🖍️George E P Box - Collected Quotes

"Statistical criteria should (1) be sensitive to change in the specific factors tested, (2) be insensitive to changes, of a magnitude likely to occur in practice, in extraneous factors." (George E P Box, 1955)

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

"To find out what happens to a system when you interfere with it you have to interfere with it (not just passively observe it)." (George E P Box, "Use and Abuse of Regression", 1966)

"A man in daily muddy contact with field experiments could not be expected to have much faith in any direct assumption of independently distributed normal errors." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)

"For the theory-practice iteration to work, the scientist must be, as it were, mentally ambidextrous; fascinated equally on the one hand by possible meanings, theories, and tentative models to be induced from data and the practical reality of the real world, and on the other with the factual implications deducible from tentative theories, models and hypotheses." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)

"One important idea is that science is a means whereby learning is achieved, not by mere theoretical speculation on the one hand, nor by the undirected accumulation of practical facts on the other, but rather by a motivated iteration between theory and practice." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)

"Since all models are wrong the scientist cannot obtain a ‘correct’ one by excessive elaboration. On the contrary following William of Occam he should seek an economical description of natural phenomena. Just as the ability to devise simple but evocative models is the signature of the great scientist so overelaboration and overparameterization is often the mark of mediocrity." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)

"Since all models are wrong the scientist must be alert to what is importantly wrong. It is inappropriate to be concerned about mice when there are tigers abroad." (George E P Box, "Science and Statistics", Journal of the American Statistical Association 71, 1976)

"Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful." (George E P Box, "Empirical Model-Building and Response Surfaces", 1987)

"The fact that [the model] is an approximation does not necessarily detract from its usefulness because models are approximations. All models are wrong, but some are useful." (George E P Box, 1987)

"Statistics is, or should be, about scientific investigation and how to do it better, but many statisticians believe it is a branch of mathematics." (George E P Box, Commentary, Technometrics 32, 1990)

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

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

"All models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind." (George E P Box & Norman R Draper, "Response Surfaces, Mixtures, and Ridge Analyses", 2007)

"In my view, statistics has no reason for existence except as the catalyst for investigation and discovery." (George E P Box)

🖍️Cathy O'Neil - Collected Quotes

"A model, after all, is nothing more than an abstract representation of some process, be it a baseball game, an oil company’s supply chain, a foreign government’s actions, or a movie theater’s attendance. Whether it’s running in a computer program or in our head, the model takes what we know and uses it to predict responses in various situations. All of us carry thousands of models in our heads. They tell us what to expect, and they guide our decisions." (Cathy O'Neil, "Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy", 2016)

"Big Data processes codify the past. They do not invent the future. Doing that requires moral imagination, and that’s something only humans can provide. We have to explicitly embed better values into our algorithms, creating Big Data models that follow our ethical lead. Sometimes that will mean putting fairness ahead of profit." (Cathy O'Neil, "Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy", 2016)

"No model can include all of the real world’s complexity or the nuance of human communication. Inevitably, some important information gets left out. […] To create a model, then, we make choices about what’s important enough to include, simplifying the world into a toy version that can be easily understood and from which we can infer important facts and actions.[…] Sometimes these blind spots don’t matter. […] A model’s blind spots reflect the judgments and priorities of its creators. […] Our own values and desires influence our choices, from the data we choose to collect to the questions we ask. Models are opinions embedded in mathematics." (Cathy O'Neil, "Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy", 2016)

"The first question: Even if the participant is aware of being modeled, or what the model is used for, is the model opaque, or even invisible? […] the second question: Does the model work against the subject’s interest? In short, is it unfair? Does it damage or destroy lives? […] The third question is whether a model has the capacity to grow exponentially. As a statistician would put it, can it scale?" (Cathy O'Neil, "Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy", 2016)

"Whether or not a model works is also a matter of opinion. After all, a key component of every model, whether formal or informal, is its definition of success." (Cathy O'Neil, "Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy", 2016)

"While Big Data, when managed wisely, can provide important insights, many of them will be disruptive. After all, it aims to find patterns that are invisible to human eyes. The challenge for data scientists is to understand the ecosystems they are wading into and to present not just the problems but also their possible solutions." (Cathy O'Neil, "Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy", 2016)

🖍️Darell Huff - Collected Quotes

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

"Extrapolations are useful, particularly in the form of soothsaying called forecasting trends. But in looking at the figures or the charts made from them, it is necessary to remember one thing constantly: The trend to now may be a fact, but the future trend represents no more than an educated guess. Implicit in it is 'everything else being equal' and 'present trends continuing'. And somehow everything else refuses to remain equal." (Darell Huff, "How to Lie with Statistics", 1954)

"If you can't prove what you want to prove, demonstrate something else and pretend that they are the something. In the daze that follows the collision of statistics with the human mind, hardly anybody will notice the difference." (Darell Huff, "How to Lie with Statistics", 1954)

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

"Only when there is a substantial number of trials involved is the law of averages a useful description or prediction." (Darell Huff, "How to Lie with Statistics", 1954)

"Percentages offer a fertile field for confusion. And like the ever-impressive decimal they can lend an aura of precision to the inexact. […] Any percentage figure based on a small number of cases is likely to be misleading. It is more informative to give the figure itself. And when the percentage is carried out to decimal places, you begin to run the scale from the silly to the fraudulent." (Darell Huff, "How to Lie with Statistics", 1954)

"Place little faith in an average or a graph or a trend when those important figures are missing."  (Darell Huff, "How to Lie with Statistics", 1954)

"Sometimes the big ado is made about a difference that is mathematically real and demonstrable but so tiny as to have no importance. This is in defiance of the fine old saying that a difference is a difference only if it makes a difference." (Darell Huff, "How to Lie with Statistics", 1954)

"The fact is that, despite its mathematical base, statistics is as much an art as it is a science. A great many manipulations and even distortions are possible within the bounds of propriety. Often the statistician must choose among methods, a subjective process, and find the one that he will use to represent the facts." (Darell Huff, "How to Lie with Statistics", 1954)

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

"The secret language of statistics, so appealing in a fact-minded culture, is employed to sensationalize, inflate, confuse, and oversimplify. Statistical methods and statistical terms are necessary in reporting the mass data of social and economic trends, business conditions, 'opinion' polls, the census. But without writers who use the words with honesty and understanding and readers who know what they mean, the result can only be semantic nonsense." (Darell Huff, "How to Lie with Statistics", 1954)

"There are often many ways of expressing any figure. […] The method is to choose the one that sounds best for the purpose at hand and trust that few who read it will recognize how imperfectly it reflects the situation." (Darell Huff, "How to Lie with Statistics", 1954)

"To be worth much, a report based on sampling must use a representative sample, which is one from which every source of bias has been removed." (Darell Huff, "How to Lie with Statistics", 1954)

"When numbers in tabular form are taboo and words will not do the work well as is often the case. There is one answer left: Draw a picture. About the simplest kind of statistical picture or graph, is the line variety. It is very useful for showing trends, something practically everybody is interested in showing or knowing about or spotting or deploring or forecasting." (Darell Huff, "How to Lie with Statistics", 1954)

"When you are told that something is an average you still don't know very much about it unless you can find out which of the common kinds of average it is-mean, median, or mode. [...] The different averages come out close together when you deal with data, such as those having to do with many human characteristics, that have the grace to fall close to what is called the normal distribution. If you draw a curve to represent it you get something shaped like a bell, and mean, median, and mode fall at the same point." (Darell Huff, "How to Lie with Statistics", 1954)

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

🖍️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)

"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)

"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)

"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)

"However, because ML algorithms are biased to look for different types of patterns, and because there is no one learning bias across all situations, there is no one best ML algorithm. In fact, a theorem known as the 'no free lunch theorem' states that there is no one best ML algorithm that on average outperforms all other algorithms across all possible data sets." (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)

🖍️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)

🖍️Dianne Cook - Collected Quotes

"A common myth is that non-linear dimension reduction captures non-linear patterns in the high-dimensional data. It may or may not do this. The term means that the methods transform the data non-linearly into a useful (or not) visual representation." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"Bias and variance are conceptual constructs. Bias is not possible to quantify unless a true model is known. It is used for setting up simulations and comparing various models, because in these controlled scenarios bias and variance can be computed. In practice, it is not possible to compute. Using high-dimensional visualisation can help with understanding the shape of the class and separation between classes. This provides a better sense about whether a particular approach will be able to capture the shape of the boundary or not, and will thus likely have low or high bias." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"Defining an appropriate distance metric from the context ofthe problem is a most important decision. For example, if your variables are all numeric, and on the same scale, then Euclidean distance might be best. If your variables are categorical, you might need to use something like Hamming distance." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"Hierarchical clustering is summarised by a dendrogram, which sequentially shows points being joined to form a cluster, with the corresponding distances. Breaking the data into clusters is done by cutting the dendrogram at the long edges. [...] Plotting the dendrogram in the data space can help you understand how the hierarchical clustering has collected the points together into clusters. You can learn if the algorithm has been confused by nuisance patterns in the data, and how different choices of linkage method affect the result." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"High-dimensional data spaces are fascinating places. You may think that there are a lot of ways to plot one or two variables, and a lot of types of patterns that can be found. You might use a density plot and see skewness or a dot plot to find outliers. A scatterplot of two variables might reveal a non-linear relationship or a barrier beyond which no observations exist. We don’t as yet have so many different choices of plot types for high dimensions, but these types of patterns are also what we seek in scatterplots of high-dimensional data. The additional dimensions can clarify these patterns, so that clusters are likely to be more distinct. Observations that did not appear to be very different can be seen to be lonely anomalies in high dimensions, and that no other observations have quite the same combination of values." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"It is important to visualise your data because you might discover things that you could never have anticipated. Although there are many resources available for data visualisation, there are few comprehensive resources on high-dimensional data visualisation. High-dimensional (or multivariate) data arises when many different things are measured for each observation. While we can learn many things from plotting with 1D and 2D or 3D methods there are likely more structures hidden in the higher dimensions." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"Non-linear dimension reduction (NLDR) aims to find a single low-dimensional representation of the high-dimensional data that shows the main features of the data. If there are separated clusters present, then it might be a layout where the clusters are all distinct, in a way that a single linear projection could not reveal. For observations falling on a low-dimensional non-linear manifold in high dimensions the NLDR might unfold or unroll it so that they are represented in a plane where the distances are similar to their distance along the manifold." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"PCA (Principal Component Analysis) is very broadly useful for summarising linear association by using combinations of the variables that are highly correlated. However, high correlation can also occur when there are outliers or clustering. PCA is commonly used to detect these patterns also, although this might NOT be a reliable way to do so. To detect clustering or anomalies, using a different approach that is specifically focused on these types of patterns is advisable. To some extent capturing clustering or anomalies using PCA is actually finding problematic patterns that adversely affect conducting appropriate dimension reduction." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"PCA (Principal Component Analysis) is not very effective when the distribution of the variables is highly skewed, so it can be helpful to transform variables to make them more symmetrically distributed before conducting PCA. It is also possible to summarise different types of structure by generalising the optimisation criteria to any function of projected data, f(XA), which is called projection pursuit (PP)." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"Unsupervised classification, or cluster analysis, organizes observations into similar groups. Clusteranalysis is a commonly used, appealing, and conceptually intuitive statistical method. Some of its uses include market segmentation, where customers are grouped into clusters with similar attributes for targeted marketing; gene expression analysis, where genes with similar expression patterns are grouped together; and the creation of taxonomies for animals, insects, or plants. Clustering can be used as a way of reducing a massive amount of data because observations within a cluster can be summarised by its centre. Also, clustering effectively subsets the data thus simplifying analysis because observations in each cluster can be analysed separately." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"The way variables are scaled can affect the appearance of dimensionity. If the variables are scaled together, using global values, some variables may have smaller variance than others. Scaling variables individually shifts the focus to association between variables, as the predominant reason for reduced dimension." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"To determine which variables are responsible for the reduced dimension look for the axes that extend out of the point cloud. These contribute to smaller variation in the observations, and thus indicate possible dimension reduction using these variables." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"To understand variance, we need to know how the model fit changes when a different training sample is used to fit the model. This is achieved by dividing the training sample into folds and fitting a model to each fold. This is more difficult to evaluate with visual methods because it would require examining multiple samples for small differences." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"Viewing the dendrograms in high dimensions provides insight into how the algorithm has joined points to clusters. For example, single linkage often has edges leading to a single focal point, which might not yield a useful clustering but might help to 

identify outliers. If the edges point to multiple focal points, with long edges bridging gaps in the data, the result is more likely yielding a useful clustering." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

"When exploring the implicit dimensionality of multivariate data we are looking for projections where the points do not fill the plotting canvas fully. This would indicate that the observed values do not fully populate the high dimensions." (Dianne Cook & Ursula Laa, "Interactively Exploring High-Dimensional Data and Models in R", 2026)

🖍️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)

🖍️Cheryl Cihon - Collected Quotes

"A combination of graphical and tabular presentations may be used to good advantage. The former illustrates most effectively qualitative characteristics (e.g., changes of data with time or sequence) while the latter is the best means to present quantitative information." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"Each systematic error associated with a given measurement process is always of the same sign and magnitude. It persists measurement after measurement. When its existence is established, such an error is called a bias, and reasonable effort should be made to correct for it. Sometimes the observed bias is the result of the concurrence of several biases that cannot or at least have not been individually identified. One of the purposes of statistical treatment of data is to decide whether an apparently erroneous result is real and indicates a bias or whether it could happen as the result of chance variability, even in a well-behaved measurement system. There can be, of course, biases that have not been identified as such. Also, there are limits to how well one can correct for known biases, and this inadequacy must be considered when limits of uncertainty are assigned to data." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"Essentially, the null hypothesis is that there is not a significant difference between two results. It will be seen that differences may have to be quite large in some instances before they are statistically significant, especially in the case of small data sets of high variability. Statistics will not say whether or not an apparent difference is real, but will only give the probability that it could have been as large as it is by chance alone. Often, the answer will be that there is no reason to believe a difference exists other than due to a chance occurrence, based on the statistical evidence available. Remember that this is not saying that there is no difference but that the evidence presented is insufficient to support the belief that the difference is not more than a random effect." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"Frequency distributions, commonly called histograms, are special kinds of bar charts that are used widely for displaying variability of scientific and technical information. Such displays may be used to demonstrate that a normal distribution is or is not achieved [...]. Generally, a minimum of 25 data points is required to prepare a good bar chart, and considerably more is highly desirable. The data are divided into groups bounded by cells of fixed limits. The number of cells chosen to cover the range of values for the data is somewhat arbitrary. If too few, a distribution can lack resolution; if too many, there can be numerous unpopulated cells in the case of small data sets. Trial and error may be used in a specific case to decide what is most effective." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"Nomographs are effective ways to graphically calculate various functionally related quantities. Nomographs are really graphical computational devices. They were once used widely in engineering situations when calculating was more laborious than at the present time, and they still can be useful when complex relationships are concerned. In brief, scales are laid out in which the scale intervals and placement of the lines are chosen by well-established procedures. A straight edge can then be used to interconnect independent variables so the corresponding values of dependent variables can be read." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"Pie charts are more comprehensible as the sectors are approximately equal. A feeling of relationship is lost as very small sectors are placed alongside very large ones. In any case, numerical values need to be inserted in the sectors or related to them by lines or arrows to provide numerical significance, since the eye is not a good quantitative judge of the relative areas of sectors. The total number of sectors used should be reasonably small. While not a hard and fast rule, a maximum of eight sectors is a reasonable number. Sectors may be homogeneous or consist of conglomerates of several items. The information contained in a sector may be displayed as a separate pie chart. This is an effective way to handle conglomerates." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"The inevitability of variability complicates the evaluation and use of data. It must be recognized that many uses require data quality that may be difficult to achieve. There are minimum quality standards required for every measurement situation (sometimes called data quality objectives). These standards should be established in advance and both the producer and the user must be able to determine whether they have been met. The only way that this can be accomplished is to attain statistical control of the measurement process and to apply valid statistical procedures in the analysis of the data." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"The quantitative accuracy of what is measured is an obvious indicator of data quality. Because of inescapable variability, data will always have some degree of uncertainty. When measurement plans are properly made and adequately executed, it is possible to assign quantitative limits of uncertainty to measured values." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"The second type of uncertainty results from random causes that produce fluctuations in both sign and magnitude, the latter within well-defined limits, however. In the long run, the random error averages out to zero. The random error accounts for the variability of individual measurements and it will be shown that it can be statistically characterized by what is called a standard deviation. This term is thus a measure of the dispersion of the data around a mean or average value. When the value of the standard deviation is small, the data cluster closely around the mean; when it is large, the spread is greater." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"The use of tables is perhaps the most common method for presentation of data. The format will vary, depending on what information is needed to be conveyed. Even a cursory perusal of the scientific literature will reveal many examples of both good and poor tables. A good table is simply one that presents data in an easily understandable manner. Tables should be relatively simple in order to promote understanding and the columns should have a clear relationship to each other. Column titles should be as brief as possible, consistent with clarity. Footnotes may be needed in some cases to provide further explanation of the headings." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

"Variability is inevitable in a measurement process. The operation of a measurement process does not produce one number but a variety of numbers. Each time it is applied to a measurement situation it can be expected to produce a slightly different number or sets of numbers. The means of sets of numbers will differ among themselves, but to a lesser degree than the individual values. One must distinguish between natural variability and instability. Gross instability can arise from many sources, including lack of control of the process. Failure to control steps that introduce bias also can introduce variability. Thus, any variability in calibration, done to minimize bias, can produce variability of measured values." (Cheryl Cihon & John K Taylor, "Statistical Techniques for Data Analysis" 2nd. ed., 2005)

🖍️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)