse these two phases, you may end up with something that resembles a data story but doesn’t have the same effect. Yes, it may have numbers, charts, and annotations, but because it’s poorly formed, it won’t achieve the same results." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)

"While visuals are an essential part of data storytelling, data visualizations can serve a variety of purposes from analysis to communication to even art. Most data charts are designed to disseminate information in a visual manner. Only a subset of data compositions is focused on presenting specific insights as opposed to just general information. When most data compositions combine both visualizations and text, it can be difficult to discern whether a particular scenario falls into the realm of data storytelling or not." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)

On Data Analysis (2000-2009)

"Data are generally collected as a basis for action. However, unless potential signals are separated from probable noise, the actions taken may be totally inconsistent with the data. Thus, the proper use of data requires that you have simple and effective methods of analysis which will properly separate potential signals from probable noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"No matter what the data, and no matter how the values are arranged and presented, you must always use some method of analysis to come up with an interpretation of the data. [...] While every data set contains noise, some data sets may contain signals. Therefore, before you can detect a signal within any given data set, you must first filter out the noise." (Donald J Wheeler," Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"The purpose of analysis is insight. The best analysis is the simplest analysis which provides the needed insight." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Without meaningful data there can be no meaningful analysis. The interpretation of any data set must be based upon the context of those data." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Statistical analysis of data can only be performed within the context of selected assumptions, models, and/or prior distributions. A statistical analysis is actually the extraction of substantive information from data and assumptions. And herein lies the rub, understood well by Disraeli and others skeptical of our work: For given data, an analysis can usually be selected which will result in 'information' more favorable to the owner of the analysis then is objectively warranted." (Stephen B Vardeman & Max D Morris, "Statistics and Ethics: Some Advice for Young Statisticians", The American Statistician vol 57, 2003)

"Exploratory Data Analysis is more than just a collection of data-analysis techniques; it provides a philosophy of how to dissect a data set. It stresses the power of visualisation and aspects such as what to look for, how to look for it and how to interpret the information it contains. Most EDA techniques are graphical in nature, because the main aim of EDA is to explore data in an open-minded way. Using graphics, rather than calculations, keeps open possibilities of spotting interesting patterns or anomalies that would not be apparent with a calculation (where assumptions and decisions about the nature of the data tend to be made in advance)." (Alan Graham, "Developing Thinking in Statistics", 2006)

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

"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)

"Data analysis is careful thinking about evidence." (Michael Milton, "Head First Data Analysis", 2009)

"Doing data analysis without explicitly defining your problem or goal is like heading out on a road trip without having decided on a destination." (Michael Milton, "Head First Data Analysis", 2009)

On Data Analysis (1980-1989)

"[...] any hope that we are smart enough to find even transiently optimum solutions to our data analysis problems is doomed to failure, and, indeed, if taken seriously, will mislead us in the allocation of effort, thus wasting both intellectual and computational effort." (John W Tukey, "Choosing Techniques for the Analysis of Data", 1981)

"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)

"Exploratory data analysis, EDA, calls for a relatively free hand in exploring the data, together with dual obligations: (•) to look for all plausible alternatives and oddities - and a few implausible ones, (graphic techniques can be most helpful here) and (•) to remove each appearance that seems large enough to be meaningful - ordinarily by some form of fitting, adjustment, or standardization [...] so that what remains, the residuals, can be examined for further appearances." (John W Tukey, "Introduction to Styles of Data Analysis Techniques", 1982)

"A competent data analysis of an even moderately complex set of data is a thing of trials and retreats, of dead ends and branches." (John W Tukey, Computer Science and Statistics: Proceedings of the 14th Symposium on the Interface, 1983)

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

"Iteration and experimentation are important for all of data analysis, including graphical data display. In many cases when we make a graph it is immediately clear that some aspect is inadequate and we regraph the data. In many other cases we make a graph, and all is well, but we get an idea for studying the data in a different way with a different graph; one successful graph often suggests another." (William S Cleveland, "The Elements of Graphing Data", 1985)

"There are some who argue that a graph is a success only if the important information in the data can be seen within a few seconds. While there is a place for rapidly-understood graphs, it is too limiting to make speed a requirement in science and technology, where the use of graphs ranges from, detailed, in-depth data analysis to quick presentation." (William S Cleveland, "The Elements of Graphing Data", 1985)

"A first analysis of experimental results should, I believe, invariably be conducted using flexible data analytical techniques - looking at graphs and simple statistics - that so far as possible allow the data to 'speak for themselves'. The unexpected phenomena that such a approach often uncovers can be of the greatest importance in shaping and sometimes redirecting the course of an ongoing investigation." (George Box, "Signal to Noise Ratios, Performance Criteria, and Transformations", Technometrics 30, 1988)

"Data analysis is an art practiced by individuals who are skilled at quantitative reasoning and have much experience in looking at numbers and detecting  patterns in data. Usually these individuals have some background in statistics." (David Lubinsky, Daryl Pregibon , "Data analysis as search", Journal of Econometrics Vol. 38 (1–2), 1988)

"Like a detective, a data analyst will experience many dead ends, retrace his steps, and explore many alternatives before settling on a single description of the evidence in front of him." (David Lubinsky & Daryl Pregibon , "Data analysis as search", Journal of Econometrics Vol. 38 (1–2), 1988)

On Data Analysis (1950-1969)

"In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data." (James C Maxwell, [letter to Lewis Campbell] 1851)

"Not even the most subtle and skilled analysis can overcome completely the unreliability of basic data." (Roy D G Allen, "Statistics for Economists", 1951)

"The technical analysis of any large collection of data is a task for a highly trained and expensive man who knows the mathematical theory of statistics inside and out. Otherwise the outcome is likely to be a collection of drawings - quartered pies, cute little battleships, and tapering rows of sturdy soldiers in diversified uniforms - interesting enough in the colored Sunday supplement, but hardly the sort of thing from which to draw reliable inferences." (Eric T Bell, "Mathematics: Queen and Servant of Science", 1951)

"If data analysis is to be well done, much of it must be a matter of judgment, and ‘theory’ whether statistical or non-statistical, will have to guide, not command." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics, Vol. 33 (1), 1962)

"The most important maxim for data analysis to heed, and one which many statisticians seem to have shunned is this: ‘Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.’ Data analysis must progress by approximate answers, at best, since its knowledge of what the problem really is will at best be approximate." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics, Vol. 33, No. 1, 1962)

"The first step in data analysis is often an omnibus step. We dare not expect otherwise, but we equally dare not forget that this step, and that step, and other step, are all omnibus steps and that we owe the users of such techniques a deep and important obligation to develop ways, often varied and competitive, of replacing omnibus procedures by ones that are more sharply focused." (John W Tukey, "The Future of Processes of Data Analysis", 1965)

"The basic general intent of data analysis is simply stated: to seek through a body of data for interesting relationships and information and to exhibit the results in such a way as to make them recognizable to the data analyzer and recordable for posterity. Its creative task is to be productively descriptive, with as much attention as possible to previous knowledge, and thus to contribute to the mysterious process called insight." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"Comparable objectives in data analysis are (l) to achieve more specific description of what is loosely known or suspected; (2) to find unanticipated aspects in the data, and to suggest unthought-of-models for the data's summarization and exposure; (3) to employ the data to assess the (always incomplete) adequacy of a contemplated model; (4) to provide both incentives and guidance for further analysis of the data; and (5) to keep the investigator usefully stimulated while he absorbs the feeling of his data and considers what to do next." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"Data analysis must be iterative to be effective. [...] The iterative and interactive interplay of summarizing by fit and exposing by residuals is vital to effective data analysis. Summarizing and exposing are complementary and pervasive." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"Every student of the art of data analysis repeatedly needs to build upon his previous statistical knowledge and to reform that foundation through fresh insights and emphasis." (John W Tukey, "Data Analysis, Including Statistics", 1968)

"[...] bending the question to fit the analysis is to be shunned at all costs." (John W Tukey, "Analyzing Data: Sanctification or Detective Work?", 1969)

On Data: Longitudinal Data

 "Longitudinal data sets are comprised of repeated observations of an outcome and a set of covariates for each of many subjects. One objective of statistical analysis is to describe the marginal expectation of the outcome variable as a function of the covariates while accounting for the correlation among the repeated observations for a given subject." (Scott L Zeger & Kung-Yee Liang, "Longitudinal Data Analysis for Discrete and Continuous Outcomes", Biometrics Vol. 42(1), 1986)

"Longitudinal data sets in which the outcome variable cannot be transformed to be Gaussian are more difficult to analyze for two reasons. First, simple models for the conditional expectation of the outcome do not imply equally simple models for the marginal expectation, as is the case for Gaussian data. Hence, the analyst must choose to model either the marginal or conditional expectation. Second, likelihood analyses often lead to estimators of the regression coefficients which are consistent only when the time dependence is correctly specified." (Scott L Zeger & Kung-Yee Liang, "Longitudinal Data Analysis for Discrete and Continuous Outcomes", Biometrics Vol. 42(1), 1986)

"Longitudinal data comprise repeated observations over time on each of many individuals. Longitudinal data are in contrast to cross-sectional data where only a single response is available for each person. The statistical analysis of longitudinal data presents special opportunities and challenges because the repeated outcomes for one individual tend to be correlated with one another." (Scott L Zeger & Kung‐Yee Liang, "An overview of methods for the analysis of longitudinal data", Statistics in medicine vol. 11, 1992)

"We have two objectives for statistical models of longitudinal data: (1) to adopt the conventional regression tools, which relate the response variables to the explanatory variables; and (2) to account for the within subject correlation." (Scott L Zeger & Kung‐Yee Liang, "An overview of methods for the analysis of longitudinal data", Statistics in medicine vol. 11, 1992)

"Analysis of longitudinal data tends to be simpler because subjects can usually be assumed independent. Valid inferences can be made by borrowing strength across people. That is, the consistency of a pattern across subjects is the basis for substantive conclusions. For this reason, inferences from longitudinal studies can be made more robust to model assumptions than those from time series data, particularly to assumptions about the nature of the correlation." (Peter J Diggle et al, "Analysis of Longitudinal Data", 2002)

"The defining feature of a longitudinal data set is repeated observations on individuals enabling direct study of change. Longitudinal data require special statistical methods because the set of observations on one subject tends to be intercorrelated. This correlation must be taken into account to draw valid scientific inferences." (Peter J Diggle et al, "Analysis of Longitudinal Data", 2002)

David Spiegelhalter - Collected Quotes

"A classification tree is perhaps the simplest form of algorithm, since it consists of a series of yes/no questions, the answer to each deciding the next question to be asked, until a conclusion is reached." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"Bootstrapping provides an intuitive, computer-intensive way of assessing the uncertainty in our estimates, without making strong assumptions and without using probability theory. But the technique is not feasible when it comes to, say, working out the margins of error on unemployment surveys of 100,000 people. Although bootstrapping is a simple, brilliant and extraordinarily effective idea, it is just too clumsy to bootstrap such large quantities of data, especially when a convenient theory exists that can generate formulae for the width of uncertainty intervals." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"But [bootstrap-based] simulations are clumsy and time-consuming, especially with large data sets, and in more complex circumstances it is not straightforward to work out what should be simulated. In contrast, formulae derived from probability theory provide both insight and convenience, and always lead to the same answer since they don’t depend on a particular simulation. But the flip side is that this theory relies on assumptions, and we should be careful not to be deluded by the impressive algebra into accepting unjustified conclusions." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"[...] data often has some errors, outliers and other strange values, but these do not necessarily need to be individually identified and excluded. It also points to the benefits of using summary measures that are not unduly affected by odd observations [...] are known as robust measures, and include the median and the inter-quartile range." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"Even in an era of open data, data science and data journalism, we still need basic statistical principles in order not to be misled by apparent patterns in the numbers." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"[...] in the statistical world, what we see and measure around us can be considered as the sum of a systematic mathematical idealized form plus some random contribution that cannot yet be explained. This is the classic idea of the signal and the noise." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"It is convenient to use a single number to summarize a steadily increasing or decreasing relationship between the pairs of numbers shown on a scatter-plot. This is generally chosen to be the Pearson correlation coefficient [...]. A Pearson correlation runs between −1 and 1, and expresses how close to a straight line the dots or data-points fall. A correlation of 1 occurs if all the points lie on a straight line going upwards, while a correlation of −1 occurs if all the points lie on a straight line going downwards. A correlation near 0 can come from a random scatter of points, or any other pattern in which there is no systematic trend upwards or downwards [...]." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"It is not enough to give a single summary for a distribution - we need to have an idea of the spread, sometimes known as the variability. [...] The range is a natural choice, but is clearly very sensitive to extreme values [...] In contrast the inter-quartile range (IQR) is unaffected by extremes. This is the distance between the 25th and 75th percentiles of the data and so contains the ‘central half’ of the numbers [...] Finally the standard deviation is a widely used measure of spread. It is the most technically complex measure, but is only really appropriate for well-behaved symmetric data since it is also unduly influenced by outlying values." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"[...] just because we act, and something changes, it doesn’t mean we were responsible for the result. Humans seem to find this simple truth difficult to grasp - we are always keen to construct an explanatory narrative, and even keener if we are at its centre. Of course sometimes this interpretation is true - if you flick a switch, and the light comes on, then you are usually responsible. But sometimes your actions are clearly not responsible for an outcome: if you don’t take an umbrella, and it rains, it is not your fault (although it may feel that way). But the consequences of many of our actions are less clear-cut. [...] We have a strong psychological tendency to attribute change to intervention, and this makes before-and-after comparisons treacherous." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"Mean-averages can be highly misleading when the raw data do not form a symmetric pattern around a central value but instead are skewed towards one side [...], typically with a large group of standard cases but with a tail of a few either very high (for example, income) or low (for example, legs) values." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"Statistical models have two main components. First, a mathematical formula that expresses a deterministic, predictable component, for example the fitted straight line that enables us to make a prediction [...]. But the deterministic part of a model is not going to be a perfect representation of the observed world [...] and the difference between what the model predicts, and what actually happens, is the second component of a model and is known as the residual error - although it is important to remember that in statistical modelling, ‘error’ does not refer to a mistake, but the inevitable inability of a model to exactly represent what we observe." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"[...] the Central Limit Theorem [...] says that the distribution of sample means tends towards the form of a normal distribution with increasing sample size, almost regardless of the shape of the original data distribution." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"The first rule of communication is to shut up and listen, so that you can get to know about the audience for your communication, whether it might be politicians, professionals or the general public. We have to understand their inevitable limitations and any misunderstandings, and fight the temptation to be too sophisticated and clever, or put in too much detail." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"The second rule of communication is to know what you want to achieve. Hopefully the aim is to encourage open debate, and informed decision-making. But there seems no harm in repeating yet again that numbers do not speak for themselves; the context, language and graphic design all contribute to the way the communication is received. We have to acknowledge we are telling a story, and it is inevitable that people will make comparisons and judgements, no matter how much we only want to inform and not persuade. All we can do is try to pre-empt inappropriate gut reactions by design or warning." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"There is no ‘correct’ way to display sets of numbers: each of the plots we have used has some advantages: strip-charts show individual points, box-and-whisker plots are convenient for rapid visual summaries, and histograms give a good feel for the underlying shape of the data distribution." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"This common view of statistics as a basic ‘bag of tools’ is now facing major challenges. First, we are in an age of data science, in which large and complex data sets are collected from routine sources such as traffic monitors, social media posts and internet purchases, and used as a basis for technological innovations such as optimizing travel routes, targeted advertising or purchase recommendation systems [...]. Statistical training is increasingly seen as just one necessary component of being a data scientist, together with skills in data management, programming and algorithm development, as well as proper knowledge of the subject matter." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"Unfortunately, when an ‘average’ is reported in the media, it is often unclear whether this should be interpreted as the mean or median." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"When it comes to presenting categorical data, pie charts allow an impression of the size of each category relative to the whole pie, but are often visually confusing, especially if they attempt to show too many categories in the same chart, or use a three-dimensional representation that distorts areas. [...] Multiple pie charts are generally not a good idea, as comparisons are hampered by the difficulty in assessing the relative sizes of areas of different shapes. Comparisons are better based on height or length alone in a bar chart." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"When we have all the data, it is straightforward to produce statistics that describe what has been measured. But when we want to use the data to draw broader conclusions about what is going on around us, then the quality of the data becomes paramount, and we need to be alert to the kind of systematic biases that can jeopardize the reliability of any claims." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"With the growing availability of massive data sets and user-friendly analysis software, it might be thought that there is less need for training in statistical methods. This would be naïve in the extreme. Far from freeing us from the need for statistical skills, bigger data and the rise in the number and complexity of scientific studies makes it even more difficult to draw appropriate conclusions. More data means that we need to be even more aware of what the evidence is actually worth." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"We over-fit when we go too far in adapting to local circumstances, in a worthy but misguided effort to be ‘unbiased’ and take into account all the available information. Usually we would applaud the aim of being unbiased, but this refinement means we have less data to work on, and so the reliability goes down. Over-fitting therefore leads to less bias but at a cost of more uncertainty or variation in the estimates, which is why protection against over-fitting is sometimes known as the bias/variance trade-off." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

Mental Models LXIII (Limitations VIII)

"Beliefs are generalizations about the past projected onto the present and future to shape it in the image of the past. [...] When we generalize from incomplete or unrepresentative experience, we form mental models that make the wrong predictions, but because beliefs act as self-fulfilling prophecies it is hard to find out, because we are less open to counter examples." (Joseph O’Connor, "Leading With NLP: Essential Leadership Skills for Influencing and Managing People", 1998)

"People’s mental models are apt to be deficient in a number of ways, perhaps including contradictory, erroneous, and unnecessary concepts. As designers, it is our duty to develop systems and instructional materials that aid users to develop more coherent, useable mental models. As teachers, it is our duty to develop conceptual models that will aid the learner to develop adequate and appropriate mental models. And as scientists who are interested in studying people’s mental models, we must develop appropriate experimental methods and discard our hopes of finding neat, elegant mental models, but instead learn to understand the messy, sloppy, incomplete, and indistinct structures that people actually have." (Donald A Norman, "Some Observations on Mental Models" [in "Mental Models", Ed(s). Dedre Gentner & Albert L Stevens], 1983)

"To begin with, we must understand that any mindset consists of mental models, or concepts, that influence our interpretation of situations and predispose us to certain responses. These models, which are replete with beliefs and assumptions, thus strongly determine the way we understand the world and act in it. The irony is, they become so ingrained in us, as tendencies and predispositions, that we seldom pay attention to them." (Stephen G Haines, "The Manager's Pocket Guide to Strategic and Business Planning", 1998)

"Short-term memory can hold 7 ± 2 chunks of information at once. This puts a rather sharp limit on the effective size and complexity of a causal map. Presenting a complex causal map all at once makes it hard to see the loops, understand which are important, or understand how they generate the dynamics. Resist the temptation to put all the loops you and your clients have identified into a single comprehensive diagram." (John D Sterman, "Business Dynamics Systems Thinking and Modeling for a Complex World", 2000)

"Our mental maps are often not terribly accurate, based as they are on our own selective experience, our knowledge and ignorance, and the information and misinformation we gain from others; nevertheless, these are the maps we depend on every day." (Peter Turchi, "Maps of the Imagination: The writer as cartographer", 2004)

"The most serious problem in applied ethics, or at least in business ethics, is not that we frame experiences; it is not that these mental models are incomplete, sometimes biased, and surely parochial. The larger problem is that most of us either individually or as managers do not realize that we are framing, disregarding data, ignoring counterevidence, or not taking into account other points of view." (Patricia H Werhane "A Place for Philosophers in Applied Ethics and the Role of Moral Reasoning in Moral Imagination", Business Ethics Quarterly 16 (3), 2007)

"Although good ethical decision-making requires us carefully to take into account as much relevant information as is available to us, we have good reason to think that we commonly fall well short of this standard – either by overlooking relevant facts completely or by underestimating their significance. The mental models we employ can contribute to this problem. As we have explained, mental models frame our experiences in ways that both aid and hinder our perceptions. They enable us to focus selectively on ethically relevant matters. By their very nature, they provide incomplete perspectives, resulting in bounded awareness and bounded ethicality. Insofar as our mental modeling practices result in unwarranted partiality, or even ethical blindness, the desired reflective process is distorted. This distortion is aggravated by the fact that our mental models can have this distorting effect without our consciously realizing it. Thus, although we cannot do without mental models, they leave us all vulnerable to blindness and, insofar as we are unaware of this, self-deception." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)

"Mental models serve to conceptualize, focus and shape our experiences, but in so doing, they sometimes cause us to ignore data and occlude critical reflection that might be relevant or, indeed, necessary to practical decision-making. [...] distorting mental models are the foundation

or underpinning of many of the impediments to effective ethical decision-making." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience",  2013)

"We identify and analyze distorting mental models that constitute experience in a manner that occludes the moral dimension of situations from view, thereby thwarting the first step of ethical decision-making. Examples include an unexamined moral self-image, viewing oneself as merely a bystander, and an exaggerated conception of self-sufficiency. These mental models, we argue, generate blind spots to ethics, in the sense that they limit our ability to see facts that are right before our eyes – sometimes quite literally, as in the many examples of managers and employees who see unethical behavior take place in front of them, but do not recognize it as such." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience",  2013)

On Series III: Time Series

"Diagrams are sometimes used, not merely to convey several pieces of information such as several time series on one chart, but also to provide visual evidence of relationships between the series." (Alfred R Ilersic, "Statistics", 1959)

"Numerical data, which have been recorded at intervals of time, form what is generally described as a time series. [...] The purpose of analyzing time series is not always the determination of the trend by itself. Interest may be centered on the seasonal movement displayed by the series and, in such a case, the determination of the trend is merely a stage in the process of measuring and analyzing the seasonal variation. If a regular basic or under- lying seasonal movement can be clearly established, forecasting of future movements becomes rather less a matter of guesswork and more a matter of intelligent forecasting." (Alfred R Ilersic, "Statistics", 1959)

"Time series analysis often requires more knowledge of the data and relevant information about their background than it does of statistical techniques. Whereas the data in some other fields may be controlled so as to increase their representativeness, economic data are so changeable in their nature that it is usually impossible to sort out the separate effects of the various influences. Attempts to isolate cyclical, seasonal and irregular, or random movements, are made primarily in the hope that some underlying pattern of change over time may be revealed."  (Alfred R Ilersic, "Statistics", 1959)

"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)

"A time series is a sequence of observations, usually ordered in time, although in some cases the ordering may be according to another dimension. The feature of time series analysis which distinguishes it from other statistical analysis is the explicit recognition of the importance of the order in which the observations are made. While in many problems the observations are statistically independent, in time series successive observations may be dependent, and the dependence may depend on the positions in the sequence. The nature of a series and the structure of its generating process also may involve in other ways the sequence in which the observations are taken." (Theodore W Anderson, "The Statistical Analysis of Time Series", 1971)

"Entropy theory, on the other hand, is not concerned with the probability of succession in a series of items but with the overall distribution of kinds of items in a given arrangement." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1974) 

"This transition from uncertainty to near certainty when we observe long series of events, or large systems, is an essential theme in the study of chance." (David Ruelle, "Chance and Chaos", 1991)

"System dynamics models are not derived statistically from time-series data. Instead, they are statements about system structure and the policies that guide decisions. Models contain the assumptions being made about a system. A model is only as good as the expertise which lies behind its formulation. A good computer model is distinguished from a poor one by the degree to which it captures the essence of a system that it represents. Many other kinds of mathematical models are limited because they will not accept the multiple-feedback-loop and nonlinear nature of real systems." (Jay W Forrester, "Counterintuitive Behavior of Social Systems", 1995)

"Like modeling, which involves making a static one-time prediction based on current information, time-series prediction involves looking at current information and predicting what is going to happen. However, with time-series predictions, we typically are looking at what has happened for some period back through time and predicting for some point in the future. The temporal or time element makes time-series prediction both more difficult and more rewarding. Someone who can predict the future based on what has occurred in the past can clearly have tremendous advantages over someone who cannot." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"Many of the basic functions performed by neural networks are mirrored by human abilities. These include making distinctions between items (classification), dividing similar things into groups (clustering), associating two or more things (associative memory), learning to predict outcomes based on examples (modeling), being able to predict into the future (time-series forecasting), and finally juggling multiple goals and coming up with a good-enough solution (constraint satisfaction)." (Joseph P Bigus,"Data Mining with Neural Networks: Solving business problems from application development to decision support", 1996)

"Averages, ranges, and histograms all obscure the time-order for the data. If the time-order for the data shows some sort of definite pattern, then the obscuring of this pattern by the use of averages, ranges, or histograms can mislead the user. Since all data occur in time, virtually all data will have a time-order. In some cases this time-order is the essential context which must be preserved in the presentation." (Donald J Wheeler," Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"No comparison between two values can be global. A simple comparison between the current figure and some previous value and convey the behavior of any time series. […] While it is simple and easy to compare one number with another number, such comparisons are limited and weak. They are limited because of the amount of data used, and they are weak because both of the numbers are subject to the variation that is inevitably present in weak world data. Since both the current value and the earlier value are subject to this variation, it will always be difficult to determine just how much of the difference between the values is due to variation in the numbers, and how much, if any, of the difference is due to real changes in the process." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"Prior to the discovery of the butterfly effect it was generally believed that small differences averaged out and were of no real significance. The butterfly effect showed that small things do matter. This has major implications for our notions of predictability, as over time these small differences can lead to quite unpredictable outcomes. For example, first of all, can we be sure that we are aware of all the small things that affect any given system or situation? Second, how do we know how these will affect the long-term outcome of the system or situation under study? The butterfly effect demonstrates the near impossibility of determining with any real degree of accuracy the long term outcomes of a series of events." (Elizabeth McMillan, Complexity, "Management and the Dynamics of Change: Challenges for practice", 2008)

"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)

"Using random processes in our models allows economists to capture the variability of time series data, but it also poses challenges to model builders. As model builders, we must understand the uncertainty from two different perspectives. Consider first that of the econometrician, standing outside an economic model, who must assess its congruence with reality, inclusive of its random perturbations. An econometrician’s role is to choose among different parameters that together describe a family of possible models to best mimic measured real world time series and to test the implications of these models. I refer to this as outside uncertainty. Second, agents inside our model, be it consumers, entrepreneurs, or policy makers, must also confront uncertainty as they make decisions. I refer to this as inside uncertainty, as it pertains to the decision-makers within the model. What do these agents know? From what information can they learn? With how much confidence do they forecast the future? The modeler’s choice regarding insiders’ perspectives on an uncertain future can have significant consequences for each model’s equilibrium outcomes." (Lars P Hansen, "Uncertainty Outside and Inside Economic Models", [Nobel lecture] 2013)

"With time series though, there is absolutely no substitute for plotting. The pertinent pattern might end up being a sharp spike followed by a gentle taper down. Or, maybe there are weird plateaus. There could be noisy spikes that have to be filtered out. A good way to look at it is this: means and standard deviations are based on the naïve assumption that data follows pretty bell curves, but there is no corresponding 'default' assumption for time series data (at least, not one that works well with any frequency), so you always have to look at the data to get a sense of what’s normal. [...] Along the lines of figuring out what patterns to expect, when you are exploring time series data, it is immensely useful to be able to zoom in and out." (Field Cady, "The Data Science Handbook", 2017)

"[Making reasoned macro calls] starts with having the best and longest-time-series data you can find. You may have to take some risks in terms of the quality of data sources, but it amazes me how people are often more willing to act based on little or no data than to use data that is a challenge to assemble." (Robert J Shiller)

On Inquiry XIII: Inquiry in Data Science III

 "To find signals in data, we must learn to reduce the noise - not just the noise that resides in the data, but also the noise that resides in us. It is nearly impossible for noisy minds to perceive anything but noise in data. […] Signals always point to something. In this sense, a signal is not a thing but a relationship. Data becomes useful knowledge of something that matters when it builds a bridge between a question and an answer. This connection is the signal." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)

"[...] a data scientist role goes beyond the collection and reporting on data; it must involve looking at a business The role of a data scientist goes beyond the collection and reporting on data. application or process from multiple vantage points and determining what the main questions and follow-ups are, as well as recommending the most appropriate ways to employ the data at hand." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)

"A data story starts out like any other story, with a beginning and a middle. However, the end should never be a fixed event, but rather a set of options or questions to trigger an action from the audience. Never forget that the goal of data storytelling is to encourage and energize critical thinking for business decisions." (James Richardson, 2017)

"A notable difference between many fields and data science is that in data science, if a customer has a wish, even an experienced data scientist may not know whether it’s possible. Whereas a software engineer usually knows what tasks software tools are capable of performing, and a biologist knows more or less what the laboratory can do, a data scientist who has not yet seen or worked with the relevant data is faced with a large amount of uncertainty, principally about what specific data is available and about how much evidence it can provide to answer any given question. Uncertainty is, again, a major factor in the data scientific process and should be kept at the forefront of your mind when talking with customers about their wishes."  (Brian Godsey, "Think Like a Data Scientist", 2017)

"In terms of characteristics, a data scientist has an inquisitive mind and is prepared to explore and ask questions, examine assumptions and analyse processes, test hypotheses and try out solutions and, based on evidence, communicate informed conclusions, recommendations and caveats to stakeholders and decision makers." (Jesús Rogel-Salazar, "Data Science and Analytics with Python", 2017)

"Again, classical statistics only summarizes data, so it does not provide even a language for asking [a counterfactual] question. Causal inference provides a notation and, more importantly, offers a solution. As with predicting the effect of interventions [...], in many cases we can emulate human retrospective thinking with an algorithm that takes what we know about the observed world and produces an answer about the counterfactual world." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Bayesian networks inhabit a world where all questions are reducible to probabilities, or (in the terminology of this chapter) degrees of association between variables; they could not ascend to the second or third rungs of the Ladder of Causation. Fortunately, they required only two slight twists to climb to the top." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Creating effective visualizations is hard. Not because a dataset requires an exotic and bespoke visual representation - for many problems, standard statistical charts will suffice. And not because creating a visualization requires coding expertise in an unfamiliar programming language [...]. Rather, creating effective visualizations is difficult because the problems that are best addressed by visualization are often complex and ill-formed. The task of figuring out what attributes of a dataset are important is often conflated with figuring out what type of visualization to use. Picking a chart type to represent specific attributes in a dataset is comparatively easy. Deciding on which data attributes will help answer a question, however, is a complex, poorly defined, and user-driven process that can require several rounds of visualization and exploration to resolve." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"[…] deep learning has succeeded primarily by showing that certain questions or tasks we thought were difficult are in fact not. It has not addressed the truly difficult questions that continue to prevent us from achieving humanlike AI." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"Premature enumeration is an equal-opportunity blunder: the most numerate among us may be just as much at risk as those who find their heads spinning at the first mention of a fraction. Indeed, if you’re confident with numbers you may be more prone than most to slicing and dicing, correlating and regressing, normalizing and rebasing, effortlessly manipulating the numbers on the spreadsheet or in the statistical package - without ever realizing that you don’t fully understand what these abstract quantities refer to. Arguably this temptation lay at the root of the last financial crisis: the sophistication of mathematical risk models obscured the question of how, exactly, risks were being measured, and whether those measurements were something you’d really want to bet your global banking system on." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

On Inquiry XII: Inquiry in Data Science II

"Modeling involves a style of scientific thinking in which the argument is structured by the model, but in which the application is achieved via a narrative prompted by an external fact, an imagined event or question to be answered." (Uskali Mäki, "Fact and Fiction in Economics: Models, Realism and Social Construction", 2002)

"Statistics depend on collecting information. If questions go unasked, or if they are asked in ways that limit responses, or if measures count some cases but exclude others, information goes ungathered, and missing numbers result. Nevertheless, choices regarding which data to collect and how to go about collecting the information are inevitable." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)

"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)

"Even in the best of circumstances, statistical analysis rarely unveils 'the truth'. We are usually building a circumstantial case based on imperfect data. As a result, there are numerous reasons that intellectually honest individuals may disagree about statistical results or their implications. At the most basic level, we may disagree on the question that is being answered." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 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)

"Don’t just do the calculations. Use common sense to see whether you are answering the correct question, the assumptions are reasonable, and the results are plausible. If a statistical argument doesn’t make sense, think about it carefully - you may discover that the argument is nonsense." (Gary Smith, "Standard Deviations", 2014)

"Mathematical modeling is the application of mathematics to describe real-world problems and investigating important questions that arise from it." (Sandip Banerjee, "Mathematical Modeling: Models, Analysis and Applications", 2014)

"The search for better numbers, like the quest for new technologies to improve our lives, is certainly worthwhile. But the belief that a few simple numbers, a few basic averages, can capture the multifaceted nature of national and global economic systems is a myth. Rather than seeking new simple numbers to replace our old simple numbers, we need to tap into both the power of our information age and our ability to construct our own maps of the world to answer the questions we need answering." (Zachary Karabell, "The Leading Indicators: A short history of the numbers that rule our world", 2014)

"We are seduced by patterns and we want explanations for these patterns. When we see a string of successes, we think that a hot hand has made success more likely. If we see a string of failures, we think a cold hand has made failure more likely. It is easy to dismiss such theories when they involve coin flips, but it is not so easy with humans. We surely have emotions and ailments that can cause our abilities to go up and down. The question is whether these fluctuations are important or trivial." (Gary Smith, "Standard Deviations", 2014)

"We don’t need new indicators that replace old simple numbers with new simple numbers. We need instead bespoke indicators, tailored to the specific needs and specific questions of governments, businesses, communities, and individuals." (Zachary Karabell, "The Leading Indicators: A short history of the numbers that rule our world", 2014)

On Data (1940-1949)

"Scientific data are not taken for museum purposes; they are taken as a basis for doing something. If nothing is to be done with the data, then there is no use in collecting any. The ultimate purpose of taking data is to provide a basis for action or a recommendation for action. The step intermediate between the collection of data and the action is prediction." (William E Deming, "On a Classification of the Problems of Statistical Inference", Journal of the American Statistical Association Vol. 37 (218), 1942)

"The faith of scientists in the power of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation. The promiscuous collection and tabulation of data have given way to a process of assigning possible meanings, merely supposed real entities, to mathematical terms, working out the logical results, and then staging certain crucial experiments to check the hypothesis against the actual, empirical results. But the facts [...] accepted by virtue of these tests are not actually observed at all." (Susanne K Langer, "Philosophy in a New Key", 1942)

"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  & Alan Stuart,, "Advanced Theory of Statistics", Vol. 1, 1943)

"True, the universe is more than a collection of objective experimental data; more than the complexus of theories, abstractions, and special assumptions devised to hold the data together; more, indeed, than any construct modeled on this cold objectivity. For there is a deeper, more subjective world, a world of sensation and emotion, of aesthetic, moral, and religious values as yet beyond the grasp of objective science. And towering majestically over all, inscrutable and inescapable, is the awful mystery of Existence itself, to confound the mind with an eternal enigma." (Banesh Hoffmann, "The Strange Story of the Quantum", 1947)

"There is only one kind of whiskey, but two broad classes of data, good and bad." (William E Deming, "On the Classification of Statistics", The American Statistician Vol. 2 (2), 1948)

Tim Harford - Collected Quotes

"An algorithm, meanwhile, is a step-by-step recipe for performing a series of actions, and in most cases 'algorithm' means simply 'computer program'." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Big data is revolutionizing the world around us, and it is easy to feel alienated by tales of computers handing down decisions made in ways we don’t understand. I think we’re right to be concerned. Modern data analytics can produce some miraculous results, but big data is often less trustworthy than small data. Small data can typically be scrutinized; big data tends to be locked away in the vaults of Silicon Valley. The simple statistical tools used to analyze small datasets are usually easy to check; pattern-recognizing algorithms can all too easily be mysterious and commercially sensitive black boxes." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Each decision about what data to gather and how to analyze them is akin to standing on a pathway as it forks left and right and deciding which way to go. What seems like a few simple choices can quickly multiply into a labyrinth of different possibilities. Make one combination of choices and you’ll reach one conclusion; make another, equally reasonable, and you might find a very different pattern in the data." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Each of us is sweating data, and those data are being mopped up and wrung out into oceans of information. Algorithms and large datasets are being used for everything from finding us love to deciding whether, if we are accused of a crime, we go to prison before the trial or are instead allowed to post bail. We all need to understand what these data are and how they can be exploited." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"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)

"[…] in a world where so many people seem to hold extreme views with strident certainty, you can deflate somebody’s overconfidence and moderate their politics simply by asking them to explain the details." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"It’d be nice to fondly imagine that high-quality statistics simply appear in a spreadsheet somewhere, divine providence from the numerical heavens. Yet any dataset begins with somebody deciding to collect the numbers. What numbers are and aren’t collected, what is and isn’t measured, and who is included or excluded are the result of all-too-human assumptions, preconceptions, and oversights." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Making big data work is harder than it seems. Statisticians have spent the past two hundred years figuring out what traps lie in wait when we try to understand the world through data. The data are bigger, faster, and cheaper these days, but we must not pretend that the traps have all been made safe. They have not." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Many people have strong intuitions about whether they would rather have a vital decision about them made by algorithms or humans. Some people are touchingly impressed by the capabilities of the algorithms; others have far too much faith in human judgment. The truth is that sometimes the algorithms will do better than the humans, and sometimes they won’t. If we want to avoid the problems and unlock the promise of big data, we’re going to need to assess the performance of the algorithms on a case-by-case basis. All too often, this is much harder than it should be. […] So the problem is not the algorithms, or the big datasets. The problem is a lack of scrutiny, transparency, and debate." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Much of the data visualization that bombards us today is decoration at best, and distraction or even disinformation at worst. The decorative function is surprisingly common, perhaps because the data visualization teams of many media organizations are part of the art departments. They are led by people whose skills and experience are not in statistics but in illustration or graphic design. The emphasis is on the visualization, not on the data. It is, above all, a picture." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Numbers can easily confuse us when they are unmoored from a clear definition." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Premature enumeration is an equal-opportunity blunder: the most numerate among us may be just as much at risk as those who find their heads spinning at the first mention of a fraction. Indeed, if you’re confident with numbers you may be more prone than most to slicing and dicing, correlating and regressing, normalizing and rebasing, effortlessly manipulating the numbers on the spreadsheet or in the statistical package - without ever realizing that you don’t fully understand what these abstract quantities refer to. Arguably this temptation lay at the root of the last financial crisis: the sophistication of mathematical risk models obscured the question of how, exactly, risks were being measured, and whether those measurements were something you’d really want to bet your global banking system on." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Sample error reflects the risk that, purely by chance, a randomly chosen sample of opinions does not reflect the true views of the population. The 'margin of error' reported in opinion polls reflects this risk, and the larger the sample, the smaller the margin of error. […] sampling error has a far more dangerous friend: sampling bias. Sampling error is when a randomly chosen sample doesn’t reflect the underlying population purely by chance; sampling bias is when the sample isn’t randomly chosen at all." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Statistical metrics can show us facts and trends that would be impossible to see in any other way, but often they’re used as a substitute for relevant experience, by managers or politicians without specific expertise or a close-up view." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Statisticians are sometimes dismissed as bean counters. The sneering term is misleading as well as unfair. Most of the concepts that matter in policy are not like beans; they are not merely difficult to count, but difficult to define. Once you’re sure what you mean by 'bean', the bean counting itself may come more easily. But if we don’t understand the definition, then there is little point in looking at the numbers. We have fooled ourselves before we have begun."(Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"So information is beautiful - but misinformation can be beautiful, too. And producing beautiful misinformation is becoming easier than ever." (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 world is full of patterns that are too subtle or too rare to detect by eyeballing them, and a pattern doesn’t need to be very subtle or rare to be hard to spot without a statistical lens." (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)

"Those of us in the business of communicating ideas need to go beyond the fact-check and the statistical smackdown. Facts are valuable things, and so is fact-checking. But if we really want people to understand complex issues, we need to engage their curiosity. If people are curious, they will learn." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Unless we’re collecting data ourselves, there’s a limit to how much we can do to combat the problem of missing data. But we can and should remember to ask who or what might be missing from the data we’re being told about. Some missing numbers are obvious […]. Other omissions show up only when we take a close look at the claim in question." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"We don’t need to become emotionless processors of numerical information - just noticing our emotions and taking them into account may often be enough to improve our judgment. Rather than requiring superhuman control over our emotions, we need simply to develop good habits." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"We filter new information. If it accords with what we expect, we’ll be more likely to accept it. […] Our brains are always trying to make sense of the world around us based on incomplete information. The brain makes predictions about what it expects, and tends to fill in the gaps, often based on surprisingly sparse data." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"We should conclude nothing because that pair of numbers alone tells us very little. If we want to understand what’s happening, we need to step back and take in a broader perspective." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"[…] when it comes to interpreting the world around us, we need to realize that our feelings can trump our expertise. […] The more extreme the emotional reaction, the harder it is to think straight. […] It is not easy to master our emotions while assessing information that matters to us, not least because our emotions can lead us astray in different directions. […] We often find ways to dismiss evidence that we don’t like. And the opposite is true, too: when evidence seems to support our preconceptions, we are less likely to look too closely for flaws." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"When we are trying to understand a statistical claim - any statistical claim - we need to start by asking ourselves what the claim actually means. [...] A surprising statistical claim is a challenge to our existing worldview. It may provoke an emotional response - even a fearful one." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020) 

Charles Wheelan - Collected Quotes

"A statistical index has all the potential pitfalls of any descriptive statistic - plus the distortions introduced by combining multiple indicators into a single number. By definition, any index is going to be sensitive to how it is constructed; it will be affected both by what measures go into the index and by how each of those measures is weighted." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Correlation measures the degree to which two phenomena are related to one another. [...] Two variables are positively correlated if a change in one is associated with a change in the other in the same direction, such as the relationship between height and weight. [...] A correlation is negative if a positive change in one variable is associated with a negative change in the other, such as the relationship between exercise and weight." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Descriptive statistics give us insight into phenomena that we care about. […] Although the field of statistics is rooted in mathematics, and mathematics is exact, the use of statistics to describe complex phenomena is not exact. That leaves plenty of room for shading the truth." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Even if you have a solid indicator of what you are trying to measure and manage, the challenges are not over. The good news is that 'managing by statistics' can change the underlying behavior of the person or institution being managed for the better. If you can measure the proportion of defective products coming off an assembly line, and if those defects are a function of things happening at the plant, then some kind of bonus for workers that is tied to a reduction in defective products would presumably change behavior in the right kinds of ways. Each of us responds to incentives (even if it is just praise or a better parking spot). Statistics measure the outcomes that matter; incentives give us a reason to improve those outcomes." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Even in the best of circumstances, statistical analysis rarely unveils 'the truth'. We are usually building a circumstantial case based on imperfect data. As a result, there are numerous reasons that intellectually honest individuals may disagree about statistical results or their implications. At the most basic level, we may disagree on the question that is being answered." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"If the distance from the mean for one variable tends to be broadly consistent with distance from the mean for the other variable (e.g., people who are far from the mean for height in either direction tend also to be far from the mean in the same direction for weight), then we would expect a strong positive correlation. If distance from the mean for one variable tends to correspond to a similar distance from the mean for the second variable in the other direction (e.g., people who are far above the mean in terms of exercise tend to be far below the mean in terms of weight), then we would expect a strong negative correlation. If two variables do not tend to deviate from the mean in any meaningful pattern (e.g., shoe size and exercise) then we would expect little or no correlation." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Once these different measures of performance are consolidated into a single number, that statistic can be used to make comparisons […] The advantage of any index is that it consolidates lots of complex information into a single number. We can then rank things that otherwise defy simple comparison […] Any index is highly sensitive to the descriptive statistics that are cobbled together to build it, and to the weight given to each of those components. As a result, indices range from useful but imperfect tools to complete charades." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Probability is the study of events and outcomes involving an element of uncertainty." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"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)

"Statistics cannot be any smarter than the people who use them. And in some cases, they can make smart people do dumb things." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"The correlation coefficient has two fabulously attractive characteristics. First, for math reasons that have been relegated to the appendix, it is a single number ranging from –1 to 1. A correlation of 1, often described as perfect correlation, means that every change in one variable is associated with an equivalent change in the other variable in the same direction. A correlation of –1, or perfect negative correlation, means that every change in one variable is associated with an equivalent change in the other variable in the opposite direction. The closer the correlation is to 1 or –1, the stronger the association. […] The second attractive feature of the correlation coefficient is that it has no units attached to it. […] The correlation coefficient does a seemingly miraculous thing: It collapses a complex mess of data measured in different units (like our scatter plots of height and weight) into a single, elegant descriptive statistic." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"The problem is that the mechanics of regression analysis are not the hard part; the hard part is determining which variables ought to be considered in the analysis and how that can best be done. Regression analysis is like one of those fancy power tools. It is relatively easy to use, but hard to use well - and potentially dangerous when used improperly." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"There are limits on the data we can gather and the kinds of experiments we can perform."(Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"While the main point of statistics is to present a meaningful picture of things we care about, in many cases we also hope to act on these numbers." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

John D Kelleher - Collected Quotes

"A predictive model overfits the training set when at least some of the predictions it returns are based on spurious patterns present in the training data used to induce the model. Overfitting happens for a number of reasons, including sampling variance and noise in the training set. The problem of overfitting can affect any machine learning algorithm; however, the fact that decision tree induction algorithms work by recursively splitting the training data means that they have a natural tendency to segregate noisy instances and to create leaf nodes around these instances. Consequently, decision trees overfit by splitting the data on irrelevant features that only appear relevant due to noise or sampling variance in the training data. The likelihood of overfitting occurring increases as a tree gets deeper because the resulting predictions are based on smaller and smaller subsets as the dataset is partitioned after each feature test in the path." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"Decision trees are also discriminative models. Decision trees are induced by recursively partitioning the feature space into regions belonging to the different classes, and consequently they define a decision boundary by aggregating the neighboring regions belonging to the same class. Decision tree model ensembles based on bagging and boosting are also discriminative models." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"Decision trees are also considered nonparametric models. The reason for this is that when we train a decision tree from data, we do not assume a fixed set of parameters prior to training that define the tree. Instead, the tree branching and the depth of the tree are related to the complexity of the dataset it is trained on. If new instances were added to the dataset and we rebuilt the tree, it is likely that we would end up with a (potentially very) different tree." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

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

"The main advantage of decision tree models is that they are interpretable. It is relatively easy to understand the sequences of tests a decision tree carried out in order to make a prediction. This interpretability is very important in some domains. [...] Decision tree models can be used for datasets that contain both categorical and continuous descriptive features. A real advantage of the decision tree approach is that it has the ability to model the interactions between descriptive features. This arises from the fact that the tests carried out at each node in the tree are performed in the context of the results of the tests on the other descriptive features that were tested at the preceding nodes on the path from the root. Consequently, if there is an interaction effect between two or more descriptive features, a decision tree can model this."  (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"There are two kinds of mistakes that an inappropriate inductive bias can lead to: underfitting and overfitting. Underfitting occurs when the prediction model selected by the algorithm is too simplistic to represent the underlying relationship in the dataset between the descriptive features and the target feature. Overfitting, by contrast, occurs when the prediction model selected by the algorithm is so complex that the model fits to the dataset too closely and becomes sensitive to noise in the data."(John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"Tree pruning identifies and removes subtrees within a decision tree that are likely to be due to noise and sample variance in the training set used to induce it. In cases where a subtree is deemed to be overfitting, pruning the subtree means replacing the subtree with a leaf node that makes a prediction based on the majority target feature level (or average target feature value) of the dataset created by merging the instances from all the leaf nodes in the subtree. Obviously, pruning will result in decision trees being created that are not consistent with the training set used to build them. In general, however, we are more interested in creating prediction models that generalize well to new data rather than that are strictly consistent with training data, so it is common to sacrifice consistency for generalization capacity." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"When datasets are small, a parametric model may perform well because the strong assumptions made by the model - if correct - can help the model to avoid overfitting. However, as the size of the dataset grows, particularly if the decision boundary between the classes is very complex, it may make more sense to allow the data to inform the predictions more directly. Obviously the computational costs associated with nonparametric models and large datasets cannot be ignored. However, support vector machines are an example of a nonparametric model that, to a large extent, avoids this problem. As such, support vector machines are often a good choice in complex domains with lots of data." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"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)

"A neural network consists of a set of neurons that are connected together. A neuron takes a set of numeric values as input and maps them to a single output value. At its core, a neuron is simply a multi-input linear-regression function. The only significant difference between the two is that in a neuron the output of the multi-input linear-regression function is passed through another function that is called the activation function." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"Data scientists should have some domain expertise. Most data science projects begin with a real-world, domain-specific problem and the need to design a data-driven solution to this problem. As a result, it is important for a data scientist to have enough domain expertise that they understand the problem, why it is important, an dhow a data science solution to the problem might fit into an organization’s processes. This domain expertise guides the data scientist as she works toward identifying an optimized solution." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"One of the biggest myths is the belief that data science is an autonomous process that we can let loose on our data to find the answers to our problems. In reality, data science requires skilled human oversight throughout the different stages of the process. [...] The second big myth of data science is that every data science project needs big data and needs to use deep learning. In general, having more data helps, but having the right data is the more important requirement. [...] A third data science myth is that modern data science software is easy to use, and so data science is easy to do. [...] The last myth about data science [...] is the belief that data science pays for itself quickly. The truth of this belief depends on the context of the organization. Adopting data science can require significant investment in terms of developing data infrastructure and hiring staff with data science expertise. Furthermore, data science will not give positive results on every project." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"One of the most important skills for a data scientist is the ability to frame a real-world problem as a standard data science task." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"Presenting data in a graphical format makes it much easier to see and understand what is happening with the data. Data visualization applies to all phases of the data science process."  (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"The goal of data science is to improve decision making by basing decisions on insights extracted from large data sets. As a field of activity, data science encompasses a set of principles, problem definitions, algorithms, and processes for extracting nonobvious and useful patterns from large data sets. It is closely related to the fields of data mining and machine learning, but it is broader in scope." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"The patterns that we extract using data science are useful only if they give us insight into the problem that enables us to do something to help solve the problem." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"The promise of data science is that it provides a way to understand the world through data." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"Using data science, we can uncover the important patterns in a data set, and these patterns can reveal the important attributes in the domain. The reason why data science is used in so many domains is that it doesn’t matter what the problem domain is: if the right data are available and the problem can be clearly defined, then data science can help."  (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"We humans are reasonably good at defining rules that check one, two, or even three attributes (also commonly referred to as features or variables), but when we go higher than three attributes, we can start to struggle to handle the interactions between them. By contrast, data science is often applied in contexts where we want to look for patterns among tens, hundreds, thousands, and, in extreme cases, millions of attributes." (John D Kelleher & Brendan Tierney, "Data Science", 2018)