📉Graphical Representation: Statistics (Just the Quotes)

"Graphical statistics can be defined as: 'the expression of statistical facts by means of geometric processes' (Levasseur). Its general usefulness consists of replacing figures which, by their multiplicity, confuse memory, with a figure whose general appearance can be discovered all at once and, by speaking to the eyes, is more easily engraved in the memory." (Armand Julin, "Summary for a Course of Statistics, General and Applied", 1910)

"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)

"The primary purpose of a graph is to show diagrammatically how the values of one of two linked variables change with those of the other. One of the most useful applications of the graph occurs in connection with the representation of statistical data." (John F Kenney & E S Keeping, "Mathematics of Statistics" Vol. I 3rd Ed., 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)

"Indeed the language of statistics is rarely as objective as we imagine. The way statistics are presented, their arrangement in a particular way in tables, the juxtaposition of sets of figures, in itself reflects the judgment of the author about what is significant and what is trivial in the situation which the statistics portray." (Ely Devons, "Essays in Economics", 1961)

"[…] an outlier is an observation that lies an 'abnormal' distance from other values in a batch of data. There are two possible explanations for the occurrence of an outlier. One is that this happens to be a rare but valid data item that is either extremely large or extremely small. The other is that it isa mistake – maybe due to A good rule of thumb for deciding how long the analysis of the data actually will take is (1) to add up all the time for everything you can think of - editing the data, checking for errors, calculating various statistics, thinking about the results, going back to the data to try out a new idea, and (2) then multiply the estimate obtained in this first step by five." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Statistical techniques do not solve any of the common-sense difficulties about making causal inferences. Such techniques may help organize or arrange the data so that the numbers speak more clearly to the question of causality - but that is all statistical techniques can do. All the logical, theoretical, and empirical difficulties attendant to establishing a causal relationship persist no matter what type of statistical analysis is applied." (Edward R Tufte, "Data Analysis for Politics and Policy", 1974)

"Just like the spoken or written word, statistics and graphs can lie. They can lie by not telling the full story. They can lead to wrong conclusions by omitting some of the important facts. [...] Always look at statistics with a critical eye, and you will not be the victim of misleading information." (Dyno Lowenstein, "Graphs", 1976)

"Learning to make graphs involves two things: (l) the techniques of plotting statistics, which might be called the artist's job; and" (2) understanding the statistics. When you know how to work out graphs, all kinds of statistics will probably become more interesting to you." (Dyno Lowenstein, "Graphs", 1976)

"Of course, statistical graphics, just like statistical calculations, are only as good as what goes into them. An ill-specified or preposterous model or a puny data set cannot be rescued by a graphic (or by calculation), no matter how clever or fancy. A silly theory means a silly graphic." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"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)

"There is an interplay between statistical models and graphics, so it is advantageous to think about models before making a series of plots." (Daniel B Carr, "Looking at Large Data Sets Using Binned Data Plots", [in "Computing and Graphics in Statistics"] 1991)

"There are two components to visualizing the structure of statistical data - graphing and fitting. Graphs are needed, of course, because visualization implies a process in which information is encoded on visual displays. Fitting mathematical functions to data is needed too. Just graphing raw data, without fitting them and without graphing the fits and residuals, often leaves important aspects of data undiscovered." (William S Cleveland, "Visualizing Data", 1993)

"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)

"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)

"Estimating the missing values in a dataset solves one problem - imputing reasonable values that have well-defined statistical properties. It fails to solve another, however - drawing inferences about parameters in a model fit to the estimated data. Treating imputed values as if they were known (like the rest of the observed data) causes confidence intervals to be too narrow and tends to bias other estimates that depend on the variability of the imputed values (such as correlations)." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"The consequence of distinguishing statistical methods from the graphics displaying them is to separate form from function. That is, the same statistic can be represented by different types of graphics, and the same type of graphic can be used to display two different statistics. […] This separability of statistical and geometric objects is what gives a system a wide range of representational opportunities." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"Oftentimes a statistical graphic provides the evidence for a plausible story, and the evidence, though perhaps only circumstantial, can be quite convincing. […] But such graphical arguments are not always valid. Knowledge of the underlying phenomena and additional facts may be required." (Howard Wainer, "Graphic Discovery: A trout in the milk and other visuals" 2nd, 2008)

"Placing a fact within a context increases its value greatly. […] . An efficacious way to add context to statistical facts is by embedding them in a graphic. Sometimes the most helpful context is geographical, and shaded maps come to mind as examples. Sometimes the most helpful context is temporal, and time-based line graphs are the obvious choice. But how much time? The ending date (today) is usually clear, but where do you start? The starting point determines the scale. […] The starting point and hence the scale are determined by the questions that we expect the graph to answer." (Howard Wainer, "Graphic Discovery: A trout in the milk and other visuals" 2nd, 2008)

"Eye-catching data graphics tend to use designs that are unique (or nearly so) without being strongly focused on the data being displayed. In the world of Infovis, design goals can be pursued at the expense of statistical goals. In contrast, default statistical graphics are to a large extent determined by the structure of the data (line plots for time series, histograms for univariate data, scatterplots for bivariate nontime-series data, and so forth), with various conventions such as putting predictors on the horizontal axis and outcomes on the vertical axis. Most statistical graphs look like other graphs, and statisticians often think this is a good thing." (Andrew Gelman & Antony Unwin, "Infovis and Statistical Graphics: Different Goals, Different Looks" , Journal of Computational and Graphical Statistics Vol. 22(1), 2013)

"After all, we do agree that statistical data analysis is concerned with generating and evaluating hypotheses about data. For us, generating hypotheses means that we are searching for patterns in the data - trying to 'see what the data seem to say'. And evaluating hypotheses means that we are seeking an explanation or at least a simple description of what we find - trying to verify what we believe we see." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

📉Graphical Representation: Confusion (Just the Quotes)

"First, it is generally inadvisable to attempt to portray a series of more than four or five categories by means of pie charts. If, for example, there are six, eight, or more categories, it may be very confusing to differentiate the relative values portrayed, especially if several small sectors are of approximately the same size. Second, the pie chart may lose its effectiveness if an attempt is made to compare the component values of several circles, as might be found in a temporal or geographical series. In such case the one-hundred percent bar or column chart is more appropriate. Third, although the proportionate values portrayed in a pie chart are measured as distances along arcs about the circle, actually there is a tendency to estimate values in terms of areas of sectors or by the size of subtended angles at the center of the circle." (Calvin F Schmid, "Handbook of Graphic Presentation", 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)

"The eye can accurately appraise only very few features of a diagram, and consequently a complicated or confusing diagram will lead the reader astray. The fundamental rule for all charting is to use a plan which is simple and which takes account, in its arrangement of the facts to be presented, of the above-mentioned capacities of the eye."  (William L Crum et al, "Introduction to Economic Statistics", 1938)

"Besides being easier to construct than a bar chart, the line chart possesses other advantages. It is easier to read, for while the bars stand out more prominently than the line, they tend to become confusing if numerous, and especially so when they record alternate increase and decrease. It is easier for the eye to follow a line across the face of the chart than to jump from bar top to bar top, and the slope of the line connecting two points is a great aid in detecting minor changes. The line is also more suggestive of movement than arc bars, and movement is the very essence of a time series. Again, a line chart permits showing two or more related variables on the same chart, or the same variable over two or more corresponding periods." (Walter E Weld, "How to Chart; Facts from Figures with Graphs", 1959)

"If two or more data paths ate to appear on the graph, it is essential that these lines be labeled clearly, or at least a reference should be provided for the reader to make the necessary identifications. While clarity seems to be a most obvious goal, graphs with inadequate or confusing labeling do appear in publications, The user should not find identification of data paths troublesome or subject to misunderstanding. The designer normally should place no more than three data paths on the graph to prevent confusion - particularly if the data paths intersect at one or more points on the Cartesian plane." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

"The information on a plot should be relevant to the goals of the analysis. This means that in choosing graphical methods we should match the capabilities of the methods to our needs in the context of each application. [...] Scatter plots, with the views carefully selected as in draftsman's displays, casement displays, and multiwindow plots, are likely to be more informative. We must be careful, however, not to confuse what is relevant with what we expect or want to find. Often wholly unexpected phenomena constitute our most important findings." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"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)

"What about confusing clutter? Information overload? Doesn't data have to be ‘boiled down’ and  ‘simplified’? These common questions miss the point, for the quantity of detail is an issue completely separate from the difficulty of reading. Clutter and confusion are failures of design, not attributes of information. Often the less complex and less subtle the line, the more ambiguous and less interesting is the reading. Stripping the detail out of data is a style based on personal preference and fashion, considerations utterly indifferent to substantive content." (Edward R Tufte, "Envisioning Information", 1990)

"Grouped area graphs sometimes cause confusion because the viewer cannot determine whether the areas for the data series extend down to the zero axis. […] Grouped area graphs can handle negative values somewhat better than stacked area graphs but they still have the problem of all or portions of data curves being hidden by the data series towards the front." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"Technically, there is no limit as to the number of data series that can be plotted on a single graph. Practically, if the number goes above three or four the graph becomes confusing." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"When it comes to drawing a picture of continuous data, you need to think through carefully where one interval ends and the next one begins. Failing to do this can result in overlaps or gaps between adjacent intervals, which can cause confusion." (Alan Graham, "Developing Thinking in Statistics", 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)

"Using colour, itʼs possible to increase the density of information even further. A single colour can be used to represent two variables simultaneously. The difficulty, however, is that there is a limited amount of information that can be packed into colour without confusion." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"Bear in mind is that the use of color doesn’t always help. Use it sparingly and with a specific purpose in mind. Remember that the reader’s brain is looking for patterns, and will expect both recurrence itself and the absence of expected recurrence to carry meaning. If you’re using color to differentiate categorical data, then you need to let the reader know what the categories are. If the dimension of data you’re encoding isn’t significant enough to your message to be labeled or explained in some way - or if there is no dimension to the data underlying your use of difference colors - then you should limit your use so as not to confuse the reader." (Noah Iliinsky & Julie Steel, "Designing Data Visualizations", 2011)

"Graphs should not be mere decoration, to amuse the easily bored. A useful graph displays data accurately and coherently, and helps us understand the data. Chartjunk, in contrast, distracts, confuses, and annoys. Chartjunk may be well-intentioned, but it is misguided. It may also be a deliberate attempt to mystify." (Gary Smith, "Standard Deviations", 2014)

"Uncertainty confuses many people because they have the unreasonable expectation that science and statistics will unearth precise truths, when all they can yield is imperfect estimates that can always be subject to changes and updates." (Alberto Cairo, "How Charts Lie", 2019)

"Bad complexity neither elucidates important salient points nor shows coherent broader trends. It will obfuscate, frustrate, tax the mind, and ultimately convey trendlessness and confusion to the viewer. Good complexity, in contrast, emerges from visualizations that use more data than humans can reasonably process to form a few salient points." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

📉Graphical Representation: Groups (Just the Quotes)

"Pencil and paper for construction of distributions, scatter diagrams, and run-charts to compare small groups and to detect trends are more efficient methods of estimation than statistical inference that depends on variances and standard errors, as the simple techniques preserve the information in the original data." (William E Deming, "On Probability as Basis for Action" American Statistician Vol. 29 (4), 1975)

"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)

"The space between columns, on the other hand, should be just sufficient to separate them clearly, but no more. The columns should not, under any circumstances, be spread out merely to fill the width of the type area. […] Sometimes, however, it is difficult to avoid undesirably large gaps between columns, particularly where the data within any given column vary considerably in length. This problem can sometimes be solved by reversing the order of the columns […]. In other instances the insertion of additional space after every fifth entry or row can be helpful, […] but care must be taken not to imply that the grouping has any special meaning." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"Scatter charts show the relationships between information, plotted as points on a grid. These groupings can portray general features of the source data, and are useful for showing where correlationships occur frequently. Some scatter charts connect points of equal value to produce areas within the grid which consist of similar features." (Bruce Robertson, "How to Draw Charts & Diagrams", 1988)

"A good chart delineates and organizes information. It communicates complex ideas, procedures, and lists of facts by simplifying, grouping, and setting and marking priorities. By spatial organization, it should lead the eye through information smoothly and efficiently." (Mary H Briscoe, "Preparing Scientific Illustrations: A guide to better posters, presentations, and publications" 2nd ed., 1995)

"Grouped area graphs sometimes cause confusion because the viewer cannot determine whether the areas for the data series extend down to the zero axis. […] Grouped area graphs can handle negative values somewhat better than stacked area graphs but they still have the problem of all or portions of data curves being hidden by the data series towards the front." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"When analyzing data it is many times advantageous to generate a variety of graphs using the same data. This is true whether there is little or lots of data. Reasons for this are: (1) Frequently, all aspects of a group of data can not be displayed on a single graph. (2) Multiple graphs generally result in a more in-depth understanding of the information. (3) Different aspects of the same data often become apparent. (4) Some types of graphs cause certain features of the data to stand out better (5) Some people relate better to one type of graph than another." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996) 

"If you want to hide data, try putting it into a larger group and then use the average of the group for the chart. The basis of the deceit is the endearingly innocent assumption on the part of your readers that you have been scrupulous in using a representative average: one from which individual values do not deviate all that much. In scientific or statistical circles, where audiences tend to take less on trust, the 'quality' of the average (in terms of the scatter of the underlying individual figures) is described by the standard deviation, although this figure is itself an average." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"We tend automatically to think of all the categories represented on the horizontal axis of a column Chart as being equally important. They vary of course on the value axis. Otherwise, there would be little point in the chart, but there is somehow this feeling that they are in other respects similar members of a group. This convention can be put to good use to manipulate the message of the most boring bar or column chart." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"Where there is no natural ordering to the categories it can be helpful to order them by size, as this can help you to pick out any patterns or compare the relative frequencies across groups. As it can be difficult to discern immediately the numbers represented in each of the categories it is good practice to include the number of observations on which the chart is based, together with the percentages in each category." (Jenny Freeman et al, "How to Display Data", 2008)

"Grouping charts according to a theme and in sequence with the message and putting them all on the same sheet or slide helps you find the thread of the message (even if the charts are separated again later)." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"The law of connectivity tells us that objects connected to other objects tend to be seen as a group. […] The law of common fate tells us that objects moving in the same direction are seen as a group."  (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"The law of continuity states that we interpret images so as not to generate abrupt transitions or otherwise create images that are more complex. […] we can arbitrarily fill in the missing elements to complete a pattern. It’s also the case of time series, in which we assume that data points in the future will be a smooth continuation of the past. […] In a line chart, those series with a similar slope (that is, they appear to follow the same direction) are understood as belonging to the same group." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"The law of segregation tells us that objects within a closed shape are seen as a group. A frame around objects (charts or legends, for example) has this function, but it’s also useful for adding visual annotations."  (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"A histogram represents the frequency distribution of the data. Histograms are similar to bar charts but group numbers into ranges. Also, a histogram lets you show the frequency distribution of continuous data. This helps in analyzing the distribution (for example, normal or Gaussian), any outliers present in the data, and skewness." (Umesh R Hodeghatta & Umesha Nayak, "Business Analytics Using R: A Practical Approach", 2017)

"Another problem is that while data visualizations may appear to be objective, the designer has a great deal of control over the message a graphic conveys. Even using accurate data, a designer can manipulate how those data make us feel. She can create the illusion of a correlation where none exists, or make a small difference between groups look big." (Carl T Bergstrom & Jevin D West, "Calling Bullshit: The Art of Skepticism in a Data-Driven World", 2020)

📉Graphical Representation: Mosaic Plots (Just the Quotes)

"We have so consistently inveighed against the use of areas to illustrate quantities that the reader will indeed be surprised at some coming retractions. [...] But the fact is that we now propose to turn to advantage the very feature of areas which has previously been their greatest fault. [...] We now come to data in which we wish to show simultaneously three ratios or sets of ratios, one of which is always the product of the other two. In other words, we wish to show two factors or sets of factors and their product." (Karl Karsten, "Charts and Graphs", 1925)

"A contingency table specifies the joint distribution of a number of discrete variables. The numbers in a contingency table are represented by rectangles of areas proportional to the numbers, with shape and position chosen to expose deviations from independence models. The collection of rectangles for the contingency table is called a mosaic." (John A Hartigan & B Kleiner, "Mosaics for Contingency Tables", 1981)

"Mosaic displays represent the counts in a contingency table by tiles whose size is proportional to the cell count. This graphical display for categorical data generalizes readily to multiway tables."  (Michael Friendly, "Mosaic Displays for Loglinear Models", Proceedings of the Statistical Graphics, 1992)

"Although the basic mosaic display shows the data in any contingency table, it does not in general provide a visual representation of the fit of the data to a specified model. In the two-way case independence is shown when the tiles in each row align vertically, but visual assessment of other models is more difficult." (Michael Friendly, "Mosaic Displays for Loglinear Models", Proceedings of the Statistical Graphics, 1992)

"Categorical data are most often modeled using loglinear models. For certain loglinear models, mosaic plots have unique shapes that do not depend on the actual data being modeled. These shapes reflect the structure of a model, defined by the presence and absence of particular model coefficients. Displaying the expected values of a loglinear model allows one to incorporate the residuals of the model graphically and to visually judge the adequacy of the loglinear fit. This procedure leads to stepwise interactive graphical modeling of loglinear models. We show that it often results in a deeper understanding of the structure of the data. Linking mosaic plots to other inter- active displays offers additional power that allows the investigation of more complex dependence models than provided by static displays." (Martin Theus & Stephan R W Lauer, "Visualizing Loglinear Models", Journal of Computational and Graphical Statistics Vol. 8 (3), 1999)

"The scatterplot matrix shows all pairwise (bivariate marginal) views of a set of variables in a coherent display. One analog for categorical data is a matrix of mosaic displays showing some aspect of the bivariate relation between all pairs of variables. The simplest case shows the bivariate marginal relation for each pair of variables. Another case shows the conditional relation between each pair, with all other variables partialled out. For quantitative data this represents (a) a visualization of the conditional independence relations studied by graphical models, and (b) a generalization of partial residual plots. The conditioning plot, or coplot, shows a collection of partial views of several quantitative variables, conditioned by the values of one or more other variables. A direct analog of the coplot for categorical data is an array of mosaic plots of the dependence among two or more variables, stratified by the values of one or more given variables. Each such panel then shows the partial associations among the foreground variables; the collection of such plots shows how these associations change as the given variables vary." (Michael Friendly, "Extending Mosaic Displays: Marginal, Conditional, and Partial Views of Categorical Data", 199)

"A graphical display of a p-dimensional contingency table, the empirical distribution of p categorical variables, is a mosaic plot. Each tile (or bin) corresponds to one cell of the contingency table, its size to the number of the cell's entries. The shape of a tile is calculated during the (strictly hierarchical) construction." (Heike Hoffmann, "Generalized Odds Ratios for Visual Modeling", Journal of Computational and Graphical Statistics Vol. 10 (4), 2001)

"Mosaics are space-filling designs composed of contiguous shapes ('tiles')." (Michael Friendly, "A Brief History of the Mosaic Display", Journal of Computational and Graphical Statistics, Vol. 11 (1), 2002)

"The principal graphical ideas [of mosaic plots] are: (*) using area = height x width, to represent a quantity which depends on a product of two other variables, each of interest; (*) using recursive subsdivision to show any number of variables; (*) using shading to display some other attribute of the data; (*) purely multiplicative relations (e.g., Pij = Pi+P+j) produce equal subdivisions; (*) for two or more variables, the levels of subdivision are spaced with larger gaps at the earlier levels, to allow easier perception of the groupings at various levels, and to provide for empty cells." (Michael Friendly, "A Brief History of the Mosaic Display", Journal of Computational and Graphical Statistics, Vol. 11 (1), 2002)

"Due to their recursive definition, switching the order of variables in a mosaic plot has a strong impact on what can be read from the plot. For instance, exchanging the two variables in a two-dimensional mosaic plot results in a completely new plot rather than in a mere graphically transposed version of the original plot." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)  

"Mosaic plots are defined recursively, i.e., each variable that is introduced in a mosaic plot is plotted conditioned on the groups already established in the plot. As with barcharts, the area of bars or tiles is proportional to the number of observations (or the sum of the observation weights of a class). The direction along which bars are divided by a newly introduced variable is usually alternating, starting with the x-direction." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009) 

"Mosaic plots become more difficult to read for variables with more than two or three categories. One way out is to assign a constant space for all possible crossings of categories. This way, the data from the r×c table are plotted in a table-like layout. Whereas this regular layout makes it much easier to compare values across rows and columns, the plot space is used less efficiently than in a mosaic plot." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)

"Conceptually, mosaic plots for s + 1 factors in strength s designs can be used for any s; in practice, the idea is limited by space constraints, especially for accommodating labels for the factor levels. All four margins are used for four-factor projections; with the next dimension, one margin has to be used for two factors. In practice, one will rarely consider mosaic plots for more factors than four at a time." (Ulrike Grömping, "Mosaic Plots are Useful for Visualizing Low-Order Projections of Factorial Designs", The American Statistician Vol. 68 (2), 2014)

"Mosaic plots are particularly useful for design and analysis of orthogonal main effect plans. [...] mosaic plots do not reflect geometric properties relevant for designs in quantitative factors. Nevertheless, mosaic plots can also be used to visualize founding severity for designs with quantitative factors [...]" (Ulrike Grömping, "Mosaic Plots are Useful for Visualizing Low-Order Projections of Factorial Designs", The American Statistician Vol. 68 (2), 2014)

"Mosaic plots can get quite messy when increasing the number of variables, which is presumably the reason many commercial software products offer them for two variables only." (Ulrike Grömping, "Mosaic Plots are Useful for Visualizing Low-Order Projections of Factorial Designs", The American Statistician Vol. 68 (2), 2014)

"The way that the model differs from the data gives us clues about how we can improve our model. We can use mosaic displays to find the specific ways in which the model is different from the data, since mosaics show the residuals (or differences) of the cells with respect to the model. Looking at these differences, we can observe patterns in the deviation that will help us in our search." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

📉Graphical Representation: Problems (Just the Quotes)

"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)

"One of the greatest values of the graphic chart is its use in the analysis of a problem. Ordinarily, the chart brings up many questions which require careful consideration and further research before a satisfactory conclusion can be reached. A properly drawn chart gives a cross-section picture of the situation. While charts may bring out hidden facts in tables or masses of data, they cannot take the place of careful, analysis. In fact, charts may be dangerous devices when in the hands of those unwilling to base their interpretations upon careful study. This, however, does not detract from their value when they are properly used as aids in solving statistical problems." (John R Riggleman & Ira N Frisbee, "Business Statistics", 1938)

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

"Visual thinking can begin with the three basic shapes we all learned to draw before kindergarten: the triangle, the circle, and the square. The triangle encourages you to rank parts of a problem by priority. When drawn into a triangle, these parts are less likely to get out of order and take on more importance than they should. While the triangle ranks, the circle encloses and can be used to include and/or exclude. Some problems have to be enclosed to be managed. Finally, the square serves as a versatile problem-solving tool. By assigning it attributes along its sides or corners, we can suddenly give a vague issue a specific place to live and to move about." (Terry Richey, "The Marketer's Visual Tool Kit", 1994)

"When visualization tools act as a catalyst to early visual thinking about a relatively unexplored problem, neither the semantics nor the pragmatics of map signs is a dominant factor. On the other hand, syntactics (or how the sign-vehicles, through variation in the visual variables used to construct them, relate logically to one another) are of critical importance." (Alan M MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"Although in most cases the actual value designated by a bar is determined by the location of the end of the bar, many people associate the length or area of the bar with its value. As long as the scale is linear, starts at zero, is continuous, and the bars are the same width, this presents no problem. When any of these conditions are changed, the potential exists that the graph will be misinterpreted." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"Grouped area graphs sometimes cause confusion because the viewer cannot determine whether the areas for the data series extend down to the zero axis. […] Grouped area graphs can handle negative values somewhat better than stacked area graphs but they still have the problem of all or portions of data curves being hidden by the data series towards the front." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"Pie charts have severe perceptual problems. Experiments in graphical perception have shown that compared with dot charts, they convey information far less reliably. But if you want to display some data, and perceiving the information is not so important, then a pie chart is fine." (Richard Becker & William S Cleveland," S-Plus Trellis Graphics User's Manual", 1996)

"The ordinary histogram is constructed by binning data on a uniform grid. Although this is probably the most widely used statistical graphic, it is one of the more difficult ones to compute. Several problems arise, including choosing the number of bins (bars) and deciding where to place the cutpoints between bars." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"Scatterplots are still the go-to visualization when one is examining relationships between continuous variables. One of the problems with the traditional scatterplot is that all data points are presented as if they are on equal footing. [...] Bubble maps are scatterplots with added dimensions. The most common usage is to add weight to individual data points based on population." (Christopher Lysy, "Developments in Quantitative Data Display and Their Implications for Evaluation", 2013) 

"One of the main problems with the visual approach to statistical data analysis is that it is too easy to generate too many plots: We can easily become totally overwhelmed by the shear number and variety of graphics that we can generate. In a sense, we have been too successful in our goal of making it easy for the user: Many, many plots can be generated, so many that it becomes impossible to understand our data." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

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

"Another problem is that while data visualizations may appear to be objective, the designer has a great deal of control over the message a graphic conveys. Even using accurate data, a designer can manipulate how those data make us feel. She can create the illusion of a correlation where none exists, or make a small difference between groups look big." (Carl T Bergstrom & Jevin D West, "Calling Bullshit: The Art of Skepticism in a Data-Driven World", 2020)

"Whatever approach you take, it’s always a good idea to define a range of reusable colour palettes so you don’t need to face the same colour design problems every time you want to create a chart or map. There will always be exceptions that require a different treatment, but it’s good to have a solid default starting point." (Alan Smith, "How Charts Work: Understand and explain data with confidence", 2022)

📉Graphical Representation: Values (Just the Quotes)

"By [diagrams] it is possible to present at a glance all the facts which could be obtained from figures as to the increase, fluctuations, and relative importance of prices, quantities, and values of different classes of goods and trade with various countries; while the sharp irregularities of the curves give emphasis to the disturbing causes which produce any striking change." (Arthur L Bowley, "A Short Account of England's Foreign Trade in the Nineteenth Century, its Economic and Social Results", 1905)

"To summarize - with the ordinary arithmetical scale, fluctuations in large factors are very noticeable, while relatively greater fluctuations in smaller factors are barely apparent. The logarithmic scale permits the graphic representation of changes in every quantity without respect to the magnitude of the quantity itself. At the same time, the logarithmic scale shows the actual value by reference to the numbers in the vertical scale. By indicating both absolute and relative values and changes, the logarithmic scale combines the advantages of both the natural and the percentage scale without the disadvantages of either." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"With the ordinary scale, fluctuations in large factors are very noticeable, while relatively greater fluctuations in smaller factors are barely apparent. The semi-logarithmic scale permits the graphic representation of changes in every quantity on the same basis, without respect to the magnitude of the quantity itself. At the same time, it shows the actual value by reference to the numbers in the scale column. By indicating both absolute and relative value and changes to one scale, it combines the advantages of both the natural and percentage scale, without the disadvantages of either." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"An important rule in the drafting of curve charts is that the amount scale should begin at zero. In comparisons of size the omission of the zero base, unless clearly indicated, is likely to give a misleading impression of the relative values and trend." (Rufus R Lutz, "Graphic Presentation Simplified", 1949)

"The function of the regression lines, as approximate representations of means of arrays, is to isolate the mean value of one variable corresponding to any given value of the other; the variation of the first variable about its mean is ignored. A regression line is an average relation, and with it there is a variation of values about the average. In the regression of y on x, the variation ignored is in the vertical direction, a variation of y up and down about the line." (Roy D G Allen, "Statistics for Economists", 1951)

"First, it is generally inadvisable to attempt to portray a series of more than four or five categories by means of pie charts. If, for example, there are six, eight, or more categories, it may be very confusing to differentiate the relative values portrayed, especially if several small sectors are of approximately the same size. Second, the pie chart may lose its effectiveness if an attempt is made to compare the component values of several circles, as might be found in a temporal or geographical series. In such case the one-hundred percent bar or column chart is more appropriate. Third, although the proportionate values portrayed in a pie chart are measured as distances along arcs about the circle, actually there is a tendency to estimate values in terms of areas of sectors or by the size of subtended angles at the center of the circle." (Calvin F Schmid, "Handbook of Graphic Presentation", 1954)

"The primary purpose of a graph is to show diagrammatically how the values of one of two linked variables change with those of the other. One of the most useful applications of the graph occurs in connection with the representation of statistical data." (John F Kenney & E S Keeping, "Mathematics of Statistics" Vol. I 3rd Ed., 1954)

"Where the values of a series are such that a large part the grid would be superfluous, it is the practice to break the grid thus eliminating the unused portion of the scale, but at the same time indicating the zero line. Failure to include zero in the vertical scale is a very common omission which distorts the data and gives an erroneous visual impression." (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)

"To be useful data must be consistent - they must reflect periodic recordings of the value of the variable or at least possess logical internal connections. The definition of the variable under consideration cannot change during the period of measurement or enumeration. Also. if the data are to be valuable, they must be relevant to the question to be answered." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

"Missing data values pose a particularly sticky problem for symbols. For instance, if the ray corresponding to a missing value is simply left off of a star symbol, the result will be almost indistinguishable from a minimum (i.e., an extreme) value. It may be better either (i) to impute a value, perhaps a median for that variable, or a fitted value from some regression on other variables, (ii) to indicate that the value is missing, possibly with a dashed line, or (iii) not to draw the symbol for a particular observation if any value is missing." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"[...] error bars are more effectively portrayed on dot charts than on bar charts. […] On the bar chart the upper values of the intervals stand out well, but the lower values are visually deemphasized and are not as well perceived as a result of being embedded in the bars. This deemphasis does not occur on the dot chart." (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38 (4) 1984)

"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)

"It is common for positive data to be skewed to the right: some values bunch together at the low end of the scale and others trail off to the high end with increasing gaps between the values as they get higher. Such data can cause severe resolution problems on graphs, and the common remedy is to take logarithms. Indeed, it is the frequent success of this remedy that partly accounts for the large use of logarithms in graphical data display." (William S Cleveland, "The Elements of Graphing Data", 1985)

"Use a reference line when there is an important value that must be seen across the entire graph, but do not let the line interfere with the data." (William S Cleveland, "The Elements of Graphing Data", 1985)

"Scatter charts show the relationships between information, plotted as points on a grid. These groupings can portray general features of the source data, and are useful for showing where correlationships occur frequently. Some scatter charts connect points of equal value to produce areas within the grid which consist of similar features." (Bruce Robertson, "How to Draw Charts & Diagrams", 1988)

"A coordinate is a number or value used to locate a point with respect to a reference point, line, or plane. Generally the reference is zero. […] The major function of coordinates is to provide a method for encoding information on charts, graphs, and maps in such a way that viewers can accurately decode the information after the graph or map has been generated."  (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996) 

"Area graphs are generally not used to convey specific values. Instead, they are most frequently used to show trends and relationships, to identify and/or add emphasis to specific information by virtue of the boldness of the shading or color, or to show parts-of-the-whole." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996) 

"Grouped area graphs sometimes cause confusion because the viewer cannot determine whether the areas for the data series extend down to the zero axis. […] Grouped area graphs can handle negative values somewhat better than stacked area graphs but they still have the problem of all or portions of data curves being hidden by the data series towards the front." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"If you want to show the growth of numbers which tend to grow by percentages, plot them on a logarithmic vertical scale. When plotted against a logarithmic vertical axis, equal percentage changes take up equal distances on the vertical axis. Thus, a constant annual percentage rate of change will plot as a straight line. The vertical scale on a logarithmic chart does not start at zero, as it shows the ratio of values (in this case, land values), and dividing by zero is impossible." (Herbert F Spirer et al, "Misused Statistics" 2nd Ed, 1998)

"Estimating the missing values in a dataset solves one problem - imputing reasonable values that have well-defined statistical properties. It fails to solve another, however - drawing inferences about parameters in a model fit to the estimated data. Treating imputed values as if they were known (like the rest of the observed data) causes confidence intervals to be too narrow and tends to bias other estimates that depend on the variability of the imputed values (such as correlations)." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"Use a logarithmic scale when it is important to understand percent change or multiplicative factors. […] Showing data on a logarithmic scale can cure skewness toward large values." (Naomi B Robbins, "Creating More effective Graphs", 2005)

"A useful feature of a stem plot is that the values maintain their natural order, while at the same time they are laid out in a way that emphasizes the overall distribution of where the values are concentrated (that is, where the longer branches are). This enables you easily to pick out key values such as the median and quartiles." (Alan Graham, "Developing Thinking in Statistics", 2006)

"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)

"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)

"The biggest difference between line graphs and sparklines is that a sparkline is compact with no grid lines. It isnʼt meant to give precise values; rather, it should be considered just like any other word in the sentence. Its general shape acts as another term and lends additional meaning in its context. The driving forces behind these compact sparklines are speed and convenience." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"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)

"Histograms are often mistaken for bar charts but there are important differences. Histograms show distribution through the frequency of quantitative values (y axis) against defined intervals of quantitative values (x axis). By contrast, bar charts facilitate comparison of categorical values. One of the distinguishing features of a histogram is the lack of gaps between the bars [...]" (Andy Kirk, "Data Visualization: A successful design process", 2012)

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

"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)

"A scatterplot reveals the strength and shape of the relationship between a pair of variables. A scatterplot represents the two variables by axes drawn at right angles to each other, showing the observations as a cloud of points, each point located according to its values on the two variables. Various lines can be added to the plot to help guide our search for understanding." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"The simplest and most common way to represent the empirical distribution of a numerical variable is by showing the individual values as dots arranged along a line. The main difficulty with this plot concerns how to treat tied values. We usually don't want to represent them by the same point, since that means that the two values look like one. What we can do is 'jitter' the points a bit (i.e., move them back and forth at right angles to the plot axis) so that all points are visible. […] In addition to permitting you to identify individual points, dotplots allow you to look into some of the distributional properties of a variable. […] Dotplots can also be good for looking for modality. " (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"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)

"A time series is a sequence of values, usually taken in equally spaced intervals. […] Essentially, anything with a time dimension, measured in regular intervals, can be used for time series analysis." (Andy Kriebel & Eva Murray, "#MakeoverMonday: Improving How We Visualize and Analyze Data, One Chart at a Time", 2018)

"Data is dirty. Let's just get that out there. How is it dirty? In all sorts of ways. Misspelled text values, date format problems, mismatching units, missing values, null values, incompatible geospatial coordinate formats, the list goes on and on." (Ben Jones, "Avoiding Data Pitfalls: How to Steer Clear of Common Blunders When Working with Data and Presenting Analysis and Visualizations", 2020) 

"Another cardinal sin of data visualization is what is called 'breaking the bar' - that is, using a squiggly line or shape to show that you've cropped one or more of the bars. It's tempting to do this when you have an outlier, but it distorts the relative values between the bars." (Jonathan Schwabish, "Better Data Visualizations: A guide for scholars, researchers, and wonks", 2021)

📉Graphical Representation: Shape (Just the Quotes)

"The impression created by a chart depends to a great extent on the shape of the grid and the distribution of time and amount scales. When your individual figures are a part of a series make sure your own will harmonize with the other illustrations in spacing of grid rulings, lettering, intensity of lines, and planned to take the same reduction by following the general style of the presentation." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"A good graphic must give the impression that its various parts all belong together. They must be arranged in such a way that the illustration looks like a single entity. A good graphic chart should be more than just the sum of its individual lines, shapes, and shades. It should be more than the individual bars in a bar chart, more than the pieces of a pie chart, more than the boxes in a flow chart. Unity requires the establishment of coherent relationships among the component parts of the drawing. These relationships can be depicted in a very direct manner through the use of connecting lines that serve to connect shapes." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"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)

"The more complex the shape of any object, the more difficult it is to perceive it. The nature of thought based on the visual apprehension of objective forms suggests, therefore, the necessity to keep all graphics as simple as possible. Otherwise, their meaning will be lost or ambiguous, and the ability to convey the intended information and to persuade will be inhibited." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"Maps containing marks that indicate a variety of features at specific locations are easy to produce and often revealing for the reader. You can use dots, numbers, and shapes, with or without keys. The basic map must always be simple and devoid of unnecessary detail. There should be no ambiguity about what happens where." (Bruce Robertson, "How to Draw Charts & Diagrams", 1988)

"Visual thinking can begin with the three basic shapes we all learned to draw before kindergarten: the triangle, the circle, and the square. The triangle encourages you to rank parts of a problem by priority. When drawn into a triangle, these parts are less likely to get out of order and take on more importance than they should. While the triangle ranks, the circle encloses and can be used to include and/or exclude. Some problems have to be enclosed to be managed. Finally, the square serves as a versatile problem-solving tool. By assigning it attributes along its sides or corners, we can suddenly give a vague issue a specific place to live and to move about." (Terry Richey, "The Marketer's Visual Tool Kit", 1994)

"Functional visualizations are more than innovative statistical analyses and computational algorithms. They must make sense to the user and require a visual language system that uses color, shape, line, hierarchy and composition to communicate clearly and appropriately, much like the alphabetic and character-based languages used worldwide between humans." (Matt Woolman, "Digital Information Graphics", 2002)

"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)

"Symmetry and skewness can be judged, but boxplots are not entirely useful for judging shape. It is not possible to use a boxplot to judge whether or not a dataset is bell-shaped, nor is it possible to judge whether or not a dataset may be bimodal." (Jessica M Utts & Robert F Heckard, "Mind on Statistics", 2007)

"The biggest difference between line graphs and sparklines is that a sparkline is compact with no grid lines. It isnʼt meant to give precise values; rather, it should be considered just like any other word in the sentence. Its general shape acts as another term and lends additional meaning in its context. The driving forces behind these compact sparklines are speed and convenience." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"[...] the form of a technological object must depend on the tasks it should help with. This is one of the most important principles to remember when dealing with infographics and visualizations: The form should be constrained by the functions of your presentation. There may be more than one form a data set can adopt so that readers can perform operations with it and extract meanings, but the data cannot adopt any form. Choosing visual shapes to encode information should not be based on aesthetics and personal tastes alone." (Alberto Cairo, "The Functional Art", 2011)

"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)

"Data is more than numbers, and to visualize it, you must know what it represents. Data represents real life. It’s a snapshot of the world in the same way that a photograph captures a small moment in time. […] The connection between data and what it represents is key to visualization that means something. It is key to thoughtful data analysis. It is key to a deeper understanding of your data. Computers do a bulk of the work to turn numbers into shapes and colors, but you must make the connection between data and real life, so that you or the people you make graphics for extract something of value." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"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)

"The ability to see meaningful shapes in the data represents the highest level of data visualization, because it represents the highest level of data integration and a richer graphical landscape. Line charts and scatter plots are frequently used for this shape visualization." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"Some scientists (e.g., econometricians) like to work with mathematical equations; others" (e.g., hard-core statisticians) prefer a list of assumptions that ostensibly summarizes the structure of the diagram. Regardless of language, the model should depict, however qualitatively, the process that generates the data - in other words, the cause-effect forces that operate in the environment and shape the data generated." (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

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

"Data that is well prepared makes the analysis easier and allows a deeper exploration of patterns. It helps the analyst sift through the data with less friction. Data that is well crafted holds up to rigorous analysis and presentation. It removes the wall between us and the data and allows us to see the patterns. Well-shaped data isn't only functional, it's also aesthetic." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"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: Value (Just the Quotes)

"All charts should be given a comprehensive title, that there may be no doubt as to what data the chart is intended to cover. This is especially necessary in connection with separate exhibits used for illustrating statements in special reports, as when the charts are not given distinct titles they are valueless as records when detached from the reports." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"One of the greatest values of the graphic chart is its use in the analysis of a problem. Ordinarily, the chart brings up many questions which require careful consideration and further research before a satisfactory conclusion can be reached. A properly drawn chart gives a cross-section picture of the situation. While charts may bring out, hidden facts in tables or masses of data, they cannot take the place of careful, analysis. In fact, charts may be dangerous devices when in the hands of those unwilling to base their interpretations upon careful study. This, however, does not detract from their value when they are properly used as aids in solving statistical problems." (John R Riggleman & Ira N Frisbee, "Business Statistics", 1938)

"The great trouble with all business data upon which the statisticians and economists base their forecasts is that they are ancient history before they ever become available. They pertain to conditions which existed some weeks or months previous. The figures for what is going on at the moment in all lines of business are never available. A business index, while of great interest and value, is always historical and never predictive." (Walter E Weld, "How to Chart; Facts from Figures with Graphs", 1959)

"In some situations. the terms describing the data are common knowledge and can be expected to be understood by most individuals. In others. the data is to be used by experts in a particular field, who also can be expected to know the terms. But when technical terms may be misunderstood by the reader. they should be clearly defined. This also implies that terms and concepts should be clearly defined before the original data is gathered. Obviously. one has to know what kind of information to gather for that stage to be of any value." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

"Understandability implies that the graph will mean something to the audience. If the presentation has little meaning to the audience, it has little value. Understandability is the difference between data and information. Data are facts. Information is facts that mean something and make a difference to whoever receives them. Graphic presentation enhances understanding in a number of ways. Many people find that the visual comparison and contrast of information permit relationships to be grasped more easily. Relationships that had been obscure become clear and provide new insights." (Anker V Andersen, "Graphing Financial Information: How accountants can use graphs to communicate", 1983)

"When the data are magnitudes, it is helpful to have zero included in the scale so we can see its value relative to the value of the data. But the need for zero is not so compelling that we should allow its inclusion to ruin the resolution of the data on the graph." (William S Cleveland, "The Elements of Graphing Data", 1985)

"The real value of dashboard products lies in their ability to replace hunt‐and‐peck data‐gathering techniques with a tireless, adaptable, information‐flow mechanism. Dashboards transform data repositories into consumable information." (Gregory L Hovis, "Stop Searching for Information Monitor it with Dashboard Technology," DM Direct, 2002)"A diagram is a graphic shorthand. Though it is an ideogram, it is not necessarily an abstraction. It is a representation of something in that it is not the thing itself. In this sense, it cannot help but be embodied. It can never be free of value or meaning, even when it attempts to express relationships of formation and their processes. At the same time, a diagram is neither a structure nor an abstraction of structure." (Peter Eisenman, "Written Into the Void: Selected Writings", 1990-2004, 2007)

"A graphic display has many purposes, but it achieves its highest value when it forces us to see what we were not expecting." (Howard Wainer, "Graphic Discovery: A trout in the milk and other visuals" 2nd, 2008)

"Placing a fact within a context increases its value greatly. […] . An efficacious way to add context to statistical facts is by embedding them in a graphic. Sometimes the most helpful context is geographical, and shaded maps come to mind as examples. Sometimes the most helpful context is temporal, and time-based line graphs are the obvious choice. But how much time? The ending date (today) is usually clear, but where do you start? The starting point determines the scale. […] The starting point and hence the scale are determined by the questions that we expect the graph to answer." (Howard Wainer, "Graphic Discovery: A trout in the milk and other visuals" 2nd, 2008)

"Communication is the primary goal of data visualization. Any element that hinders - rather than helps - the reader, then, needs to be changed or removed: labels and tags that are in the way, colors that confuse or simply add no value, uncomfortable scales or angles. Each element needs to serve a particular purpose toward the goal of communicating and explaining information. Efficiency matters, because if you’re wasting a viewer’s time or energy, they’re going to move on without receiving your message." (Noah Iliinsky & Julie Steel, "Designing Data Visualizations", 2011)

"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)

"Simplicity for data visualization often focuses on minimizing the number of elements that do not add value to your display. These include borders, gridlines, axes lines, and boxes, which can easily distract from your core message. This recommendation also relates to the information itself. You should strive to create a visualization that focuses on specific aspects of the data, rather than including all fields and metrics but not saying much about any of them." (Andy Kriebel & Eva Murray, "#MakeoverMonday: Improving How We Visualize and Analyze Data, One Chart at a Time", 2018)

📉Graphical Representation: Clarity (Just the Quotes)

"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)

"The title for any chart presenting data in the graphic form should be so clear and so complete that the chart and its title could be removed from the context and yet give all the information necessary for a complete interpretation of the data. Charts which present new or especially interesting facts are very frequently copied by many magazines. A chart with its title should be considered a unit, so that anyone wishing to make an abstract of the article in which the chart appears could safely transfer the chart and its title for use elsewhere." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919) 

"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)

"Good design looks right. It is simple (clear and uncomplicated). Good design is also elegant, and does not look contrived. A map should be aesthetically pleasing, thought provoking, and communicative." (Arthur H Robinson, "Elements of Cartography", 1953)

"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)

"Although flow charts are not used to portray or interpret statistical data, they possess definite utility for certain kinds of research and administrative problems. With a well-designed flow chart it is possible to present a large number of facts and relationships simply, clearly, and accurately, without resorting to extensive or involved verbal description." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"Charts and graphs are a method of organizing information for a unique purpose. The purpose may be to inform, to persuade, to obtain a clear understanding of certain facts, or to focus information and attention on a particular problem. The information contained in charts and graphs must, obviously, be relevant to the purpose. For decision-making purposes. information must be focused clearly on the issue or issues requiring attention. The need is not simply for 'information', but for structured information, clearly presented and narrowed to fit a distinctive decision-making context. An advantage of having a 'formula' or 'model' appropriate to a given situation is that the formula indicates what kind of information is needed to obtain a solution or answer to a specific problem." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

"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)

"If two or more data paths ate to appear on the graph. it is essential that these lines be labeled clearly, or at least a reference should be provided for the reader to make the necessary identifications. While clarity seems to be a most obvious goal, graphs with inadequate or confusing labeling do appear in publications, The user should not find identification of data paths troublesome or subject to misunderstanding. The designer normally should place no more than three data paths on the graph to prevent confusion - particularly if the data paths intersect at one or more points on the Cartesian plane." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

"It should be noted that graphics for the purpose of clarity should not be a substitute for words and numbers in the narrative text. The graphics presentation is used to supplement the narrative; otherwise. there wouldn't be anything to clarify." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"Understanding is accomplished through: (a) the use of relative size of the shapes used in the graphic; (b) the positioning of the graphic-line forms; (c) shading; (d) the use of scales of measurement; and (e) the use of words to label the forms in the graphic. In addition. in order for a person to attach meaning to a graphic it must also be simple, clear, and appropriate." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"Although arguments can be made that high data density does not imply that a graphic will be good, nor one with low density bad, it does reflect on the efficiency of the transmission of information. Obviously, if we hold clarity and accuracy constant, more information is better than less. One of the great assets of graphical techniques is that they can convey large amounts of information in a small space." (Howard Wainer, "How to Display Data Badly", The American Statistician Vol. 38(2), 1984) 

"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)

"Put everything together - from understanding data, to exploration, clarity, and adapting to an audience - and you get a general process for how to make data graphics."  (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"Understandability implies that the graph will mean something to the audience. If the presentation has little meaning to the audience, it has little value. Understandability is the difference between data and information. Data are facts. Information is facts that mean something and make a difference to whoever receives them. Graphic presentation enhances understanding in a number of ways. Many people find that the visual comparison and contrast of information permit relationships to be grasped more easily. Relationships that had been obscure become clear and provide new insights." (Anker V Andersen, "Graphing Financial Information: How accountants can use graphs to communicate", 1983)

"The effective communication of information in visual form, whether it be text, tables, graphs, charts or diagrams, requires an understanding of those factors which determine the 'legibility', 'readability' and 'comprehensibility', of the information being presented. By legibility we mean: can the data be clearly seen and easily read? By readability we mean: is the information set out in a logical way so that its structure is clear and it can be easily scanned? By comprehensibility we mean: does the data make sense to the audience for whom it is intended? Is the presentation appropriate for their previous knowledge, their present information needs and their information processing capacities?" (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"Clear vision is a vital aspect of graphs. The viewer must be able to visually disentangle the many different items that appear on a graph." (William S Cleveland, "The Elements of Graphing Data", 1985)

"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)

"Information needs representation. The idea that it is possible to communicate information in a 'pure' form is fiction. Successful risk communication requires intuitively clear representations. Playing with representations can help us not only to understand numbers (describe phenomena) but also to draw conclusions from numbers (make inferences). There is no single best representation, because what is needed always depends on the minds that are doing the communicating." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)

"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)

"Perception requires imagination because the data people encounter in their lives are never complete and always equivocal. [...] We also use our imagination and take shortcuts to fill gaps in patterns of nonvisual data. As with visual input, we draw conclusions and make judgments based on uncertain and incomplete information, and we conclude, when we are done analyzing the patterns, that out picture is clear and accurate. But is it?" (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"[...] 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)

"Usually, diagrams contain some noise - information unrelated to the diagram’s primary goal. Noise is decorations, redundant, and irrelevant data, unnecessarily emphasized and ambiguous icons, symbols, lines, grids, or labels. Every unnecessary element draws attention away from the central idea that the designer is trying to share. Noise reduces clarity by hiding useful information in a fog of useless data. You may quickly identify noise elements if you can remove them from the diagram or make them less intense and attractive without compromising the function." (Vasily Pantyukhin, "Principles of Design Diagramming", 2015)

"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)

"A well-designed graph clearly shows you the relevant end points of a continuum. This is especially important if you’re documenting some actual or projected change in a quantity, and you want your readers to draw the right conclusions. […]" (Daniel J Levitin, "Weaponized Lies", 2017)

📉Graphical Representation: Conclusions (Just the Quotes)

"Before anything can be reasoned upon to a conclusion, certain facts, principles, or data, to reason from, must be established, admitted, or denied." (Thomas Paine, "Rights of Man", 1791) 

"Graphic methods convey to the mind a more comprehensive grasp of essential features than do written reports, because one can naturally gather interesting details from a picture in far less time than from a written description. Further than this, the examination of a picture allows one to make deductions of his own, while in the case of a written description the reader must, to a great degree, accept the conclusions of the author." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"Unlimited numbers of reports, magazines, and newspapers are now giving us reams of quantitative facts. If the facts were put in graphic form, not only would there be a great saving in the time of the readers but there would be infinite gain to society, because more facts could be absorbed and with less danger of misinterpretation. Graphic methods usually require no more space than is needed if the facts are presented in the form of words. In many cases, the graphic method requires less space than is required for words and there is, besides, the great advantage that with graphic methods facts are presented so that the reader may make deductions of his own, while when words are used the reader must usually accept the ready-made conclusions handed to him." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"The preliminary examination of most data is facilitated by the use of diagrams. Diagrams prove nothing, but bring outstanding features readily to the eye; they are therefore no substitutes for such critical tests as may be applied to the data, but are valuable in suggesting such tests, and in explaining the conclusions founded upon them." (Sir Ronald A Fisher, "Statistical Methods for Research Workers", 1925)

"One of the greatest values of the graphic chart is its use in the analysis of a problem. Ordinarily, the chart brings up many questions which require careful consideration and further research before a satisfactory conclusion can be reached. A properly drawn chart gives a cross-section picture of the situation. While charts may bring out hidden facts in tables or masses of data, they cannot take the place of careful, analysis. In fact, charts may be dangerous devices when in the hands of those unwilling to base their interpretations upon careful study. This, however, does not detract from their value when they are properly used as aids in solving statistical problems." (John R Riggleman & Ira N Frisbee, "Business Statistics", 1938)

"Just like the spoken or written word, statistics and graphs can lie. They can lie by not telling the full story. They can lead to wrong conclusions by omitting some of the important facts. [...] Always look at statistics with a critical eye, and you will not be the victim of misleading information." (Dyno Lowenstein, "Graphs", 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)

"Information needs representation. The idea that it is possible to communicate information in a 'pure' form is fiction. Successful risk communication requires intuitively clear representations. Playing with representations can help us not only to understand numbers (describe phenomena) but also to draw conclusions from numbers (make inferences). There is no single best representation, because what is needed always depends on the minds that are doing the communicating." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)

"Perception requires imagination because the data people encounter in their lives are never complete and always equivocal. [...] We also use our imagination and take shortcuts to fill gaps in patterns of nonvisual data. As with visual input, we draw conclusions and make judgments based on uncertain and incomplete information, and we conclude, when we are done analyzing the patterns, that out picture is clear and accurate. But is it?" (Leonard Mlodinow, "The Drunkard’s Walk: How Randomness Rules Our Lives", 2008)

"Readability in visualization helps people interpret data and make conclusions about what the data has to say. Embed charts in reports or surround them with text, and you can explain results in detail. However, take a visualization out of a report or disconnect it from text that provides context (as is common when people share graphics online), and the data might lose its meaning; or worse, others might misinterpret what you tried to show." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"We naturally draw conclusions from what we see […]. We should also think about what we do not see […]. The unseen data may be just as important, or even more important, than the seen data. To avoid survivor bias, start in the past and look forward." (Gary Smith, "Standard Deviations", 2014)

"A well-designed graph clearly shows you the relevant end points of a continuum. This is especially important if you’re documenting some actual or projected change in a quantity, and you want your readers to draw the right conclusions. […]" (Daniel J Levitin, "Weaponized Lies", 2017)

"Just because there’s a number on it, it doesn’t mean that the number was arrived at properly. […] There are a host of errors and biases that can enter into the collection process, and these can lead millions of people to draw the wrong conclusions. Although most of us won’t ever participate in the collection process, thinking about it, critically, is easy to learn and within the reach of all of us." (Daniel J Levitin, "Weaponized Lies", 2017)