📉Graphical Representation: Interpretation (Just the Quotes)

"To a very striking degree our culture has become a Statistical culture. Even a person who may never have heard of an index number is affected [...] by [...] of those index numbers which describe the cost of living. It is impossible to understand Psychology, Sociology, Economics, Finance or a Physical Science without some general idea of the meaning of an average, of variation, of concomitance, of sampling, of how to interpret charts and tables." (Carrol D Wright, 1887)

"Except in some of the simplest cases where the line connecting the plotted data is straight, it will generally be possible to fit a number of very different forms of equation to the same curve, none of them exactly, but all agreeing with the original about equally well. Interpolation on any of these curves will usually give results within the desired degree of accuracy. The greatest caution, however, should be observed in exterpolation, or the use of the equation outside of the limits of the observations." (John B Peddle, "The Construction of Graphical Charts", 1910)

"Most authors would greatly resent it if they were told that their writings contained great exaggerations, yet many of these same authors permit their work to be illustrated with charts which are so arranged as to cause an erroneous interpretation. If authors and editors will inspect their charts as carefully as they revise their written matter, we shall have, in a very short time, a standard of reliability in charts and illustrations just as high as now found in the average printed page." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"The principles of charting and curve plotting are not at all complex, and it is surprising that many business men dodge the simplest charts as though they involved higher mathematics or contained some sort of black magic. [...] The trouble at present is that there are no standards by which graphic presentations can be prepared in accordance with definite rules so that their interpretation by the reader may be both rapid and accurate. It is certain that there will evolve for methods of graphic presentation a few useful and definite rules which will correspond with the rules of grammar for the spoken and written language." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

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

"The use of two or more amount scales for comparisons of series in which the units are unlike and, therefore, not comparable [...] generally results in an ineffective and confusing presentation which is difficult to understand and to interpret. Comparisons of this nature can be much more clearly shown by reducing the components to a comparable basis as percentages or index numbers." (Rufus R Lutz, "Graphic Presentation Simplified", 1949)

"Charts and graphs represent an extremely useful and flexible medium for explaining, interpreting, and analyzing numerical facts largely by means of points, lines, areas, and other geometric forms and symbols. They make possible the presentation of quantitative data in a simple, clear, and effective manner and facilitate comparison of values, trends, and relationships. Moreover, charts and graphs possess certain qualities and values lacking in textual and tabular forms of presentation." (Calvin F Schmid, "Handbook of Graphic Presentation", 1954)

"In line charts the grid structure plays a controlling role in interpreting facts. The number of vertical rulings should be sufficient to indicate the frequency of the plottings, facilitate the reading of the time values on the horizontal scale. and indicate the interval or subdivision of time." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"The logarithmic transformation serves several purposes:" (1) The resulting regression coefficients sometimes have a more useful theoretical interpretation compared to a regression based on unlogged variables." (2) Badly skewed distributions - in which many of the observations are clustered together combined with a few outlying values on the scale of measurement - are transformed by taking the logarithm of the measurements so that the clustered values are spread out and the large values pulled in more toward the middle of the distribution." (3) Some of the assumptions underlying the regression model and the associated significance tests are better met when the logarithm of the measured variables is taken." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"The time-series plot is the most frequently used form of graphic design. With one dimension marching along to the regular rhythm of seconds, minutes, hours, days, weeks, months, years, centuries, or millennia, the natural ordering of the time scale gives this design a strength and efficiency of interpretation found in no other graphic arrangement." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"The bar of a bar chart has two aspects that can be used to visually decode quantitative information-size" (length and area) and the relative position of the end of the bar along the common scale. The changing sizes of the bars is an important and imposing visual factor; thus it is important that size encode something meaningful. The sizes of bars encode the magnitudes of deviations from the baseline. If the deviations have no important interpretation, the changing sizes are wasted energy and even have the potential to mislead." (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38" (4) 1984)

"Good graphics can be spoiled by bad annotation. Labels must always be subservient to the information to be conveyed, and legibility should never be sacrificed for style. All the information on the sheet should be easy to read, and more important, easy to interpret. The priorities of the information should be clearly expressed by the use of differing sizes, weights and character of letters." (Bruce Robertson, "How to Draw Charts & Diagrams", 1988)

"Statistics is a tool. In experimental science you plan and carry out experiments, and then analyse and interpret the results. To do this you use statistical arguments and calculations. Like any other tool - an oscilloscope, for example, or a spectrometer, or even a humble spanner - you can use it delicately or clumsily, skillfully or ineptly. The more you know about it and understand how it works, the better you will be able to use it and the more useful it will be." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"The fact that map is a fuzzy and radial, rather than a precisely defined, category is important because what a viewer interprets a display to be will influence her expectations about the display and how she interacts with it." (Alan MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"Graphic misrepresentation is a frequent misuse in presentations to the nonprofessional. The granddaddy of all graphical offenses is to omit the zero on the vertical axis. As a consequence, the chart is often interpreted as if its bottom axis were zero, even though it may be far removed. This can lead to attention-getting headlines about 'a soar' or 'a dramatic rise" (or fall)'. A modest, and possibly insignificant, change is amplified into a disastrous or inspirational trend." (Herbert F Spirer et al, "Misused Statistics" 2nd Ed, 1998)

"Without meaningful data there can be no meaningful analysis. The interpretation of any data set must be based upon the context of those data. Unfortunately, much of the data reported to executives today are aggregated and summed over so many different operating units and processes that they cannot be said to have any context except a historical one - they were all collected during the same time period. While this may be rational with monetary figures, it can be devastating to other types of data." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"The acquisition of information is a flow from noise to order - a process converting entropy to redundancy. During this process, the amount of information decreases but is compensated by constant re-coding. In the recoding the amount of information per unit increases by means of a new symbol which represents the total amount of the old. The maturing thus implies information condensation. Simultaneously, the redundance decreases, which render the information more difficult to interpret." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Every statistical analysis is an interpretation of the data, and missingness affects the interpretation. The challenge is that when the reasons for the missingness cannot be determined there is basically no way to make appropriate statistical adjustments. Sensitivity analyses are designed to model and explore a reasonable range of explanations in order to assess the robustness of the results." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"Choose scales wisely, as they have a profound influence on the interpretation of graphs. Not all scales require that zero be included, but bar graphs and other graphs where area is judged do require it." (Naomi B Robbins, "Creating More effective Graphs", 2005)

"Data often arrive in raw form, as long lists of numbers. In this case your job is to summarize the data in a way that captures its essence and conveys its meaning. This can be done numerically, with measures such as the average and standard deviation, or graphically. At other times you find data already in summarized form; in this case you must understand what the summary is telling, and what it is not telling, and then interpret the information for your readers or viewers." (Charles Livingston & Paul Voakes, "Working with Numbers and Statistics: A handbook for journalists", 2005)

"The visual representation of a scale - an axis with ticks - looks like a ladder. Scales are the types of functions we use to map varsets to dimensions. At first glance, it would seem that constructing a scale is simply a matter of selecting a range for our numbers and intervals to mark ticks. There is more involved, however. Scales measure the contents of a frame. They determine how we perceive the size, shape, and location of graphics. Choosing a scale" (even a default decimal interval scale) requires us to think about what we are measuring and the meaning of our measurements. Ultimately, that choice determines how we interpret a graphic." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"Generally pie charts are to be avoided, as they can be difficult to interpret particularly when the number of categories is greater than five. Small proportions can be very hard to discern […] In addition, unless the percentages in each of the individual categories are given as numbers it can be much more diff i cult to estimate them from a pie chart than from a bar chart […]." (Jenny Freeman et al, "How to Display Data", 2008)

"Color can tell us where to look, what to compare and contrast, and it can give us a visual scale of measure. Because color can be so effective, it is often used for multiple purposes in the same graphic - which can create graphics that are dazzling but difficult to interpret. Separating the roles that color can play makes it easier to apply color specifically for encouraging different kinds of visual thinking. [...] Choose colors to draw attention, to label, to show relationships" (compare and contrast), or to indicate a visual scale of measure." (Felice C Frankel & Angela H DePace, "Visual Strategies", 2012)

"Done well, annotation can help explain and facilitate the viewing and interpretive experience. It is the challenge of creating a layer of user assistance and user insight: how can you maximize the clarity and value of engaging with this visualization design?" (Andy Kirk, "Data Visualization: A successful design process", 2012)

"The big problems with statistics, say its best practitioners, have little to do with computations and formulas. They have to do with judgment - how to design a study, how to conduct it, then how to analyze and interpret the results. Journalists reporting on statistics have many chances to do harm by shaky reporting, and so are also called on to make sophisticated judgments. How, then, can we tell which studies seem credible, which we should report?" (Victor Cohn & Lewis Cope, "News & Numbers: A writer’s guide to statistics" 3rd Ed, 2012)

"The main difference between journalistic and artistic infographics is that, while in the first information must try to be as objective as possible, the second supports a complete subjectivity and can lend itself to different interpretations, all of them valid. That’s the concept of 'subjective infographic', something apparently contradictory." (Jaime Serra, [interviewed] 2012)

"The universal intelligibility of a pictogram is inversely proportional to its complexity and potential for interpretive ambiguity." (Joel Katz, "Designing Information: Human factors and common sense in information design", 2012)

"While the information is of the utmost importance when it comes to soundness, what is done with the information - essentially, how it is designed - is also important. With this in mind, there are two things to consider: format and design quality. If an inappropriate format is used, the outcome will be inferior. Similarly, if the design misrepresents or skews the information deliberately or due to user error, or if the design is inappropriate given the subject matter, it cannot be considered high quality, no matter how aesthetically appealing it appears at first glance." (Jason Lankow et al, "Infographics: The power of visual storytelling", 2012)

"Visualization can be appreciated purely from an aesthetic point of view, but it’s most interesting when it’s about data that’s worth looking at. That’s why you start with data, explore it, and then show results rather than start with a visual and try to squeeze a dataset into it. It’s like trying to use a hammer to bang in a bunch of screws. […] Aesthetics isn’t just a shiny veneer that you slap on at the last minute. It represents the thought you put into a visualization, which is tightly coupled with clarity and affects interpretation." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"Graphs can help us interpret data and draw inferences. They can help us see tendencies, patterns, trends, and relationships. A picture can be worth not only a thousand words, but a thousand numbers. However, a graph is essentially descriptive - a picture meant to tell a story. As with any story, bumblers may mangle the punch line and the dishonest may lie." (Gary Smith, "Standard Deviations", 2014)

"Commonly, data do not make a clear and unambiguous statement about our world, often requiring tools and methods to provide such clarity. These methods, called statistical data analysis, involve collecting, manipulating, analyzing, interpreting, and presenting data in a form that can be used, understood, and communicated to others." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"Confirmation bias can affect nearly every aspect of the way you look at data, from sampling and observation to forecasting - so it’s something to keep in mind anytime you’re interpreting data. When it comes to correlation versus causation, confirmation bias is one reason that some people ignore omitted variables - because they’re making the jump from correlation to causation based on preconceptions, not the actual evidence." (John H Johnson & Mike Gluck, "Everydata: The misinformation hidden in the little data you consume every day", 2016)

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

"Too many simultaneous encodings will be overwhelming to the reader; colors must be easily distinguishable, and of a small enough number that the reader can interpret them. " (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

"As a first principle, any visualization should convey its information quickly and easily, and with minimal scope for misunderstanding. Unnecessary visual clutter makes more work for the reader’s brain to do, slows down the understanding" (at which point they may give up) and may even allow some incorrect interpretations to creep in." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"Even though data is being thrust on more people, it doesn’t mean everyone is prepared to consume and use it effectively. As our dependence on data for guidance and insights increases, the need for greater data literacy also grows. If literacy is defined as the ability to read and write, data literacy can be defined as the ability to understand and communicate data. Today’s advanced data tools can offer unparalleled insights, but they require capable operators who can understand and interpret data." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)

"When dealing with meaningful visual representation, aspects of a representation's meaning can be altered by modifying its visual characteristics; these characteristics are extensively explored in semiotics, the study of signs and symbols and their use or interpretation." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"As beautiful as data can be, it’s not an al fresco painting that should be open to interpretation from anyone who walks by its section of the museum. Make bold, smart color choices that leave no doubt what the purpose of the data is." (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

"But rules are open to interpretation and sometimes arbitrary or even counterproductive when it comes to producing good visualizations. They’re for responding to context, not setting it. Instead of worrying about whether a chart is right" or "wrong", focus on whether it’s good." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

"Charts used to confirm are less formal, and designed well enough to be interpreted, but they don’t always have to be presentation worthy. […] Or maybe you don’t know what you’re looking for […] This is exploratory work - rougher still in design, usually iterative, sometimes interactive. Most of us don’t do as much exploratory work as we do declarative and confirmatory; we should do more. It’s a kind of data brainstorming." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

See also: Misinterpretation 

📉Graphical Representation: Charts vs. Thousand Words (Just the Quotes)

"The drawing shows me at a glance what would be spread over ten pages in a book." (Ivan Turgenev, 1862) [2]

"Sometimes, half a dozen figures will reveal, as with a lighting-flash, the importance of a subject which ten thousand labored words with the same purpose in view, had left at last but dim and uncertain." (Mark Twain, "Life on the Mississippi", 1883) 

"One good picture is worth many pages of written description." (William Sproston Caine, 1891) [2]

"One look is worth a thousand words" (Kathleen Caffyn, 1903) 

"Use a picture. It's worth a thousand words." (Arthur Brisbane, The Post-Standard, 1911)

"One Look Is Worth A Thousand Words" ([advertisement] 1913)

"A picture is worth ten thousand words. If you can’t see the truth in these pictures you are among the vast majority that must learn only by experience." (Arthur Brisbane, 1915)

"One picture is worth ten thousand words." (Frederick R Barnard, Printer’s Ink, 1921)

"One Picture Worth Ten Thousand Words" ([Chinese proverb] 1927)

"In many instances, a picture is indeed worth a thousand words. To make this true in more diverse circumstances, much more creative effort is needed to pictorialize the output from data analysis. Naive pictures are often extremely helpful, but more sophisticated pictures can be both simple and even more informative." (John W Tukey & Martin B Wilk, "Data Analysis and Statistics: An Expository Overview", 1966)

"Graphic charts are ways of presenting quantitative as well as qualitative information in an efficient and effective visual form. Numbers and ideas presented graphically are often more easily understood. remembered. and integrated than when they are presented in narrative or tabular form. Descriptions. trends. relationships, and comparisons can be made more apparent. Less time is required to present and comprehend information when graphic methods are employed. As the old truism states, 'One picture is worth a thousand words.'" (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"One word is worth a thousand pictures. If it's the right word." (Edward Abbey, "Beyond the Wall: Essays from the Outside", 1984)

"A picture may be worth a thousand words, a formula is worth a thousand pictures." (Edsger Dijkstra, [conference at ETH Zurich] 1994)

"A magnificent picture is never worth a thousand perfect words." (John Dunning, "The Bookman's Wake", 1995)

"A picture tells a thousand words. But you get a thousand pictures from someone's voice." (Paul Fleischman, "Seek", 2001)

"If a picture is worth a thousand words, a metaphor is worth a thousand pictures." (Daniel H Pink, "A Whole New Mind: Why Right-Brainers Will Rule the Future", 2005)

"The amount of information rendered in a single financial graph is easily equivalent to thousands of words of text or a page-sized table of raw values. A graph illustrates so many characteristics of data in a much smaller space than any other means. Charts also allow us to tell a story in a quick and easy way that words cannot." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"Visual reports exploit the idea that a picture is worth a thousand words and, in particular, for many tasks a picture is more useful than a large table of numbers." (Stephen G Eick, "Graph Drawing for Data Analytics" [in "Handbook of Graph Drawing and Visualization"] , 2013)

"Graphs can help us interpret data and draw inferences. They can help us see tendencies, patterns, trends, and relationships. A picture can be worth not only a thousand words, but a thousand numbers. However, a graph is essentially descriptive - a picture meant to tell a story. As with any story, bumblers may mangle the punch line and the dishonest may lie." (Gary Smith, "Standard Deviations", 2014)

"The caption should explain what is shown, possibly also giving the data source. Captions should be detailed enough that the graphic can pretty well stand on its own. Longer is usually better than shorter. A picture may be worth a thousand words, but you need at least some words to describe and explain it." (Antony Unwin, "Graphical Data Analysis with R", 2015)

"A picture may be worth a thousand words, but not all pictures are readable, interpretable, meaningful, or relevant." (Kristen Sosulski, "Data Visualization Made Simple: Insights into Becoming Visual", 2018)

"A recurring theme in machine learning is combining predictions across multiple models. There are techniques called bagging and boosting which seek to tweak the data and fit many estimates to it. Averaging across these can give a better prediction than any one model on its own. But here a serious problem arises: it is then very hard to explain what the model is (often referred to as a 'black box'). It is now a mixture of many, perhaps a thousand or more, models." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"'A picture is worth a thousand words' is definitely true, and graphs can help you tell a story about your data that would otherwise go untold with only numerical summaries and statistics. While inferential statistics and effect size measures can help us draw relatively reliable conclusions from our data, graphs and visualizations can help make the scientific findings accessible to virtually anyone, even with minimal coursework in statistics or data science." (Daniel J Denis, "Univariate, Bivariate, and Multivariate Statistics Using R: Quantitative Tools for Data Analysis and Data Science, 2020)

"Although a picture may be worth a thousand words, a single static picture is in most cases insufficient for a valid analysis and for understanding of a complex subject. It is usual that an analyst needs to see different aspects or parts of data and look at the data from different perspectives. This means that the analyst needs to interact with the data and with the system that generates visual displays of the data: select data components and subsets for viewing, select and tune visualization techniques, transform the views, transform the data, and so on." (Natalia Andrienko et al, "Visual Analytics for Data Scientists", 2020)

"A picture really can be worth a thousand words, and human beings are adept at extracting useful information from visual presentations. Modern data analysis increasingly relies on graphical presentations to uncover meaning and convey results." (Robert I Kabacoff, "R in Action: Data analysis and graphics with R and Tidyverse", 2022)

"A good metaphor is worth a thousand pictures." (Anon) 

"As the Chinese say, 1001 words is worth more than a picture." (John McCarthy [source]) 

References:
[1] Wikipedia (2024) A picture is worth a thousand words [link]
[2] Quote Investigator (2022) A Picture Is Worth Ten Thousand Words [link] 

📉Graphical Representation: Images (Just the Quotes)

"[…] deduction consists in constructing an icon or diagram the relations of whose parts shall present a complete analogy with those of the parts of the object of reasoning, of experimenting upon this image in the imagination, and of observing the result so as to discover unnoticed and hidden relations among the parts." (Charles S Peirce, 1885)

"To analyse graphic representation precisely, it is helpful to distinguish it from musical, verbal and mathematical notations, all of which are perceived in a linear or temporal sequence. The graphic image also differs from figurative representation essentially polysemic, and from the animated image, governed by the laws of cinematographic time. Within the boundaries of graphics fall the fields of networks, diagrams and maps. The domain of graphic imagery ranges from the depiction of atomic structures to the representation of galaxies and extends into the spheres of topography and cartography." (Jacques Bertin, "Semiology of graphics" ["Semiologie Graphique"], 1967)

"A graphic is an illustration that, like a painting or drawing, depicts certain images on a flat surface. The graphic depends on the use of lines and shapes or symbols to represent numbers and ideas and show comparisons, trends, and relationships. The success of the graphic depends on the extent to which this representation is transmitted in a clear and interesting manner." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"If your words or images are not on point, making them dance in color won't make them relevant." (Edward R Tufte, "The cognitive style of PowerPoint", 2003)

"These little data lines, because of their active quality over time, are named sparklines - small, high-resolution graphics usually embedded in a full context of words, numbers, images. Sparklines are data words: data-intense, design-simple, word-sized graphics." (Edward R Tufte, "Beautiful Evidence", 2006)

"Be aware that bar charts provide ample opportunities for chart junk. The space within the bars is enticingly empty and it is tempting to put images or textures in the background. Some designers even swap out the standard bars for graphics." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"Geographic maps have the advantage of being true to scale - great for walking. Diagrams have the advantage of being easily imaged and remembered, often true to a non-pedestrian experience, and the ability to open up congestion, reduce empty space, and use real estate efficiently. Hybrids 'mapograms' ? - often have the disadvantages of both map and diagram with none of the corresponding advantages." (Joel Katz, "Designing Information: Human factors and common sense in information design", 2012)

"A great infographic leads readers on a visual journey, telling them a story along the way. Powerful infographics are able to capture people’s attention in the first few seconds with a strong title and visual image, and then reel them in to digest the entire message. Infographics have become an effective way to speak for the creator, conveying information and image simultaneously." (Justin Beegel, "Infographics For Dummies", 2014)

"Upon discovering a visual image, the brain analyzes it in terms of primitive shapes and colors. Next, unity contours and connections are formed. As well, distinct variations are segmented. Finally, the mind attracts active attention to the significant things it found. That process is permanently running to react to similarities and dissimilarities in shapes, positions, rhythms, colors, and behavior. It can reveal patterns and pattern-violations among the hundreds of data values. That natural ability is the most important thing used in diagramming." (Vasily Pantyukhin, "Principles of Design Diagramming", 2015)

"Most of us have difficulty figuring probabilities and statistics in our heads and detecting subtle patterns in complex tables of numbers. We prefer vivid pictures, images, and stories. When making decisions, we tend to overweight such images and stories, compared to statistical information. We also tend to misunderstand or misinterpret graphics." (Daniel J Levitin, "Weaponized Lies", 2017)

"People tend to comprehend visual images quicker and with fewer errors than words on a page. Visual images also activate memories better than words." (John Hoffmann, "Principles of Data Management and Presentation", 2017)

"Heatmap is another representational way in which the frequencies of the various parameters of the data set is represented in different colors, much like an image captured by a thermal imaging camera in which the graph consists of varying temperatures and the temperatures are differentiated according to the colors." (Shreyans Pathak & Shashwat Pathak, "Data Visualization Techniques, Model and Taxonomy", 2020)

"Cartographers employed a minimalist visual language and the simplicity of lines and geometry to lend an air of objectivity, universality and clarity. The sparse treatment of visuals suggests a more direct correspondence between the data and the representation, and less human involvement. It communicates that the image has been reduced to its bare minimum. It has been polished through successive passes to remove the unnecessary and the contingent. And in doing so, it indicates something essential and closer to a transcendent type, or perhaps an ideal." (Peter A Hall & Patricio Dávila, "Critical Visualization: Rethinking the Representation of Data", 2022)

"Representing data in visual form is a powerful rhetorical device precisely because it can collapse a complex array of data into a single strong and persuasive image. Visualizations, especially those that give a strong shape to the data, tend to have the effect of erasing the work that led to the making of the visualization." (Peter A Hall & Patricio Dávila, "Critical Visualization: Rethinking the Representation of Data", 2022)

💠SQL Server: Window Functions 🆕

Introduction

     In the past, in the absence or in parallel with other techniques, aggregate functions proved to be quite useful in order to solve several types of problems that involve the retrieval of first/last record or the display of details together with averages and other aggregates. Typically their use involves two or more joins between a dataset and an aggregation based on the same dataset or a subset of it. An aggregation can involve one or more columns that make the object of analysis. Sometimes it might be needed multiple such aggregations based on different sets of columns. Each such aggregation involves at least a join. Such queries can become quite complex, though they were a price to pay in order to solve such problems.

Partitions

     The introduction of analytic functions in Oracle and of window functions, a similar concept, in SQL Server, allowed the approach of such problems from a different simplified perspective. Central to this feature it’s the partition (of a dataset), its meaning being same as of mathematical partition of a set, defined as a division of a set into non-overlapping and non-empty parts that cover the whole initial set. The introduction of partitions it’s not necessarily something new, as the columns used in a GROUP BY clause determines (implicitly) a partition in a dataset. The difference in analytic/window functions is that the partition is defined explicitly inline together with a ranking or average function evaluated within a partition. If the concept of partition is difficult to grasp, let’s look at the result-set based on two Products (the examples are based on AdventureWorks database):
 

-- Price Details for 2 Products 
SELECT A.ProductID  
, A.StartDate 
, A.EndDate 
, A.StandardCost  
FROM [Production].[ProductCostHistory] A 
WHERE A.ProductID IN (707, 708) 
ORDER BY A.ProductID 
, A.StartDate 

   In this case a partition is “created” based on the first Product (ProductId = 707), while a second partition is based on the second Product (ProductId = 708). As a parenthesis, another partitioning could be created based on ProductId and StartDate; considering that the two attributes are a key in the table, this will partition the dataset in partitions of 1 record (each partition will have exactly one record).

Details and Averages

     In order to exemplify the use of simple versus window aggregate functions, let’s consider a problem in which is needed to display Standard Price details together with the Average Standard Price for each ProductId. When a GROUP BY clause is applied in order to retrieve the Average Standard Cost, the query is written under the form: 

-- Average Price for 2 Products 
SELECT A.ProductID  
, AVG(A.StandardCost) AverageStandardCost 
FROM [Production].[ProductCostHistory] A 
WHERE A.ProductID IN (707, 708) 
GROUPBY A.ProductID  
ORDERBY A.ProductID 

 

    In order to retrieve the details, the query can be written with the help of a FULL JOIN as follows:

-- Price Details with Average Price for 2 Products - using JOINs 
SELECT A.ProductID  
, A.StartDate 
, A.EndDate 
, A.StandardCost 
, B.AverageStandardCost 
, A.StandardCost - B.AverageStandardCost DiffStandardCost 
FROM [Production].[ProductCostHistory] A    
  JOIN ( -- average price        
    SELECT A.ProductID         
    , AVG(A.StandardCost) AverageStandardCost         
    FROM [Production].[ProductCostHistory] A        
    WHERE A.ProductID IN (707, 708)        
    GROUP BY A.ProductID      
) B  
    ON A.ProductID = B.ProductID 
WHERE A.ProductID IN (707, 708) 
ORDERBY A.ProductID 
, A.StartDate 

    

    As pointed above the partition is defined by ProductId. The same query written with window functions becomes:

-- Price Details with Average Price for 2 Products - using AVG window function 
SELECT A.ProductID  
, A.StartDate 
, A.EndDate 
, A.StandardCost 
, AVG(A.StandardCost) OVER(PARTITION BY A.ProductID) AverageStandardCost 
, A.StandardCost - AVG(A.StandardCost) OVER(PARTITION BY A.ProductID) DiffStandardCost 
FROM [Production].[ProductCostHistory] A 
WHERE A.ProductID IN (707, 708) 
ORDER BY A.ProductID 
, A.StartDate 

    As can be seen, in the second example, the AVG function is defined using the OVER clause with PartitionId as partition. Even more, the function is used in a formula to calculate the Difference Standard Cost. More complex formulas can be written making use of multiple window functions.  

The Last Record

     Let’s consider the problem of retrieving the nth record. Because with aggregate functions is easier to retrieve the first or last record, let’s consider that is needed to retrieve the last Standard Price for each ProductId. The aggregate function helps to retrieve the greatest Start Date, which farther helps to retrieve the record containing the Last Standard Price.

-- Last Price Details for 2 Products - using JOINs 
SELECT A.ProductID  
, A.StartDate 
, A.EndDate 
, A.StandardCost 
FROM [Production].[ProductCostHistory] A  
    JOIN ( -- average price          
    SELECT A.ProductID          
    , Max(A.StartDate) LastStartDate          
    FROM [Production].[ProductCostHistory] A          
    WHERE A.ProductID IN (707, 708)          
    GROUP BY A.ProductID      
) B      
   ON A.ProductID = B.ProductID  
  AND A.StartDate = B.LastStartDate 
WHERE A.ProductID IN (707, 708) 
ORDERBY A.ProductID 
,A.StartDate 

  

With window functions the query can be rewritten as follows:

-- Last Price Details for 2 Products - using AVG window function 
SELECT * 
FROM (-- ordered prices      
    SELECT A.ProductID      
    , A.StartDate      
    , A.EndDate      
    , A.StandardCost      
    , RANK() OVER(PARTITION BY A.ProductID ORDER BY A.StartDate DESC) Ranking      
    FROM [Production].[ProductCostHistory] A     
    WHERE A.ProductID IN (707, 708) 
  ) A 
WHERE Ranking = 1 
ORDER BY A.ProductID 
, A.StartDate 

  

   As can be seen, in order to retrieve the Last Standard Price, was considered the RANK function, the results being ordered descending by StartDate. Thus, the Last Standard Price will be always positioned on the first record. Because window functions can’t be used in WHERE clauses, it’s needed to encapsulate the initial logic in a subquery. Similarly could be retrieved the First Standard Price, this time ordering ascending the StartDate. The last query can be easily modified to retrieve the nth records (this can prove to be more difficult with simple average functions), the first/last nth records.

Conclusion

    Without going too deep into details, I shown above two representative scenarios in which solutions based on average functions could be simplified by using window functions. In theory the window functions provide greater flexibility but they have their own trade offs too. In the next posts I will attempt to further detail their use, especially in the context of Statistics.

📉Graphical Representation: Power (Just the Quotes)

"But law is no explanation of anything; law is simply a generalization, a category of facts. Law is neither a cause, nor a reason, nor a power, nor a coercive force. It is nothing but a general formula, a statistical table." (Florence Nightingale, "Suggestions for Thought", 1860)

"The wandering of a line is more powerful in its effect on the mind than a tabulated statement; it shows what is happening and what is likely to take place just as quickly as the eye is capable of working." (A Lester Boddington, "Statistics And Their Application To Commerce", 1921)

"Seeing color isn't always as simple as it may seem. Some colors are not easy to see unless the conditions are just right; some are so easy to see that they overpower everything else; some are easy to see but difficult to distinguish. […] Large masses of color become too visible and easily overwhelm the entire chart. The more visible the color the easier it is to use too much of it." (Kenneth W Haemer, "Color in Chart Presentation", The American Statistician Vol. 4" (2) , 1950)

"To see is to reason. Thus, the use of visual forms of communication has great potential for influencing what a person thinks. Graphic presentation is always much more than a way to present just facts or information. Rather, it is a way to influence thought, and, as such, graphics can be a powerful mode of persuasion." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"An especially effective device for enhancing the explanatory power of time-series displays is to add spatial dimensions to the design of the graphic, so that the data are moving over space (in two or three dimensions) as well as over time. […] Occasionally graphics are belligerently multivariate, advertising the technique rather than the data." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Modern data graphics can do much more than simply substitute for small statistical tables. At their best, graphics are instruments for reasoning about quantitative information. Often the most effective way to describe, explore, and summarize a set of numbers even a very large set - is to look at pictures of those numbers. Furthermore, of all methods for analyzing and communicating statistical information, well-designed data graphics are usually the simplest and at the same time the most powerful." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"The logarithm is an extremely powerful and useful tool for graphical data presentation. One reason is that logarithms turn ratios into differences, and for many sets of data, it is natural to think in terms of ratios. […] Another reason for the power of logarithms is resolution. Data that are amounts or counts are often very skewed to the right; on graphs of such data, there are a few large values that take up most of the scale and the majority of the points are squashed into a small region of the scale with no resolution." (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38" (4) 1984)

"Confusion and clutter are failures of design, not attributes of information. And so the point is to find design strategies that reveal detail and complexity - rather than to fault the data for an excess of complication. Or, worse, to fault viewers for a lack of understanding. Among the most powerful devices for reducing noise and enriching the content of displays is the technique of layering and separation, visually stratifying various aspects of the data." (Edward R Tufte, "Envisioning Information", 1990)

"Sometimes, when visualization thoroughly reveals the structure of a set of data, there is a tendency to underrate the power of the method for the application. Little effort is expended in seeing the structure once the right visualization method is used, so we are mislead into thinking nothing exciting has occurred." (William S Cleveland, "Visualizing Data", 1993)

"Dashboards aren't all that different from some of the other means of presenting information, but when properly designed the single-screen display of integrated and finely tuned data can deliver insight in an especially powerful way." (Richard Brath & Michael Peters, "Dashboard Design: Why Design is Important," DM Direct, 2004)

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

"Most dashboards fail to communicate efficiently and effectively, not because of inadequate technology (at least not primarily), but because of poorly designed implementations. No matter how great the technology, a dashboard's success as a medium of communication is a product of design, a result of a display that speaks clearly and immediately. Dashboards can tap into the tremendous power of visual perception to communicate, but only if those who implement them understand visual perception and apply that understanding through design principles and practices that are aligned with the way people see and think." (Stephen Few, "Information Dashboard Design", 2006)

"Arbitrary category sequence and misplaced pie chart emphasis lead to general confusion and weaken messages. Although this can be used for quite deliberate and targeted deceit, manipulation of the category axis only really comes into its own with techniques that bend the relationship between the data and the optics in a more calculated way. Many of these techniques are just twins of similar ruses on the value axis. but are none the less powerful for that." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"Design has the power to enrich our lives by engaging our emotions through image, form, texture, color, sound, and smell. The intrinsically human-centered nature of design thinking points to the next step: we can use our empathy and understanding of people to design experiences that create opportunities for active engagement and participation." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Histograms are powerful in cases where meaningful class breaks can be defined and classes are used to select intervals and groups in the data. However, they often perform poorly when it comes to the visualization of a distribution." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)

"Colour is a very powerful way to draw attention to specific portions of the design. Colour evokes feelings and emotions, making it an essential component in branding." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

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

"An infographic (short for information graphic) is a type of picture that blends data with design, helping individuals and organizations concisely communicate messages to their audience." (Mark Smiciklas, "The Power of Infographics: Using Pictures to Communicate and Connect with Your Audiences", 2012)

"Color can modify - and possibly even contradict - our intuitive response to value, because of its own powerful connotations." (Joel Katz, "Designing Information: Human factors and common sense in information design", 2012)

"The simplicity of the process behavior chart can be deceptive. This is because the simplicity of the charts is based on a completely different concept of data analysis than that which is used for the analysis of experimental data. When someone does not understand the conceptual basis for process behavior charts they are likely to view the simplicity of the charts as something that needs to be fixed.  Out of these urges to fix the charts all kinds of myths have sprung up resulting in various levels of complexity and obstacles to the use of one of the most powerful analysis techniques ever invented." (Donald J Wheeler, "Myths About Data Analysis", International Lean & Six Sigma Conference, 2012)

"A great infographic leads readers on a visual journey, telling them a story along the way. Powerful infographics are able to capture people’s attention in the first few seconds with a strong title and visual image, and then reel them in to digest the entire message. Infographics have become an effective way to speak for the creator, conveying information and image simultaneously." (Justin Beegel, "Infographics For Dummies", 2014)

"Statistical characterization of datasets is a very powerful approach, but it has the intrinsic limitation of losing information through summarization. " (Tamara Munzner, "Visualization Analysis and Design", 2014)

"The most powerful depth cue is occlusion, where some objects can not be seen because they are hidden behind others. The visible objects are interpreted as being closer than the occluded ones. The occlusion relationships between objects change as we move around; this motion parallax allows us to build up an understanding of the relative distances between objects in the world. " (Tamara Munzner, "Visualization Analysis and Design", 2014)

"The power of infographics is that it keeps things short and sweet. [...] The concise, pointed nature of an infographic works well with the fact that people’s attention span is decreasing significantly." (Justin Beegel, "Infographics For Dummies", 2014)

"Maps also have the disadvantage that they consume the most powerful encoding channels in the visualization toolbox - position and size - on an aspect that is held constant. This leaves less effective encoding channels like color for showing the dimension of interest." (Danyel Fisher & Miriah Meyer, "Making Data Visual", 2018)

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

"Aligning on data ink can be a powerful way to build relationships across charts. It can be used to obscure the lines between charts, making the composition feel more seamless. [....] Alignment paradigms can also influence the layout design needed. [...] The layout added to the alignment further supports this relationship." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"When the colors are dull and neutral, they can communicate a sense of uniformity and an aura of calmness. Grays do a great job of mapping out the context of your story so that the more sharp colors highlight what you’re trying to explain. The power of gray comes in handy for all of our supporting details such as the axis, gridlines, and nonessential data that is included for comparative purposes. By using gray as the primary color in a visualization, we automatically draw our viewers’ eyes to whatever isn’t gray. That way, if we are interested in telling a story about one data point, we can do so quite easily. " (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

"Graphic design is not just about making things look good. It is a powerful combination of form and function that uses visual elements to communicate a message. Form refers to the physical appearance of a design, such as its shape, color, and typography. Function refers to the purpose of a design, such as what it is trying to communicate or achieve. A good graphic design is both visually appealing and functional. It uses the right combination of form and function to communicate its message effectively. Graphic design is also a strategic and thoughtful craft. It requires careful planning and execution to create a design that is both effective and aesthetically pleasing." (Faith Aderemi, "The Essential Graphic Design Handbook", 2024)

📉Graphical Representation: Experience (Just the Quotes)

"It is not possible to lay down any hard and fast rules for determining what chart is the best for any given problem. Ordinarily that one is the best which will produce the quickest and clearest results. but unfortunately it is not always possible to construct the clearest one in the least time. Experience is the best guide. Generally speaking, a rectilinear chart is best adapted for equations of the first degree, logarithmic for those other than the first degree and not containing over two variables, and alignment charts where there are three or more variables. However, nearly every person becomes more or less familiar with one type of chart and prefers to adhere to the use of that type because he does not care to take the time and trouble to find out how to use the others. It is best to know what the possibilities of all types are and to be governed accordingly when selecting one or the other for presenting or working out certain data." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"The number of grid lines should be kept to a minimum. This means that there should be just enough coordinate lines in the field so that the eye can readily interpret the values at any point on the curve. No definite rule can be specified as to the optimum number of lines in a grid. This must be left to the discretion of the chart-maker and can come only from experience. The size of the chart, the type and range of the data. the number of curves, the length and detail of the period covered, as well as other factors, will help to determine the number of grid lines." (Calvin F Schmid, "Handbook of Graphic Presentation", 1954)

"The art of using the language of figures correctly is not to be over-impressed by the apparent air of accuracy, and yet to be able to take account of error and inaccuracy in such a way as to know when, and when not, to use the figures. This is a matter of skill, judgment, and experience, and there are no rules and short cuts in acquiring this expertness." (Ely Devons, "Essays in Economics", 1961)

"Nearly all those who produce graphics for mass publication are trained exclusively in the fine arts and have had little experience with the analysis of data. Such experiences are essential for achieving precision and grace in the presence of statistics. [...] Those who get ahead are those who beautified data, never mind statistical integrity." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Design has the power to enrich our lives by engaging our emotions through image, form, texture, color, sound, and smell. The intrinsically human-centered nature of design thinking points to the next step: we can use our empathy and understanding of people to design experiences that create opportunities for active engagement and participation." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Done well, annotation can help explain and facilitate the viewing and interpretive experience. It is the challenge of creating a layer of user assistance and user insight: how can you maximize the clarity and value of engaging with this visualization design?" (Andy Kirk, "Data Visualization: A successful design process", 2012)

"Geographic maps have the advantage of being true to scale - great for walking. Diagrams have the advantage of being easily imaged and remembered, often true to a non-pedestrian experience, and the ability to open up congestion, reduce empty space, and use real estate efficiently. Hybrids 'mapograms' ? - often have the disadvantages of both map and diagram with none of the corresponding advantages." (Joel Katz, "Designing Information: Human factors and common sense in information design", 2012)

"Visual metaphors are about integrating a certain visual quality in your work that somehow conveys that extra bit of connection between the data, the design, and the topic. It goes beyond just the choice of visual variable, though this will have a strong influence. Deploying the best visual metaphor is something that really requires a strong design instinct and a certain amount of experience." (Andy Kirk, "Data Visualization: A successful design process", 2012)

"[...] communicating with data is less often about telling a specific story and more like starting a guided conversation. It is a dialogue with the audience rather than a monologue. While some data presentations may share the linear approach of a traditional story, other data products" (analytical tools, in particular) give audiences the flexibility for exploration. In our experience, the best data products combine a little of both: a clear sense of direction defined by the author with the ability for audiences to focus on the information that is most relevant to them. The attributes of the traditional story approach combined with the self-exploration approach leads to the guided safari analogy." (Zach Gemignani et al, "Data Fluency", 2014)

"People see bar charts and line charts and pie charts all the time, and those charts are often boring. Boring graphs are forgettable. Different shapes and uncommon forms that move beyond the borders of our typical data visualization experience can draw readers in." (Jonathan Schwabish, "Better Data Visualizations: A guide for scholars, researchers, and wonks", 2021)

"A well-designed dashboard needs to provide a similar experience; information cannot be placed just anywhere on the dashboard. Charts that relate to one another are usually positioned close to one another. Important charts often appear larger and more visually prominent than less important ones. In other words, there are natural sizes for how a dashboard comprises charts based on the task and context." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"Maps are a type of chart that can convey relationships about space and relationships between objects that we relate to in the real world. Their effectiveness as a communication medium is strongly influenced by a host of factors: the nature of spatial data, the form and structure of representation, their intended purpose, the experience of the audience, and the context in the time and space in which the map is viewed. In other words, maps are a ubiquitous representation of spatial information that we can understand and relate to." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"Using symbols is one common way of applying semantics to help make sense of the world. Symbols provide clues to understanding experiences by conveying recognizable meanings that are shared by societies." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"When deeply complex charts work, we find them effective and beautiful, just as we find a symphony beautiful, which is another marvelously complex arrangement of millions of data points that we experience as a coherent whole." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

📉Graphical Representation: Tables (Just the Quotes)

"Information that is imperfectly acquired, is generally as imperfectly retained; and a man who has carefully investigated a printed table, finds, when done, that he has only a very faint and partial idea of what he has read; and that like a figure imprinted on sand, is soon totally erased and defaced." (William Playfair, "The Commercial and Political Atlas", 1786)

"In the course of executing that design, it occurred to me that tables are by no means a good form for conveying such information. [...] Making an appeal to the eye when proportion and magnitude are concerned is the best and readiest method of conveying a distinct idea." (William Playfair, "The Statistical Brewery", 1801)

"Isolated facts, those that can only be obtained by rough estimate and that require development, can only be presented in memoires; but those that can be presented in a body, with details, and on whose accuracy one can rely, may be expounded in tables." (Emmanuel Duvillard, "Memoire sur le travail du Bureau de statistique", 1806)

"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)

"But law is no explanation of anything; law is simply a generalization, a category of facts. Law is neither a cause, nor a reason, nor a power, nor a coercive force. It is nothing but a general formula, a statistical table." (Florence Nightingale, "Suggestions for Thought", 1860)

"The dominant principle which characterizes my graphic tables and my figurative maps is to make immediately appreciable to the eye, as much as possible, the proportions of numeric results. […] Not only do my maps speak, but even more, they count, they calculate by the eye." (Chatles D Minard, "Des tableaux graphiques et des cartes figuratives", 1862) 

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

"That the ten digits do not occur with equal frequency must be evident to any one making much use of logarithmic tables, and noticing how much faster the first pages wear out than the last ones." (Simon Newcomb, "Note on the frequencies of the different digits in natural numbers", Amer. J. Math 4, 1881)

"To a very striking degree our culture has become a Statistical culture. Even a person who may never have heard of an index number is affected [...] by [...] of those index numbers which describe the cost of living. It is impossible to understand Psychology, Sociology, Economics, Finance or a Physical Science without some general idea of the meaning of an average, of variation, of concomitance, of sampling, of how to interpret charts and tables." (Carrol D Wright, 1887)

"Getting information from a table is like extracting sunlight from a cucumber." (Arthur B. Farquhar & Henry Farquhar, "Economic and Industrial Delusions", 1891)

"The graphical method has considerable superiority for the exposition of statistical facts over the tabular. A heavy bank of figures is grievously wearisome to the eye, and the popular mind is as incapable of drawing any useful lessons from it as of extracting sunbeams from cucumbers." (Arthur B Farquhar & Henry Farquhar, "Economic and Industrial Delusions", 1891)

"The essential quality of graphic representations is clarity. If the diagram fails to give a clearer impression than the tables of figures it replaces, it is useless. To this end, we will avoid complicating the diagram by including too much data." (Armand Julin, "Summary for a Course of Statistics, General and Applied", 1910)

"Since a table is a collection of certain sets of data, a chart with one curve representing each set of data can be made to take the place of the table. Wherever a chart can be plotted by straight lines, the speed of this is infinitely greater than making out a table, and where the curvilinear law is known, or can be approximated by the use of the empiric law, the speed is but little less." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"Bar-charts are most flexible and can be varied to suit the individual whims of the maker. In general, however, there is one style or form which will be found most satisfactory. It consists of a horizontal grouping of bars alongside of the data. The chart is arranged in tabular form, with items or stubs in  a column to the left, with figures in a column beside the stubs and with bars in a column beside the figures. Several columns of figures are sometimes desirable, just as in the table of data, to show sources or original figures from which the charted figures are obtained. In any case, the bars should represent the most important set or column of figures, and there should be normally but one column of bars."(Karl G Karsten, "Charts and Graphs", 1925)

"Although, the tabular arrangement is the fundamental form for presenting a statistical series, a graphic representation - in a chart or diagram - is often of great aid in the study and reporting of statistical facts. Moreover, sometimes statistical data must be taken, in their sources, from graphic rather than tabular records." (William L Crum et al, "Introduction to Economic Statistics", 1938)

"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)

"We must emphasize that such terms as 'select at random', 'choose at random', and the like, always mean that some mechanical device, such as coins, cards, dice, or tables of random numbers, is used." (Frederick Mosteller et al, "Principles of Sampling", Journal of the American Statistical Association Vol. 49 (265), 1954)

"A statistical table is the logical listing of related quantitative data in vertical columns and horizontal rows of numbers with sufficient explanatory and qualifying words, phrases and statements in the form of titles, headings and notes to make clear the full meaning of data and their origin." (Alva M Tuttle, "Elementary Business and Economic Statistics", 1957)

"However informative and well designed a statistical table may be, as a medium for conveying to the reader an immediate and clear impression of its content, it is inferior to a good chart or graph. Many people are incapable of comprehending large masses of information presented in tabular form; the figures merely confuse them. Furthermore, many such people are unwilling to make the effort to grasp the meaning of such data. Graphs and charts come into their own as a means of conveying information in easily comprehensible form." (Alfred R Ilersic, "Statistics", 1959)

"All the evidence obtained from the reproduction of the study mentioned here indicates that the graphic method is 'better' than the tabular. Tables, since graphs are based on them, are necessary, but they are like background rocks, heavy and uninteresting. Graphs, on the other hand, spice the reports; clarify them, and make them interesting and palatable." (Karl M Dallenbach, 1963)

"The statistician has no magic touch by which he may come in at the stage of tabulation and make something of nothing. Neither will his advice, however wise in the early stages of a study, ensure successful execution and conclusion. Many a study, launched on the ways of elegant statistical design, later boggled in execution, ends up with results to which the theory of probability can contribute little." (W Edwards Deming, "Principles of Professional Statistical Practice", Annals of Mathematical Statistics, 36(6), 1965)

"The problem that still remains to be solved is that of the orderable matrix, that needs the use of imagination […] When the two components of a data table are orderable, the normal construction is the orderable matrix. Its permutations show the analogy and the complementary nature that exist between the algorithmic treatments and the graphical treatments." (Jacques Bertin, "Semiology of graphics" ["Semiologie Graphique"], 1967)

"A statistical table is a systematic arrangement of numerical data in columns and rows. Its purpose is to show quantitative facts clearly, concisely, and effectively. It should facilitate an understanding of the logical relationships among the numbers presented. Tables are used in the compilation of raw data, in the summarizing and analytic processes, and in the presentation of statistics in final form. A good table is the product of careful thinking and hard work. It is not just a package of figures put into neat compartments and ruled to make it look more attractive. It contains carefully selected data put together with thought and ingenuity to serve a specific purpose." (Peter H Selby, "Interpreting Graphs and Tables", 1976)

"Tables are [...] the backbone of most statistical reports. They provide the basic substance and foundation on which conclusions can be based. They are considered valuable for the following reasons: (1) Clarity - they present many items of data in an orderly and organized way. (2) Comprehension - they make it possible to compare many figures quickly. (3) Explicitness - they provide actual numbers which document data presented in accompanying text and charts. (4) Economy - they save space, and words. (5) Convenience - they offer easy and rapid access to desired items of information." (Peter H Selby, "Interpreting Graphs and Tables", 1976)

"We would wish ‘numerate’ to imply the possession of two attributes. The first of these is an ‘at-homeness’ with numbers and an ability to make use of mathematical skills which enable an individual to cope with the practical mathematical demands of his everyday life. The second is ability to have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables or by reference to percentage increase or decrease." (Cockcroft Committee, "Mathematics Counts: A Report into the Teaching of Mathematics in Schools", 1982)

"The basic principle which should be observed in designing tables is that of grouping related data, either by the use of space or, if necessary, rules. Items which are close together will be seen as being more closely related than items which are farther apart, and the judicious use of space is therefore vitally important. Similarly, ruled lines can be used to relate and divide information, and it is important to be sure which function is required. Rules should not be used to create closed compartments; this is time-wasting and it interferes with scanning." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"We are not saying that the primary purpose of a graph is to convey numbers with as many decimal places as possible. We agree with Ehrenberg (1975) that if this were the only goal, tables would be better. The power of a graph is its ability to enable one to take in the quantitative information, organize it, and see patterns and structure not readily revealed by other means of studying the data." (William Cleveland & Robert McGill, "Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Models", Journal of the American Statistical Association 79, 1984)

"The ease and speed with which tables can be understood depends very much on the tabulation logic. The author must ask himself what information the reader already has when he consults a particular table, and what information he is seeking from it. The row and column headings should relate to the information he already has, thus leading him to the information he seeks which is displayed in the body of the table." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"Wherever possible, numerical tables should be explicit rather than implicit, i.e. the information should be given in full. In an implicit table, the reader may be required to add together two values in order to obtain a third which is not explicitly stated in the table. […] Implicit tables save space, but require more effort on the part of the reader and may cause confusion and errors. They are particularly unsuitable for slides and other transient displays." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"This is why a 'web' of notes with links (like references) between them is far more useful than a fixed hierarchical system. When describing a complex system, many people resort to diagrams with circles and arrows. Circles and arrows leave one free to describe the interrelationships between things in a way that tables, for example, do not. The system we need is like a diagram of circles and arrows, where circles and arrows can stand for anything." (Tim Berners-Lee, "Information Management: A Proposal", 1989)

"The application of the same techniques and scales of enquiry to each and every district meant that the resultant maps and statistical tables all contained the same sorts of information and were constructed and tabulated in the same manner. They therefore obscured or denied local nuances and particular circumstances." (Matthew H Edney, "Mapping an Empire: The Geographical Construction of British India, 1765–1843", 1999)

"A good way to evaluate a model is to look at a visual representation of it. After all, what is easier to understand - a table full of mathematical relationships or a graphic displaying a decision tree with all of its splits and branches?" (Seth Paul et al. "Preparing and Mining Data with Microsoft SQL Server 2000 and Analysis", 2002)

"Computers are able to multiply useless images without taking into account that, by definition, every graphic corresponds to a table. This table allows you to think about three basic questions that go from the particular to the general level. When this last one receives an answer, you have answers for all of them. Understanding means accessing the general level and discovering significant grouping (patterns). Consequently, the function of a graphic is answering the three following questions:
Which are the X,Y, Z components of the data table? (What it’s all about?)
What are the groups in X, in Y that Z builds? (What the information at the general level is?
What are the exceptions?

These questions can be applied to every kind of problem. They measure the usefulness of whatever construction or graphical invention allowing you to avoid useless graphics." (Jacques Bertin, [interview] 2003)

"Graphs are for the forest and tables are for the trees. Graphs give you the big picture and show you the trends; tables give you the details." (Naomi B Robbins, "Creating More effective Graphs", 2005)

"Largeness comes in different forms and has many different effects. Whereas some tasks remain easy, others become obstinately difficult. Largeness is not just an increase in dataset size. [...] Largeness may mean more complexity - more variables, more detail (additional categories, special cases), and more structure (temporal or spatial components, combinations of relational data tables). Again this is not so much of a problem with small datasets, where the complexity will be by definition limited, but becomes a major problem with large datasets. They will often have special features that do not fit the standard case by variable matrix structure well-known to statisticians." (Antony Unwin et al [in "Graphics of Large Datasets: Visualizing a Million"], 2006)

"Tables are fine for viewing sections of a dataset, but simple scrolling is no longer a practical navigational option." (Antony Unwin et al [in "Graphics of Large Datasets: Visualizing a Million"], 2006)

"What distinguishes data tables from graphics is explicit comparison and the data selection that this requires. While a data table obviously also selects information, this selection is less focused than a chart's on a particular comparison. To the extent that some figures in a table are visually emphasised. say in colour or size and style of print. the table is well on its way to becoming a chart. If you're making no comparisons - because you have no particular message and so need no selection (in other words, if you are simply providing a database, number quarry or recycling facility) - tables are easier to use than charts." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"Data visualization [...] expresses the idea that it involves more than just representing data in a graphical form (instead of using a table). The information behind the data should also be revealed in a good display; the graphic should aid readers or viewers in seeing the structure in the data. The term data visualization is related to the new field of information visualization. This includes visualization of all kinds of information, not just of data, and is closely associated with research by computer scientists." (Antony Unwin et al, "Introduction" [in "Handbook of Data Visualization"], 2008) 

"Plotting data is a useful first stage to any analysis and will show extreme observations together with any discernible patterns. In addition the relative sizes of categories are easier to see in a diagram (bar chart or pie chart) than in a table. Graphs are useful as they can be assimilated quickly, and are particularly helpful when presenting information to an audience. Tables can be useful for displaying information about many variables at once, while graphs can be useful for showing multiple observations on groups or individuals. Although there are no hard and fast rules about when to use a graph and when to use a table, in the context of a report or a paper it is often best to use tables so that the reader can scrutinise the numbers directly." (Jenny Freeman et al, "How to Display Data", 2008)

"When displaying information visually, there are three questions one will find useful to ask as a starting point. Firstly and most importantly, it is vital to have a clear idea about what is to be displayed; for example, is it important to demonstrate that two sets of data have different distributions or that they have different mean values? Having decided what the main message is, the next step is to examine the methods available and to select an appropriate one. Finally, once the chart or table has been constructed, it is worth reflecting upon whether what has been produced truly reflects the intended message. If not, then refine the display until satisfied; for example if a chart has been used would a table have been better or vice versa?" (Jenny Freeman et al, "How to Display Data", 2008)

"Tables work in a variety of situations because they convey large amounts of data in a condensed fashion. Use tables in the following situations: (1) to structure data so the reader can easily pick out the information desired, (2) to display in a chart when the data contains too many variables or values, and (3) to display exact values that are more important than a visual moment in time." (Dennis K Lieu & Sheryl Sorby, "Visualization, Modeling, and Graphics for Engineering Design", 2009)

"The data [in tables] should not be so spaced out that it is difficult to follow or so cramped that it looks trapped. Keep columns close together; do not spread them out more than is necessary. If the columns must be spread out to fit a particular area, such as the width of a page, use a graphic device such as a line or screen to guide the reader’s eye across the row." (Dennis K Lieu & Sheryl Sorby, "Visualization, Modeling, and Graphics for Engineering Design", 2009)

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

"A common mistake is that all visualization must be simple, but this skips a step. You should actually design graphics that lend clarity, and that clarity can make a chart 'simple' to read. However, sometimes a dataset is complex, so the visualization must be complex. The visualization might still work if it provides useful insights that you wouldn’t get from a spreadsheet. […] Sometimes a table is better. Sometimes it’s better to show numbers instead of abstract them with shapes. Sometimes you have a lot of data, and it makes more sense to visualize a simple aggregate than it does to show every data point." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"With fast computers and plentiful data, finding statistical significance is trivial. If you look hard enough, it can even be found in tables of random numbers." (Gary Smith, "Standard Deviations", 2014)

"One thing to keep in mind with a table is that you want the design to fade into the background, letting the data take center stage. Don’t let heavy borders or shading compete for attention. Instead, think of using light borders or simply white space to set apart elements of the table." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"[...] tables interact with our verbal system, graphs interact with our visual system, which is faster at processing information." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"Using a table in a live presentation is rarely a good idea. As your audience reads it, you lose their ears and attention to make your point verbally." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"A useful way to think about tables and graphics is to visualize layers. Just as photographic files may be manipulated in photo editing software using layers, data presentations are constructed by imagining that layers of an image are placed one on top of another. There are three general layers that apply to visual data presentations: (a) a frame that is typically a rectangle or matrix, (b) axes and coordinate systems (for graphics), and (c) data presented as numbers or geometric objects." (John Hoffmann, "Principles of Data Management and Presentation", 2017)

"Most of us have difficulty figuring probabilities and statistics in our heads and detecting subtle patterns in complex tables of numbers. We prefer vivid pictures, images, and stories. When making decisions, we tend to overweight such images and stories, compared to statistical information. We also tend to misunderstand or misinterpret graphics." (Daniel J Levitin, "Weaponized Lies", 2017)

"Reference tables show a lot of data with a high degree of precision. They are designed generally to provide users with a way to find particular pieces of data. […] Summary tables provide some type of extraction of data from a reference table or a spreadsheet. The data are usually manipulated, analyzed, or summarized in some way, such as by sorting or providing summary statistics (means, percentages, ranges). The results of statistical models are usually presented in research reports using this type of table." (John Hoffmann, "Principles of Data Management and Presentation", 2017)

"The most accurate but least interpretable form of data presentation is to make a table, showing every single value. But it is difficult or impossible for most people to detect patterns and trends in such data, and so we rely on graphs and charts. Graphs come in two broad types: Either they represent every data point visually (as in a scatter plot) or they implement a form of data reduction in which we summarize the data, looking, for example, only at means or medians." (Daniel J Levitin, "Weaponized Lies", 2017)

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

"Apart from the technical challenge of working with the data itself, visualization in big data is different because showing the individual observations is just not an option. But visualization is essential here: for analysis to work well, we have to be assured that patterns and errors in the data have been spotted and understood. That is only possible by visualization with big data, because nobody can look over the data in a table or spreadsheet." (Robert Grant, "Data Visualization: Charts, Maps and Interactive Graphics", 2019)

"When visuals are applied to data, they can enlighten the audience to insights that they wouldn’t see without charts or graphs. Many interesting patterns and outliers in the data would remain hidden in the rows and columns of data tables without the help of data visualizations. They connect with our visual nature as human beings and impart knowledge that couldn’t be obtained as easily using other approaches that involve just words or numbers." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)