🖍️Thomas Carlyle - Collected Quotes

"Statistics is a science which ought to be honourable, the basis of many most important sciences; but it is not to be carried on by steam, this science, any more than others are; a wise hand is requisite for carrying it on. Conclusive facts are inseparable from unconclusive except by a head that already understands and knows." (Thomas Carlyle, "Critical and Miscellaneous Essays", 1838)

"A judicious man looks at Statistics, not to get knowledge, but to save himself from having ignorance foisted on him." (Thomas Carlyle, "Chartism", 1840)

"A witty statesman once said, you might prove anything by figures."  (Thomas Carlyle, "Chartism", 1840)

"Statistics, one may hope, will improve individually, and become good for something." (Thomas Carlyle, "Chartism", 1840)

"Inquiries wisely gone into, even on this most complex matter, will yield results worth something, not nothing. But it is a most complex matter; on which, whether for the past or the present. Statistic Inquiry, with its limited means, with its short vision and headlong extensive dogmatism, as yet too often throws not light, but error worse than darkness." (Thomas Carlyle, "Chartism", 1840)

"Tables are like cobwebs, like the sieve of Danaides; beautifully reticulated, orderly to look upon, but which will hold no conclusion. Tables are abstractions, and the object a most concrete one, so difficult to read the essence of." (Thomas Carlyle, "Chartism", 1840)

"There are innumerable circumstances; and one circumstance left out may be the vital one on which all turned. Statistics is a science which ought to be honourable, the basis

of many most important sciences; but it is not to be carried on by steam, this science, any more than others are; a wise head is requisite for carrying it on. Conclusive facts are inseparable from inconclusive except by a head that ah-eady understands and knows." (Thomas Carlyle, "Chartism", 1840)

"There is one fact which Statistic Science has communicated, and a most astonishing one ; the inference from which is pregnant as to this matter." (Thomas Carlyle, "Chartism", 1840)

"What constitutes the well-being of a man? Many things; of which the wages he gets, and the bread he buys with them, are but one preliminary item. Grant, however, that the

wages were the whole; that once knowing the wages and the price of bread, we know all; then what are the wages? Statistic Inquiry, in its present unguided condition, cannot

tell. The average rate of day's wages is not correctly ascertained for any portion of this country; not only not for half-centuries, it is not even ascertained anywhere for decades

or years: far from instituting comparisons with the past, the present itself is unknown to us." (Thomas Carlyle, "Chartism", 1840)

"A judicious man uses statistics, not to get knowledge, but to save himself from having ignorance foisted upon him." (Thomas Carlyle)

"A man protesting against error is on the way towards uniting himself with all men that believe in truth." (Thomas Carlyle)

"Conclusive facts are inseparable from inconclusive except by a head that already understands and knows." (Thomas Carlyle)

"In every phenomenon the beginning remains always the most notable moment." (Thomas Carlyle)

"Once turn to practice, error and truth will no longer consort together [...]." (Thomas Carlyle)

"Science rests on reason and experiment, and can meet an opponent with calmness." (Thomas Carlyle)

🖍️Larry A Wasserman - Collected Quotes

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

"Bayesian inference is a controversial approach because it inherently embraces a subjective notion of probability. In general, Bayesian methods provide no guarantees on long run performance." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"Bayesian inference is appealing when prior information is available since Bayes’ theorem is a natural way to combine prior information with data. Some people find Bayesian inference psychologically appealing because it allows us to make probability statements about parameters. […] In parametric models, with large samples, Bayesian and frequentist methods give approximately the same inferences. In general, they need not agree." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"Inequalities are useful for bounding quantities that might otherwise be hard to compute." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"Probability is a mathematical language for quantifying uncertainty." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"Statistical inference, or 'learning' as it is called in computer science, is the process of using data to infer the distribution that generated the data." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

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

"The Bayesian approach is based on the following postulates: (B1) Probability describes degree of belief, not limiting frequency. As such, we can make probability statements about lots of things, not just data which are subject to random variation. […] (B2) We can make probability statements about parameters, even though they are fixed constants. (B3) We make inferences about a parameter θ by producing a probability distribution for θ. Inferences, such as point estimates and interval estimates, may then be extracted from this distribution." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"The frequentist point of view is based on the following postulates: (F1) Probability refers to limiting relative frequencies. Probabilities are objective properties of the real world. (F2) Parameters are i xed, unknown constants. Because they are not fluctuating, no useful probability statements can be made about parameters. (F3) Statistical procedures should be designed to have well-defined long run frequency properties." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 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) 

"The most important aspect of probability theory concerns the behavior of sequences of random variables." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

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

"Things are changing. Statisticians now recognize that computer scientists are making novel contributions while computer scientists now recognize the generality of statistical theory and methodology. Clever data mining algorithms are more scalable than statisticians ever thought possible. Formal statistical theory is more pervasive than computer scientists had realized." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

"Undirected graphs are an alternative to directed graphs for representing independence relations. Since both directed and undirected graphs are used in practice, it is a good idea to be facile with both. The main difference between the two is that the rules for reading independence relations from the graph are different." (Larry A Wasserman, "All of Statistics: A concise course in statistical inference", 2004)

🖍️David S Salsburg - Collected Quotes

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

"All methods of dealing with big data require a vast number of mind-numbing, tedious, boring mathematical steps." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

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

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

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

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

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

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

"The elements of this cloud of uncertainty (the set of all possible errors) can be described in terms of probability. The center of the cloud is the number zero, and elements of the cloud that are close to zero are more probable than elements that are far away from that center. We can be more precise in this definition by defining the cloud of uncertainty in terms of a mathematical function, called the probability distribution." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

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

"There are other problems with Big Data. In any large data set, there are bound to be inconsistencies, misclassifications, missing data - in other words, errors, blunders, and possibly lies. These problems with individual items occur in any data set, but they are often hidden in a large mass of numbers even when these numbers are generated out of computer interactions." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"There is a constant battle between the cold abstract absolutes of pure mathematics and, the sometimes sloppy way in which mathematical methods are applied in science." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Two clouds of uncertainty may have the same center, but one may be much more dispersed than the other. We need a way of looking at the scatter about the center. We need a measure of the scatter. One such measure is the variance. We take each of the possible values of error and calculate the squared difference between that value and the center of the distribution. The mean of those squared differences is the variance." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"What properties should a good statistical estimator have? Since we are dealing with probability, we start with the probability that our estimate will be very close to the true value of the parameter. We want that probability to become greater and greater as we get more and more data. This property is called consistency. This is a statement about probability. It does not say that we are sure to get the right answer. It says that it is highly probable that we will be close to the right answer." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

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

🖍️Schuyler W Huck - Collected Quotes

"Distributional shape is an important attribute of data, regardless of whether scores are analyzed descriptively or inferentially. Because the degree of skewness can be summarized by means of a single number, and because computers have no difficulty providing such measures (or estimates) of skewness, those who prepare research reports should include a numerical index of skewness every time they provide measures of central tendency and variability." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"If a researcher checks the normality assumption by visually inspecting each sample’s data (for example, by looking at a frequency distribution or a histogram), that researcher might incorrectly think that the data are nonnormal because the distribution appears to be too tall and skinny or too flat and squatty. As a result of this misdiagnosis, the researcher might unnecessarily abandon his or her initial plan to use a parametric statistical test in favor of a different procedure, perhaps one that is thought to be distribution-free." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"If data are normally distributed, certain things are known about the group and individual scores in the group. For example, the three most frequently used measures of central tendency - the arithmetic mean, median, and mode - all have the same numerical value in a normal distribution. Moreover, if a distribution is normal, we can determine a person’s percentile if we know his or her z-score or T-score." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"It is best to think of the various kinds of central tendency indices as falling into three categories based on the computational procedures one uses to summarize the data. One category deals with means, with techniques put into this category if scores are added together and then divided by the number of scores that are summed. The second category involves different kinds of medians, with various techniques grouped here if the goal is to find some sort of midpoint. The third category contains different kinds of modes, with these techniques focused on the frequency with which scores appear in the data." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"It is dangerous to think that standard scores, such as z and T, form a normal distribution because (1) they don’t have to and (2) they often won’t. If you mistakenly presume that a set of standard scores are normally distributed (when they’re not), your conversion of z-scores (or T-scores) into percentiles can lead to great inaccuracies." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"It should be noted that any finite data set cannot “follow” the normal curve exactly. That’s because a normal curve’s two 'tails' extend out to positive and negative infinity. The curved line that forms a normal curve gets closer and closer to the baseline as the curved line moves further and further away from its middle section; however, the curved line never actually touches the abscissa." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"[…] kurtosis is influenced by the variability of the data. This fact leads to two surprising characteristics of kurtosis. First, not all rectangular distributions have the same amount of kurtosis. Second, certain distributions that are not rectangular are more platykurtic than are rectangular distributions!" (Schuyler W Huck, "Statistical Misconceptions", 2008)

"The shape of a normal curve is influenced by two things: (1) the distance between the baseline and the curve’s apex, and (2) the length, on the baseline, that’s set equal to one standard deviation. The arbitrary values chosen for these distances by the person drawing the normal curve determine the appearance of the resulting picture." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"The concept of kurtosis is often thought to deal with the 'peakedness' of a distribution. Compared to a normal distribution (which is said to have a moderate peak), distributions that have taller peaks are referred to as being leptokurtic, while those with smaller peaks are referred to as being platykurtic. Regarding the second of these terms, authors and instructors often suggest that the word flat (which rhymes with the first syllable of platykurtic) is a good mnemonic device for remembering that platykurtic distributions tend to be flatter than normal." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"[...] the term statistical misconception refers to any of several widely held but incorrect notions about statistical concepts, about procedures for analyzing data and about the meaning of results produced by such analyses. To illustrate, many people think that (1) normal curves are bell shaped, (2) a correlation coeffi cient should never be used to address questios of causality, and (3) the level of signifi cance dictates the probability of a Type I error. Some people, of course, have only one or two (rather than all three) of these misconceptions, and a few individuals realize that all three of those beliefs are false."(Schuyler W Huck, "Statistical Misconceptions", 2008)

"The second surprising feature of kurtosis is that rectangular distributions, which are flat, are not maximally platykurtic. Bimodal distributions can yield lower kurtosis values than rectangular distributions, even in those situations where the number of scores and score variability are held constant." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"There are degrees to which a distribution can deviate from normality in terms of peakedness. A platykurtic distribution, for instance, might be slightly less peaked than a normal distribution, moderately less peaked than normal, or totally lacking in any peak. One is tempted to think that any perfectly rectangular distribution, being ultraflat in its shape, would be maximally platykurtic. However, this is not the case." (Schuyler W Huck, "Statistical Misconceptions", 2008)

"Various measures of central tendency have been invented because the proper notion of the 'average' score can vary from study to study. Depending on the kind of data collected, the degree of skewness in the data, and the possible existence of outliers, it may be that the most appropriate measure of central tendency is found by doing something other than (1) dividing the sum of the scores by the number of scores (to get the mean), (2) calculating the midpoint in the distribution (to get the median), or (3) determining the most frequently observed score (to get the mode)." (Schuyler W Huck, "Statistical Misconceptions", 2008)

🖍️Field Cady - Collected Quotes

"A common misconception is that data scientists don’t need visualizations. This attitude is not only inaccurate: it is very dangerous. Most machine learning algorithms are not inherently visual, but it is very easy to misinterpret their outputs if you look only at the numbers; there is no substitute for the human eye when it comes to making intuitive sense of things." (Field Cady, "The Data Science Handbook", 2017)

"AI failed (at least relative to the hype it had generated), and it’s partly out of embarrassment on behalf of their discipline that the term 'artificial intelligence' is rarely used in computer science circles (although it’s coming back into favor, just without the over-hyping). We are as far away from mimicking human intelligence as we have ever been, partly because the human brain is fantastically more complicated than a mere logic engine." (Field Cady, "The Data Science Handbook", 2017)

"At very small time scales, the motion of a particle is more like a random walk, as it gets jostled about by discrete collisions with water molecules. But virtually any random movement on small time scales will give rise to Brownian motion on large time scales, just so long as the motion is unbiased. This is because of the Central Limit Theorem, which tells us that the aggregate of many small, independent motions will be normally distributed." (Field Cady, "The Data Science Handbook", 2017)

"By far the greatest headache in machine learning is the problem of overfitting. This means that your results look great for the data you trained them on, but they don’t generalize to other data in the future. [...] The solution is to train on some of your data and assess performance on other data." (Field Cady, "The Data Science Handbook", 2017) 

"Extracting good features is the most important thing for getting your analysis to work. It is much more important than good machine learning classifiers, fancy statistical techniques, or elegant code. Especially if your data doesn’t come with readily available features (as is the case with web pages, images, etc.), how you reduce it to numbers will make the difference between success and failure." (Field Cady, "The Data Science Handbook", 2017)

"Feature extraction is also the most creative part of data science and the one most closely tied to domain expertise. Typically, a really good feature will correspond to some real‐world phenomenon. Data scientists should work closely with domain experts and understand what these phenomena mean and how to distill them into numbers." (Field Cady, "The Data Science Handbook", 2017)

"Outliers make it very hard to give an intuitive interpretation of the mean, but in fact, the situation is even worse than that. For a real‐world distribution, there always is a mean (strictly speaking, you can define distributions with no mean, but they’re not realistic), and when we take the average of our data points, we are trying to estimate that mean. But when there are massive outliers, just a single data point is likely to dominate the value of the mean and standard deviation, so much more data is required to even estimate the mean, let alone make sense of it." (Field Cady, "The Data Science Handbook", 2017)

"The first step is always to frame the problem: understand the business use case and craft a well‐defined analytics problem (or problems) out of it. This is followed by an extensive stage of grappling with the data and the real‐world things that it describes, so that we can extract meaningful features. Finally, these features are plugged into analytical tools that give us hard numerical results." (Field Cady, "The Data Science Handbook", 2017)

"Theoretically, the normal distribution is most famous because many distributions converge to it, if you sample from them enough times and average the results. This applies to the binomial distribution, Poisson distribution and pretty much any other distribution you’re likely to encounter (technically, any one for which the mean and standard deviation are finite)." (Field Cady, "The Data Science Handbook", 2017)

"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)

"The myth of replacing domain experts comes from people putting too much faith in the power of ML to find patterns in the data. [...] ML looks for patterns that are generally pretty crude - the power comes from the sheer scale at which they can operate. If the important patterns in the data are not sufficiently crude then ML will not be able to ferret them out. The most powerful classes of models, like deep learning, can sometimes learn good-enough proxies for the real patterns, but that requires more training data than is usually available and yields complicated models that are hard to understand and impossible to debug. It’s much easier to just ask somebody who knows the domain!" (Field Cady, "Data Science: The Executive Summary: A Technical Book for Non-Technical Professionals", 2021)

🖍️Joel Best - Collected Quotes

"All human knowledge - including statistics - is created  through people's actions; everything we know is shaped by our language, culture, and society. Sociologists call this the social construction of knowledge. Saying that knowledge is socially constructed does not mean that all we know is somehow fanciful, arbitrary, flawed, or wrong. For example, scientific knowledge can be remarkably accurate, so accurate that we may forget the people and social processes that produced it." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Any statistic based on more than a guess requires some sort of counting. Definitions specify what will be counted. Measuring involves deciding how to go about counting. We cannot begin counting until we decide how we will identify and count instances of a social problem. [...] Measurement involves choices. [...] Often, measurement decisions are hidden." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

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

"But people treat mutant statistics just as they do other statistics - that is, they usually accept even the most implausible claims without question. [...] And people repeat bad statistics [...] bad statistics live on; they take on lives of their own. [...] Statistics, then, have a bad reputation. We suspect that statistics may be wrong, that people who use statistics may be 'lying' - trying to manipulate us by using numbers to somehow distort the truth. Yet, at the same time, we need statistics; we depend upon them to summarize and clarify the nature of our complex society. This is particularly true when we talk about social problems." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Changing measures are a particularly common problem with comparisons over time, but measures also can cause problems of their own. [...] We cannot talk about change without making comparisons over time. We cannot avoid such comparisons, nor should we want to. However, there are several basic problems that can affect statistics about change. It is important to consider the problems posed by changing - and sometimes unchanging - measures, and it is also important to recognize the limits of predictions. Claims about change deserve critical inspection; we need to ask ourselves whether apples are being compared to apples - or to very different objects." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Clear, precise definitions are not enough. Whatever is defined must also be measured, and meaningless measurements will produce meaningless statistics." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

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

"First, good statistics are based on more than guessing. [...] Second, good statistics are based on clear, reasonable definitions. Remember, every statistic has to define its subject. Those definitions ought to be clear and made public. [...] Third, good statistics are based on clear, reasonable measures. Again, every statistic involves some sort of measurement; while all measures are imperfect, not all flaws are equally serious. [...] Finally, good statistics are based on good samples." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"In order to interpret statistics, we need more than a checklist of common errors. We need a general approach, an orientation, a mind-set that we can use to think about new statistics that we encounter. We ought to approach statistics thoughtfully. This can be hard to do, precisely because so many people in our society treat statistics as fetishes." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Innumeracy - widespread confusion about basic mathematical ideas - means that many statistical claims about social problems don't get the critical attention they deserve. This is not simply because an innumerate public is being manipulated by advocates who cynically promote inaccurate statistics. Often, statistics about social problems originate with sincere, well-meaning people who are themselves innumerate; they may not grasp the full implications of what they are saying. Similarly, the media are not immune to innumeracy; reporters commonly repeat the figures their sources give them without bothering to think critically about them." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Knowledge is factual when evidence supports it and we have great confidence in its accuracy. What we call 'hard fact' is information supported by  strong, convincing evidence; this means evidence that, so far as we know, we cannot deny, however we examine or test it. Facts always can be questioned, but they hold up under questioning. How did people come by this information? How did they interpret it? Are other interpretations possible? The more satisfactory the answers to such questions, the 'harder' the facts." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Like definitions, measurements always involve choices. Advocates of different measures can defend their own choices and criticize those made by their opponents - so long as the various choices being made are known and understood. However, when measurement choices are kept hidden, it becomes difficult to assess the statistics based on those choices." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"No definition of a social problem is perfect, but there are two principal ways such definitions can be flawed. On the one hand, we may worry that a definition is too broad, that it encompasses more than it ought to include. That is, broad definitions identify some cases as part of the problem that we might think ought not to be included; statisticians call such cases false positives (that is, they mistakenly identify cases as part of the problem). On the other hand, a definition that is too narrow excludes cases that we might think ought to be included; these are false negatives (incorrectly identified as not being part of the problem)." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

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

"One reason we tend to accept statistics uncritically is that we assume that numbers come from experts who know what they're doing. [...] There is a natural tendency to treat these figures as straightforward facts that cannot be questioned." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"People who create or repeat a statistic often feel they have a stake in defending the number. When someone disputes an estimate and offers a very different (often lower) figure, people may rush to defend the original estimate and attack the new number and anyone who dares to use it. [...] any estimate can be defended by challenging the motives of anyone who disputes the figure." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Statistics are not magical. Nor are they always true - or always false. Nor need they be incomprehensible. Adopting a Critical approach offers an effective way of responding to the numbers we are sure to encounter. Being Critical requires more thought, but failing to adopt a Critical mind-set makes us powerless to evaluate what others tell us. When we fail to think critically, the statistics we hear might just as well be magical." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

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

"The ease with which somewhat complex statistics can produce confusion is important, because we live in a world in which complex numbers are becoming more common. Simple statistical ideas - fractions, percentages, rates - are reasonably well understood by many people. But many social problems involve complex chains of cause and effect that can be understood only through complicated models developed by experts. [...] environment has an influence. Sorting out the interconnected causes of these problems requires relatively complicated statistical ideas - net additions, odds ratios, and the like. If we have an imperfect understanding of these ideas, and if the reporters and other people who relay the statistics to us share our confusion - and they probably do - the chances are good that we'll soon be hearing - and repeating, and perhaps making decisions on the basis of - mutated statistics." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

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

"We often hear warnings that some social problem is 'epidemic'. This expression suggests that the problem's growth is rapid, widespread, and out of control. If things are getting worse, and particularly if they're getting worse fast, we need to act." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"Whenever examples substitute for definitions, there is a risk that our understanding of the problem will be distorted." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

"While some social problems statistics are deliberate deceptions, many - probably the great majority - of bad statistics are the result of confusion, incompetence, innumeracy, or selective, self-righteous efforts to produce numbers that reaffirm principles and interests that their advocates consider just and right. The best response to stat wars is not to try and guess who's lying or, worse, simply to assume that the people we disagree with are the ones telling lies. Rather, we need to watch for the standard causes of bad statistics - guessing, questionable definitions or methods, mutant numbers, and inappropriate comparisons." (Joel Best, "Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists", 2001)

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

"Good statistics are not only products of people counting; the quality of statistics also depends on people’s willingness and ability to count thoughtfully and on their decisions about what, exactly, ought to be counted so that the resulting numbers will be both accurate and meaningful." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)

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

"In short, some numbers are missing from discussions of social issues because certain phenomena are hard to quantify, and any effort to assign numeric values to them is subject to debate. But refusing to somehow incorporate these factors into our calculations creates its own hazards. The best solution is to acknowledge the difficulties we encounter in measuring these phenomena, debate openly, and weigh the options as best we can." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)

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

"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)

"When people use statistics, they assume - or, at least, they want their listeners to assume - that the numbers are meaningful. This means, at a minimum, that someone has actually counted something and that they have done the counting in a way that makes sense. Statistical information is one of the best ways we have of making sense of the world’s complexities, of identifying patterns amid the confusion. But bad statistics give us bad information." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)

🖍️Michael J Moroney - Collected Quotes

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

"A piece of self-deception - often dear to the heart of apprentice scientists - is the drawing of a 'smooth curve' (how attractive it sounds!) through a set of points which have about as much trend as the currants in plum duff. Once this is done, the mind, looking for order amidst chaos, follows the Jack-o'-lantern line with scant attention to the protesting shouts of the actual points. Nor, let it be whispered, is it unknown for people who should know better to rub off the offending points and publish the trend line which their foolish imagination has introduced on the flimsiest of evidence. Allied to this sin is that of overconfident extrapolation, i.e. extending the graph by guesswork beyond the range of factual information. Whenever extrapolation is attempted it should be carefully distinguished from the rest of the graph, e.g. by showing the extrapolation as a dotted line in contrast to the full line of the rest of the graph. [...] Extrapolation always calls for justification, sooner or later. Until this justification is forthcoming, it remains a provisional estimate, based on guesswork." (Michael J Moroney, "Facts from Figures", 1951)

"Data should be collected with a clear purpose in mind. Not only a clear purpose, but a clear idea as to the precise way in which they will be analysed so as to yield the desired information." (Michael J Moroney, "Facts from Figures", 1951)

"For the most part, Statistics is a method of investigation that is used when other methods are of no avail; it is often a last resort and a forlorn hope. A statistical analysis, properly conducted, is a delicate dissection of uncertainties, a surgery of suppositions. The surgeon must guard carefully against false incisions with his scalpel. Very often he has to sew up the patient as inoperable. The public knows too little about the statistician as a conscientious and skilled servant of true science." (Michael J Moroney, "Facts from Figures", 1951)

"It is really questionable - though bordering on heresy to put the question - whether we would be any the worse off if the whole bag of tricks were scrapped. So many of these index numbers are so ancient and so out of date, so out of touch with reality, so completely devoid of practical value when they have been computed, that their regular calculation must be regarded as a widespread compulsion neurosis. Only lunatics and public servants with no other choice go on doing silly things and liking it." (Michael J Moroney, "Facts from Figures", 1951)

"It pays to keep wide awake in studying any graph. The thing looks so simple, so frank, and so appealing that the careless are easily fooled. [...] Data and formulae should be given along with the graph, so that the interested reader may look at the details if he wishes." (Michael J Moroney, "Facts from Figures", 1951)

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

"Some distributions [...] are symmetrical about their central value. Other distributions have marked asymmetry and are said to be skew. Skew distributions are divided into two types. If the 'tail' of the distribution reaches out into the larger values of the variate, the distribution is said to show positive skewness; if the tail extends towards the smaller values of the variate, the distribution is called negatively skew." (Michael J Moroney, "Facts from Figures", 1951)

"The economists, of course, have great fun - and show remarkable skill - in inventing more refined index numbers. Sometimes they use geometric averages instead of arithmetic averages (the advantage here being that the geometric average is less upset by extreme oscillations in individual items), sometimes they use the harmonic average. But these are all refinements of the basic idea of the index number [...]" (Michael J Moroney, "Facts from Figures", 1951)

"The mode would form a very poor basis for any further calculations of an arithmetical nature, for it has deliberately excluded arithmetical precision in the interests of presenting a typical result. The arithmetic average, on the other hand, excellent as it is for numerical purposes, has sacrificed its desire to be typical in favour of numerical accuracy. In such a case it is often desirable to quote both measures of central tendency." (Michael J Moroney, "Facts from Figures", 1951)

"The statistician’s job is to draw general conclusions from fragmentary data. Too often the data supplied to him for analysis are not only fragmentary but positively incoherent, so that he can do next to nothing with them. Even the most kindly statistician swears heartily under his breath whenever this happens". (Michael J Moroney, "Facts from Figures", 1951)

"Undoubtedly one of the most elegant, powerful, and useful techniques in modern statistical method is that of the Analysis of Variation and Co-variation by which the total variation in a set of data may be reduced to components associated with possible sources of variability whose relative importance we wish to assess. The precise form which any given analysis will take is intimately connected with the structure of the investigation from which the data are obtained. A simple structure will lead to a simple analysis; a complex structure to a complex analysis." (Michael J Moroney, "Facts from Figures", 1951)

"When the mathematician speaks of the existence of a 'functional relation' between two variable quantities, he means that they are connected by a simple 'formula that is to say, if we are told the value of one of the variable quantities we can find the value of the second quantity by substituting in the formula which tells us how they are related. [...] The thing to be clear about before we proceed further is that a functional relationship in mathematics means an exact and predictable relationship, with no ifs or buts about lt. It is useful in practice so long as the ifs and buts are only tiny voices which even the most ardent protagonist of proportional representation can ignore with a clear conscience." (Michael J Moroney, "Facts from Figures", 1951)

🖍️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)