📉Graphical Representation: Space (Just the Quotes)

"The zero of the scale should appear on every chart, and should shown by a heavy line carried across the sheet. If this is not done the reader may assume the bottom of the sheet to be zero and so be misled. The scale should be graduated from zero to a little over the maximum figure to be plotted on the charts, so that there will be a space between the highest peak on the curve and the top of the chart." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"A chart without a border line has several advantages. It is not limited to a designated area. The irregular white space surrounding it makes it more adaptable to any page size. It may be more readily placed either horizontally or vertically on the page, so long as the reduction in the size of the chart does not destroy legibility of lettering." (Mary E Spear, "Charting Statistics", 1952)

"Since the chief purpose of the nomogram is to make exact data available for operational use, its chief competitor is the table. Operational tables may break Ehrenberg's two-digit rule, since they are not used to detect general trends but to provide exact data for some operational purpose. The choice  between nomogram and table involves a complex tradeoff among cost, space, convenience, accuracy, and speed. These tradeoff situations provide one good reason why no one graphic format is suitable for all purposes. Of course, there can be good methods (sarisfying solutions) for particular cases." (Michael Macdonald-Ross, "Graphics in Texts", Review of Research in Education Vol. 5, 1977)

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

"Graphical excellence is the well-designed presentation of interesting data - a matter of substance, of statistics, and of design. Graphical excellence consists of complex ideas communicated with clarity, precision, and efficiency. Graphical excellence is that which gives to the viewer the greatest number of ideas in the shortest time with the least ink in the smallest space. Graphical excellence is nearly always multivariate. And graphical excellence requires telling the truth about the data." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"A time series is a special case of the broader dependent-independent variable category. Time is the independent variable. One important property of most time series is that for each time point of the data there is only a single value of the dependent variable; there are no repeat measurements. Furthermore, most time series are measured at equally-spaced or nearly equally-spaced points in time." (William S Cleveland, "The Elements of Graphing Data", 1985)

"Binning has two basic limitations. First, binning sacrifices resolution. Sometimes plots of the raw data will reveal interesting fine structure that is hidden by binning. However, advantages from binning often outweigh the disadvantage from lost resolution. [...] Second, binning does not extend well to high dimensions. With reasonable univariate resolution, say 50 regions each covering 2% of the range of the variable, the number of cells for a mere 10 variables is exceedingly large. For uniformly distributed data, it would take a huge sample size to fill a respectable fraction of the cells. The message is not so much that binning is bad but that high dimensional space is big. The complement to the curse of dimensionality is the blessing of large samples. Even in two and three dimensions having lots of data can bc very helpful when the observations are noisy and the structure non-trivial." (Daniel B Carr, "Looking at Large Data Sets Using Binned Data Plots", [in "Computing and Graphics in Statistics"] 1991)

"Many of the applications of visualization in this book give the impression that data analysis consists of an orderly progression of exploratory graphs, fitting, and visualization of fits and residuals. Coherence of discussion and limited space necessitate a presentation that appears to imply this. Real life is usually quite different. There are blind alleys. There are mistaken actions. There are effects missed until the very end when some visualization saves the day. And worse, there is the possibility of the nearly unmentionable: missed effects." (William S Cleveland, "Visualizing Data", 1993)

"In preparing bar charts, make certain that the space separating the bars is smaller than the width of the bars. Use the most contrasting color or shading to emphasize the important item, thereby reinforcing the message title." (Gene Zelazny. "Say It with Charts: The executive’s guide to visual communication" 4th Ed., 2001)

"The suggestions for making the most of bar charts also apply to column charts: make the space between the columns smaller than the width of the columns; and use color or shading to emphasize one point in time more than others or to distinguish, say, historical from projected data." (Gene Zelazny. "Say It with Charts: The executive’s guide to visual communication" 4th Ed., 2001)

"Coordinates are sets that locate points in space. These sets are usually numbers grouped in tuples, one tuple for each point. Because spaces can be defined as sets of geometric objects plus axioms defining their behavior, coordinates can be thought of more generally as schemes for mapping elements of sets to geometric objects." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"[...] the First Principle for the analysis and presentation data: 'Show comparisons, contrasts, differences'. The fundamental analytical act in statistical reasoning is to answer the question "Compared with what?". Whether we are evaluating changes over space or time, searching big data bases, adjusting and controlling for variables, designing experiments , specifying multiple regressions, or doing just about any kind of evidence-based reasoning, the essential point is to make intelligent and appropriate comparisons. Thus visual displays, if they are to assist thinking, should show comparisons." (Edward R Tufte, "Beautiful Evidence", 2006)

"Closely spaced lines produce moiré vibration, usually at its worst when data-lines (the figure) and spaces (the ground) between data-lines are approximately equal in size, and also when figure and ground contrast strongly in color value." (Edward R Tufte, "Beautiful Evidence", 2006)

"Most techniques for displaying evidence are inherently multimodal, bringing verbal, visual. and quantitative elements together. Statistical graphics and maps arc visual-numerical fields labeled with words and framed by numbers. Even an austere image may evoke other images, new or remembered narrative, and perhaps a sense of scale and quantity. Words can simultaneously convey semantic and visual content, as the nouns on a map both name places and locate them in the two - space of latitude and longitude." (Edward R Tufte, "Beautiful Evidence", 2006)

"The notion of outcomes covering a space is a very useful mental image, as it ties in strongly with the use of Venn diagrams and tables for clarifying the nature of possible events resulting from a trial. There are two important aspects to this. First, when enumerating the various outcomes that comprise an event, the number of (equally. likely) outcomes should correspond, visually, with the area of that part of the diagram represented by the event in question - the greater the probability, the larger the area. Secondly, where events overlap (for example, when rolling a die, consider the two events 'getting an even score' and 'getting a score greater than 2' ), the various regions in the Venn diagram help to clarify the various combinations of events that might occur." (Alan Graham, "Developing Thinking in Statistics", 2006)

"Radar charts are almost always the result either of space-saving attempts or of doubtful theories about the desirability of 'symmetrical' plots, in which scores on all dimensions are similar, so giving an approximation to a circle. Their scales offer unlimited scope for manipulation in achieving this lunatic ambition." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"There are some chart types that occasionally appear in print but are so bad that they serve neither honesty nor deceit. Among these monuments to human ingenuity at the expense of common sense are the concentric donut and overlapping segments. The concentric donut is really just a bar or column chart bent back on itself to save space. However as anyone who has ever watched a two or four hundred metre race will know, to make sense of the order of arrival at the tape you have to stagger the start to take account of the bend in the track. Blithely ignoring this problem, the concentric donut uses to diminish the difference between the inner and the outer absolute values by anything up to 2.5 times." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"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)

"One big advantage of parallel coordinate plots over scatterplot matrices. (i.e., the matrix of scatterplots of all variable pairs) is that parallel coordinate plots need less space to plot the same amount of data. On the other hand, parallel coordinate plots with p variables show only p − 1 adjacencies. However, adjacent variables reveal most of the information in a parallel coordinate plot. Reordering variables in a parallel coordinate plot is therefore essential." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009) 

"Shingling is the process of dividing a continuous variable into - possibly overlapping - intervals in order to convert a continuous variable into a discrete variable. Shingling is quite different from conditioning on categorical variables. Overlapping shingles/intervals lead to multiple representation of data within a trellis display, which is not the case for categorical variables. Furthermore, it is challenging to judge which intervals/cases have been chosen to build a shingle. Trellis displays represent the shingle interval visually by an interval of the strip label. Although no plotting space is wasted, the information on the intervals is difficult to read from the strip label. Despite these drawbacks, there is a valid motivation for shingling […]." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009) 

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

"Trellis displays introduce the concept of shingling. Shingling is the process of dividing a continuous variable into - possibly overlapping - intervals in order to convert a continuous variable into a discrete variable. Shingling is quite different from conditioning on categorical variables. Overlapping shingles/intervals lead to multiple representation of data within a trellis display, which is not the case for categorical variables. Furthermore, it is challenging to judge which intervals/cases have been chosen to build a shingle. Trellis displays represent the shingle interval visually by an interval of the strip label. Although no plotting space is wasted, the information on the intervals is difficult to read from the strip label. Despite these drawbacks, there is a valid motivation for shingling," (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)

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

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

"Sparklines aren't necessarily a variation on the line chart, rather, a clever use of them. [...] They take advantage of our visual perception capabilities to discriminate changes even at such a low resolution in terms of size. They facilitate opportunities to construct particularly dense visual displays of data in small space and so are particularly applicable for use on dashboards." (Andy Kirk, "Data Visualization: A successful design process", 2012)

"Area can also make data seem more tangible or relatable, because physical objects take up space. A circle or a square uses more space than a dot on a screen or paper. There’s less abstraction between visual cue and real world." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"A space-filling layout has the property that it fills all available space in the view, as the name implies. [...] ne advantage of space-filling approaches is that they maximize the amount of room available for color coding, increasing the chance that the colored region will be large enough to be perceptually salient to the viewer. A related advantage is that the available space representing an item is often large enough to show a label embedded within it, rather than needing more room off to the side. In contrast, one disadvantage of space-filling views is that the designer cannot make use of white space in the layout; that is, empty space where there are no explicit visual elements. Many graphic design guidelines pertain to the careful use of white space for many reasons, including readability, emphasis, relative importance, and visual balance." (Tamara Munzner, "Visualization Analysis and Design", 2014)

"As with all design problems, vis design cannot be easily handled as a simple process of optimization because trade-offs abound. A design that does well by one measure will rate poorly on another. The characterization of trade-offs in the vis design space is a very open problem at the frontier of vis research." (Tamara Munzner, "Visualization Analysis and Design", 2014)

"Parallel coordinates visually encode data using two dimensions of spatial position. Of course, any individual axis requires only one spatial dimension, but the second dimension is used to lay out multiple axes. The scalability is high in terms of the number of quantitative attribute values that can be discriminated, since the high precisionchannel of planar spatial position is used. The exact number is roughly proportional to the screen space extent of the axes, in pixels. The scalability is moderate in terms of number of attributes that can be displayed: dozens is common. As the number of attributes shown increases, so does the width required to display them, so a parallel coordinates display showing many attributes is typically a wide and flat rectangle. Assuming that the axes are vertical, then the amount of vertical screen space required to distinguish position along them does not change, but the amount of horizontal screen space increases as more axes are added. One limit is that there must be enough room between the axes to discern the patterns of intersection or parallelism of the line  segments that pass between them." (Tamara Munzner, "Visualization Analysis and Design", 2014)

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

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

"When we’re at the point of communicating our analysis to our audience, we really want to be in the explanatory space, meaning you have a specific thing you want to explain, a specific story you want to tell - probably about those two pearls." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"Linking is a powerful dynamic interactive graphics technique that can help us better understand high-dimensional data. This technique works in the following way: When several plots are linked, selecting an observation's point in a plot will do more than highlight the observation in the plot we are interacting with - it will also highlight points in other plots with which it is linked, giving us a more complete idea of its value across all the variables. Selecting is done interactively with a pointing device. The point selected, and corresponding points in the other linked plots, are highlighted simultaneously. Thus, we can select a cluster of points in one plot and see if it corresponds to a cluster in any other plot, enabling us to investigate the high-dimensional shape and density of the cluster of points, and permitting us to investigate the structure of the disease space." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"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)

"Ideally, the charts are designed in a way that gives your audience clarity and lets them understand the key insights very quickly. Color choices, highlighting, annotations, and other ways of drawing attention to your findings help in the process. By leaving white or blank space around your charts, you are able to keep the focus of your audience on the key message rather than distracting or confusing them." (Andy Kriebel & Eva Murray, "#MakeoverMonday: Improving How We Visualize and Analyze Data, One Chart at a Time", 2018)

"Simplicity in design can be recognized in visualizations that are clear, easy to understand, uncluttered, and impactful. Nonessential items are removed from these visualizations so that the data stands out, giving it space and removing distractions. Simplicity in design pays careful attention to the overall layout and positioning of individual components, the balance of charts and text elements, and the choice of colors, fonts, and icons, as well as the clarity with which all of these elements communicate to the audience." (Andy Kriebel & Eva Murray, "#MakeoverMonday: Improving How We Visualize and Analyze Data, One Chart at a Time", 2018)

"The radial bar chart, also called the polar bar chart, arranges the bars to radiate outward from the center of a circle. This graph lies lowers on the perceptual ranking list because it is harder to compare the heights of the bars arranged around a circle than when they are arranged along a single flat axis. But this layout does allow you to fit more values in a compact space, and makes the radial bar chart well-suited for showing more data, frequent changes (such as monthly or daily), or changes over a long period of time." (Jonathan Schwabish, "Better Data Visualizations: A guide for scholars, researchers, and wonks", 2021)

"A semantic approach to visualization focuses on the interplay between charts, not just the selection of charts themselves. The approach unites the structural content of charts with the context and knowledge of those interacting with the composition. It avoids undue and excessive repetition by instead using referential devices, such as filtering or providing detail-on-demand. A cohesive analytical conversation also builds guardrails to keep users from derailing from the conversation or finding themselves lost without context. Functional aesthetics around color, sequence, style, use of space, alignment, framing, and other visual encodings can affect how users follow the script." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"Like multimodal reading, data literacy relies on both primary literacy skills and numeracy skills to truly make sense of the third layer: reading and understanding graphs. Charts codify numbers visually into parameters, using stylized marks to embed additional layers of meaning and space to provide quantitative relationships. Beyond the individual chart, data visualizations create ensembles of charts." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

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

"Positive and negative space help create balance, but they also draw interest." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"The sizes of charts in space reflect how we convey information to a reader. In a dashboard context, the content, size, and space that the various charts occupy should reflect the form and function of the main message. As you saw with the bento box metaphor from the introduction, there needs to be deliberate thought put into the placement and size of each individual chart so that they all work together in harmony." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

📉Graphical Representation: Qualitative vs. Quantitative (Just the Quotes)

"A model is a qualitative or quantitative representation of a process or endeavor that shows the effects of those factors which are significant for the purposes being considered. A model may be pictorial, descriptive, qualitative, or generally approximate in nature; or it may be mathematical and quantitative in nature and reasonably precise. It is important that effective means for modeling be understood such as analog, stochastic, procedural, scheduling, flow chart, schematic, and block diagrams." (Harold Chestnut, "Systems Engineering Tools", 1965)

"An organization chart is a graphic device that uses pictorial methods to show qualitative information about an organization. [...] The organization chart can be used to show one or more of three things: (1) What the various staff positions in the organization are, how they are structurally related to each other and the span of control and chain of command within the organization. (2) What the different units of the organization are and how they are arranged and related to each other. (3) What the various functions are within the organization and how they are organized and related." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

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

"Make the data stand out and avoid superfluity are two broad strategies that serve as an overall guide to the specific principles […] The data - the quantitative and qualitative information in the data region - are the reason for the existence of the graph. The data should stand out. […] We should eliminate superfluity in graphs. Unnecessary parts of a graph add to the clutter and increase the difficulty of making the necessary elements - the data - stand out." (William S Cleveland, "The Elements of Graphing Data", 1985)

"There is a technical difference between a bar chart and a histogram in that the number represented is proportional to the length of bar in the former and the area in the latter. This matters if non-uniform binning is used. Bar charts can be used for qualitative or quantitative data, whereas histograms can only be used for quantitative data, as no meaning can be attached to the width of the bins if the data are qualitative." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

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

"We need [graphic] techniques because figures do not speak for them. selves. Numbers alone seldom make a convincing case or polish their author's image - the twin goals of that other great mind bender, rhetoric. While rhetoric deals in qualitative argument, its quantitative equivalent is graphics. As rhetoric has declined in popularity, so graphics have risen along with our acceptance of quantitative arguments. In graphics, figures finally find their own means of expression." (Nicholas Strange, "Smoke and Mirrors: How to bend facts and figures to your advantage", 2007)

"Diagrams are information graphics that are made up primarily of geometric shapes, such as rectangles, circles, diamonds, or triangles, that are typically" (but not always) interconnected by lines or arrows. One of the major purposes of a diagram is to show how things, people, ideas, activities, etc. interrelate and interconnect. Unlike quantitative charts and graphs, diagrams are used to show interrelationships in a qualitative way." (Robbie T Nakatsu, "Diagrammatic Reasoning in AI", 2010)

"Data analytics is a powerful tool to increase the likelihood that you have the right problem. Both quantitative and qualitative data serve a purpose in supporting a hypothesis. They allow you to objectively measure and identify patterns and relationships." (Shonna D Watters et al, "The Practical Guide for HR Analytics: Using data to inform, transform, and empower HR decisions", 2019)

"The one unique characteristic that separates a data story from other types of stories is its fundamental basis in data. [...] The building blocks of every data story are quantitative or qualitative data, which are frequently the results of an analysis or insightful observation. Because each data story is formed from a collection of facts, each one represents a work of nonfiction. While some creativity may be used in how the story is structured and delivered, a true data story won’t stray too far from its factual underpinnings. In addition, the quality and trustworthiness of the data will determine how credible and powerful the data story is." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 2019)

📉Graphical Representation: Relations (Just the Quotes)

"There is no doubt that graphical expression will soon replace all others whenever one has at hand a movement or change of state - in a word, any phenomenon. Born before science, language is often inappropriate to express exact measures or definite relations." (Étienne-Jules Marey, "La méthode graphique dans les sciences expérimentales et principalement en physiologie et en médecine", 1878)

"[...] we can not readily break up a complicated problem into successive steps which can be taken independently. We have, in fact, to solve the problem first, by determining what are the actual mutual relations of the classes involved, and then to draw the circles to represent this final result; we cannot work step-by-step towards the conclusion by aid of our figures." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"[…] it must be noticed that these diagrams do not naturally harmonize with the propositions of ordinary life or ordinary logic. […] The great bulk of the propositions which we commonly meet with are founded, and rightly founded, on an imperfect knowledge of the actual mutual relations of the implied classes to one another. […] one very marked characteristic about these circular diagrams is that they forbid the natural expression of such uncertainty, and are therefore only directly applicable to a very small number of such propositions as we commonly meet with." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

"Whereas the Eulerian plan endeavoured at once and directly to represent propositions, or relations of class terms to one another, we shall find it best to begin by representing only classes, and then proceed to modify these in some way so as to make them indicate what our propositions have to say. How, then, shall we represent all the subclasses which two or more class terms can produce? Bear in mind that what we have to indicate is the successive duplication of the number of subdivisions produced by the introduction of each successive term. and we shall see our way to a very important departure from the Eulerian conception. All that we have to do is to draw our figures, say circles, so that each successive one which we introduce shall intersect once, and once only, all the subdivisions already existing, and we then have what may be called a general framework indicating every possible combination producible by the given class terms." (John Venn, "On the Diagrammatic and Mechanical Representation of Propositions and Reasonings", 1880)

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

"Deduction is that mode of reasoning which examines the state of things asserted in the premises, forms a diagram of that state of things, perceives in the parts of the diagram relations not explicitly mentioned in the premises, satisfies itself by mental experiments upon the diagram that these relations would always subsist, or at least would do so in a certain proportion of cases, and concludes their necessary, or probable, truth." (Charles S Peirce, "Kinds of Reasoning", cca. 1896)

"Statistics are numerical statements of facts in any department of inquiry, placed in relation to each other; statistical methods are devices for abbreviating and classifying the statements and making clear the relations." (Arthur L Bowley, "An Elementary Manual of Statistics", 1934)

"Although the pie or sector chart ranks very high in popular appeal, it is held in rather low esteem by many specialists in graphic presentation. Since the pie chart possesses more weaknesses perhaps than most graphic forms, it is especially important to observe proper discretion in its construction and application. The pie chart is used to portray component relations. The various sectors of a circle represent component parts of an aggregate or total." (Calvin F Schmid, "Handbook of Graphic Presentation", 1954)

"A system may be specified in either of two ways. In the first, which we shall call a state description, sets of abstract inputs, outputs and states are given, together with the action of the inputs on the states and the assignments of outputs to states. In the second, which we shall call a coordinate description, certain input, output and state variables are given, together with a system of dynamical equations describing the relations among the variables as functions of time. Modern mathematical system theory is formulated in terms of state descriptions, whereas the classical formulation is typically a coordinate description, for example a system of differential equations." (E S Bainbridge, "The Fundamental Duality of System Theory", 1975)

"If you want to dramatize comparisons in relation to the whole. use a pie chart. If you want to add coherence to the narrative, the pie chart also helps because it depicts a whole. If your main interest is in stressing the relationship of one factor to another, use bar charts. If you wish to achieve all these effects. you can use either type of chart. and decide on the basis of which one is more aesthetically or pictorially interesting." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"In order to be easily understood, a display of information must have a logical structure which is appropriate for the user's knowledge and needs, and this structure must be clearly represented visually. In order to indicate structure, it is necessary to be able to eemphasiz, divide and relate items of information. Visual emphasis can be used to indicate a hierarchical relationship between items of information, as in the case of systems of headings and subheadings for example. Visual separation of items can be used to indicate that they are different in kind or are unrelated functionally, and similarly a visual relationship between items will imply that they are of a similar kind or bear some functional relation to one another. This kind of visual 'coding' helps the reader to appreciate the extent and nature of the relationship between items of information, and to adopt an appropriate scanning strategy." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

📊Graphical Representation: Sense-making in Data Visualizations (Part 3: Heuristics)

Graphical Representation Series

 

Consider the following general heuristics in data visualizations (work in progress):

• plan design
• plan page composition
• text
• title, subtitles
• dates 
• refresh, filters applied
• parameters applied
• guidelines/tooltips
• annotation 
• navigation
• main page(s)
• additional views
• drill-through
• zoom in/out
• next/previous page
• landing page
• slicers/selections
• date-related
• date range
• date granularity
• functional
• metric
• comparisons
• categorical
• structural relations
• icons/images
• company logo
• button icons
• background
• pick a theme
• choose a layout and color schema
• use a color palette generator
• use a focused color schema or restricted palette
• use consistent and limited color scheme
• use suggestive icons
• use one source (with similar design)
• use formatting standards
• create a visual hierarchy 
• use placement, size and color for emphasis
• organize content around eye movement pattern
• minimize formatting changes
• 1 font, 2 weights, 4 sizes
• plan the design
• build/use predictable and consistent templates
• e.g. using Figma
• use layered design
• aim for design unity
• define & use formatting standards
• check changes
• GRACEFUL
• group visuals with white space 
• right chart type
• avoid clutter
• consistent & limited color schema
• enhanced readability 
• formatting standard
• unity of design
• layered design
• keep it simple 
• be predictable and consistent 
• focus on the message
• identify the core insights and design around them
• pick suggestive titles/subtitles
• use dynamics subtitles
• align content with the message
• avoid unnecessary complexity
• minimize visual clutter
• remove the unnecessary elements
• round numbers
• limit colors and fonts
• use a restrained color palette (<5 colors)
• stick to 1-2 fonts 
• ensure text is legible without zooming
• aggregate values
• group similar data points to reduce noise
• use statistical methods
• averages, medians, min/max
• categories when detailed granularity isn’t necessary
• highlight what matters 
• e.g. actionable items
• guide attention to key areas
• via annotations, arrows, contrasting colors 
• use conditional formatting
• do not show only the metrics
• give context 
• show trends
• via sparklines and similar visuals
• use familiar visuals
• avoid questionable visuals 
• e.g. pie charts, gauges
• avoid distortions
• preserve proportions
• scale accurately to reflect data values
• avoid exaggerated visuals
• don’t zoom in on axes to dramatize small differences
• use consistent axes
• compare data using the same scale and units across charts
• don't use dual axes or shifting baselines that can mislead viewers
• avoid manipulative scaling
• use zero-baseline on bar charts 
• use logarithmic scales sparingly
• design for usability
• intuitive interaction
• at-a-glance perception
• use contrast for clarity
• use familiar patterns
• use consistent formats the audience already knows
• design with the audience in mind
• analytical vs managerial perspectives (e.g. dashboards)
• use different level of data aggregations
•  in-depth data exploration 
• encourage scrutiny
• give users enough context to assess accuracy
• provide raw values or links to the source
• explain anomalies, outliers or notable trends
• via annotations
• group related items together
• helps identify and focus on patterns and other relationships
• diversify 
• don't use only one chart type
• pick the chart that reflects the best the data in the conrext considered
• show variance 
• absolute vs relative variance
• compare data series
• show contribution to variance
• use familiar encodings
• leverage (known) design patterns
• use intuitive navigation
• synchronize slicers
• use tooltips
• be concise
• use hover effects
• use information buttons
• enhances user interaction and understanding 
• by providing additional context, asking questions
• use the full available surface
• 1080x1920 works usually better 
• keep standards in mind 
• e.g. IBCS
• state the assumptions
• be explicit
• clearly state each assumption 
• instead of leaving it implied
• contextualize assumptions
• explain the assumption
• use evidence, standard practices, or constraints
• state scope and limitations
• mention what the assumption includes and excludes
• tie assumptions to goals & objectives
• helps to clarify what underlying beliefs are shaping the analysis
• helps identify whether the visualization achieves its intended purpose 
• show the data
• be honest (aka preserve integrity)
• avoid distortion, bias, or trickery
• support interpretation
• provide labels, axes, legends
• emphasize what's meaningful
• patterns, trends, outliers, correlations, local/global maxima/minima
• show what's important 
• e.g. facts, relationships, flow, similarities, differences, outliers, unknown
• prioritize and structure the content
• e.g. show first an overview, what's important
• make the invisible visible
• think about what we do not see
• know your (extended) users/audience
• who'll use the content, at what level, for that
• test for readability
• get (early) feedback
• have the content reviewed first
• via peer review, dry run presentation
• tell the story
• know the audience and its needs
• build momentum, expectation
• don't leave the audience to figure it out
• show the facts
• build a narrative
• show data that support it
• arrange the visuals in a logical sequence
• engage the reader
• ask questions that bridge the gaps
• e.g. in knowledge, in presentation's flow
• show the unexpected
• confirm logical deductions

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📊Graphical Representation: Sense-making in Data Visualizations (Part 2: Guidelines)

Graphical Representation Series

 

Consider the following best practices in data visualizations (work in progress):

• avoid poor labeling and annotation practices
• label data points
• considering labeling at least the important number of points
• e.g. starts, ends, local/global minima/minima
• when labels clutter the chart or there's minimal variation
• avoid abbreviations
• unless they are defined clearly upfront, consistent and/or universally understood
• can hinder understanding
• abbreviations should help compress content without losing meaning
• use font types, font sizes, and text orientation that are easy to read
• avoid stylish design that makes content hard to read
• avoid redundant information
• text should never overshadow or distort the actual message or data
• use neutral, precise wording
• avoid the use of pre-attentive attributes 
• aka visual features that our brains process almost instantly
• color
• has identity value: used to distinguish one thing from another
• carries its own connotations
• gives a visual scale of measure
• the use of color doesn’t always help
• hue 
• refers to the dominant color family of a specific color, being processed by the brain based on the different wavelengths of light
• allows to differentiate categories
• use distinct hues to represent different categories
• intensity (aka brightness)
• refers to how strong or weak a color appears
• saturation (aka chroma, intensity) 
• refers to the purity or vividness of a color
• as saturation decreases, the color becomes more muted or washed out
• highly saturated colors have little or no gray in it
• highly desaturated colors are almost gray, with none of the original colors
• use high saturation for important elements like outliers, trends, or alerts
• use low saturation for background elements
• avoid pure colors that are bright and saturated
• drive attention to the respective elements 
• avoid colors that are too similar in tone or saturation
• avoid colors hard to distinguish for color-blind users
• e.g. red-green color blindness
• brown-green, orange-red, blue-purple combinations
• avoid red-green pairings for status indicators 
• e.g. success/error
• e.g. blue-yellow color blindness
• blue-green, yellow-ping, purple-blue
• e.g. total color blindness (aka monochromacy)
• all colors appear as shades of gray
• ⇒ users must rely entirely on contrast, shape, and texture
• use icons, labels, or patterns alongside color
• use tools to test for color issues
• e.g. Color Oracle, WebAIM Contrast Checker
• use colorblind-safe palettes 
• e.g. ColorBrewer or Viridis4
• for sequential or diverging data, use one hue and vary saturation or brightness to show magnitude
• start with all-gray data elements
• use color only when it corresponds to differences in data
• ⇐ helps draw attention to whatever isn’t gray
• dull and neutral colors give a sense of uniformity
• can modify/contradict readers' intuitive response
• choose colors to draw attention, to label, to show relationships 
• form
• shape
• allows to distinguish types of data points and encode information
• well-shaped data has functional and aesthetic character
• complex shapes can become more difficult to be perceived
• size
• attribute used to encode the magnitude or extent of elements 
• should be aligned to its probable use, importance, and amount of detail involved
• larger elements draw more attention
• its encoding should be meaningful
• e.g. magnitudes of deviations from the baseline
• overemphasis can lead to distortions
• choose a size range that is appropriate for the data
• avoid using size to represent nominal or categorical data where there's no inherent order to the sizes
• orientation
• angled or rotated items stand out.
• length/width
• useful in bar charts to show quantity
• avoid stacked bar graphs
• curvature
• curved lines can contrast with straight ones.
• collinearity
• alignment can suggest grouping or flow
• highlighting
• spatial positioning
• 2D position
• placement on axes or grids conveys value 
• 3D position in 2D space
• 
  
• grouping
• proximity implies relationships.
• keep columns, respectively bars close together
• enclosure
• borders or shaded areas signal clusters.
• depth (stereoscopic or shading)
• adds dimensionality
• avoid graphical features that are purely decorative
• aka elements that don't affect understanding, structure or usability
• stylistic embellishments
• borders/frames
• ornamental lines or patterns around content
• background images
• images used for ambiance, not content
• drop shadows and gradients
• enhance depth or style but don’t add meaning.
• icons without function
• decorative icons that don’t represent actions or concepts
• non-informative imagery
• stock photos
• generic visuals that aren’t referenced in the text.
• illustrations
• added for visual interest, not explanation.
• mascots or logos
• when repeated or not tied to specific content.
• layout elements
• spacers
• transparent or blank images used to control layout
• leave the right amount of 'white' space between chart elements
• custom bullets or list markers
• designed for flair, not clarity
• visual separators
• lines or shapes that divide sections without conveying hierarchy or meaning
• avoid bias
• sampling bias
• showing data that doesn’t represent the full population
• avoid cherry-picking data
• aka selecting only the data that support a particular viewpoint while ignoring others that might contradict it
• enable users to look at both sets of data and contrast them
• enable users to navigate the data
• avoid survivor bias
• aka focusing only on the data that 'survived' a process and ignoring the data that didn’t
• use representative data
• aka the dataset includes all relevant groups
• check for collection bias
• avoid data that only comes from one source 
• avoid data that excludes key demographics
• cognitive bias
• mental shortcut that sometimes affect interpretation
• incl. confirmation bias, framing bias, pattern bias
• balance visual hierarchies
• don’t make one group look more important by overemphasizing it
• show uncertainty
• by including confidence intervals or error bars to reflect variability
• separate comparisons
• when comparing groups, use adjacent charts rather than combining them into one that implies a hierarchy
• e.g. ethnicities, region
• visual bias
• design choices that unintentionally (or intentionally) distort meaning
• respectively how viewers interpret the data
• avoid manipulating axes 
• by truncating y-axis
• exaggerates differences
• by changing scale types
• linear vs. logarithmic
• a log scale compresses large values and expands small ones, which can flatten exponential growth or make small changes seem more significant
• uneven intervals
• using inconsistent spacing between tick marks can distort trends
• by zooming in/out
• adjusting the axis to focus on a specific range can highlight or hide variability and eventually obscure the bigger picture
• by using dual axes
• if the scales differ too much, it can falsely imply correlation or exaggerate relationships 
• by distorting the aspect ration
• stretching or compressing the chart area can visually amplify or flatten trends
• e.g. a steep slope might look flat if the x-axis is stretched
• avoid inconsistent scales
• label axes clearly
• explain scale choices
• avoid overemphasis 
• avoid unnecessary repetition 
• e.g. of the same graph, of content
• avoid focusing on outliers, (short-term) trends
• avoid truncating axes, exaggerating scales
• avoid manipulating the visual hierarchy 
• avoid color bias
• bright colors draw attention unfairly
• avoid overplotting 
• too much data obscures patterns
• avoid clutter
• creates cognitive friction
• users struggle to focus on what matters because their attention is pulled in too many directions
• is about design excess
• avoid unnecessary or distracting elements 
• they don’t contribute to understanding the data
• avoid overloading 
• attempting to show too much data at once
• is about data excess
• overwhelms readers' processing capacity, making it hard to extract insights or spot patterns
• algorithmic bias 
• the use of ML or other data processing techniques can reinforce certain aspects (e.g. social inequalities, stereotypes)
• visualize uncertainty
• include error bars, confidence intervals, and notes on limitations
• audit data and algorithms
• look for bias in inputs, model assumptions and outputs
• intergroup bias
• charts tend to reflect or reinforce societal biases
• e.g. racial or gender disparities
• use thoughtful ordering, inclusive labeling
• avoid deficit-based comparisons
• avoid overcomplicating the visualizations 
• e.g. by including too much data, details, other elements
• avoid comparisons across varying dimensions 
• e.g. (two) circles of different radius, bar charts of different height, column charts of different length, 
• don't make users compare angles, areas, volumes

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📊Graphical Representation: Sense-making in Data Visualizations (Part 1: An Introduction)

Graphical Representation Series

Introduction

Creating simple charts or more complex data visualizations may appear trivial for many, though their authors shouldn't forget that readers have different backgrounds, degrees of literacy, many of them not being maybe able to make sense of graphical displays, at least not without some help.

Beginners start with a limited experience and build upon it, then, on the road to mastery, they get acquainted with the many possibilities, a deeper sense is achieved and the choices become a few. Independently of one's experience, there are seldom 'yes' and 'no' answers for the various choices, but everything is a matter of degree that varies with one's experience, available time, audience's expectations, and many more aspects might be considered in time.  

The following questions are intended to expand, respectively narrow down our choices when dealing with data visualizations from a data professional's perspective. The questions are based mainly on [1] though they were extended to include a broader perspective. 

General Questions

Where does the data come from? Is the source reliable, representative (for the whole population in scope)? Is the data source certified? Are yhe data actual? 

Are there better (usable) sources? What's the effort to consider them? Does the data overlap? To what degree? Are there any benefits in merging the data? How much this changes the overall picture? Are the changes (in trends) explainable? 

Was the data collected? How, from where, and using what method? [1] What methodology/approach was used?

What's the dataset about? Can one recognize the data, the (data) entities, respectively the structures behind? How big is the fact table (in terms of rows and columns)? How many dimensions are in scope?

What transformations, calculations or modifications have been applied? What was left out and what's the overall impact?

Any significant assumptions were made? [1] Were the assumptions clearly stated? Are they entitled? Is it more to them? 

Were any transformation applied? Do the transformations change any data characteristics? Were they adequately documented/explained? Do they make sense? Was it something important left out? What's the overall impact?

What criteria were used to include/exclude data from the display? [1] Are the criteria adequately explained/documented? Do they make sense?

Are similar data publicly available? Is it (freely) accessible/usable? To what degree? How much do the datasets overlap? Is there any benefit to analyze/use the respective data? Are the characteristics comparable? To what degree?

Dataviz Questions

What's the title/subtitle of the chart? Is it meaningful for the readers? Does the title reflect the data, respectively the findings adequately? Can it be better formulated? Is it an eye-catcher? Does it meet the expectations? 

What data is shown? Of what type? At what level is the data aggregated? 

What chart (type) is being used? [1] Are the readers familiar with the chart type? Does it needs further introduction/clarifications? Are there better means to represent the data? Does the chart offer the appropriate perspective? Does it make sense to offer different (complementary) perspective(s)? To what degree other perspectives help?

What items of data do the marks represent? What value associations do the attributes represent? [1] Are the marks visible? Are the marks adequately presented (e.g. due to missing data)? 

What range of values are displayed? [1] What approximation the values support? To what degree can the values be rounded without losing meaning?

Is the data categorical, ordinal or continuous? 

Are the axes property chosen/displayed/labeled? Is the scale properly chosen (linear, semilogarithmic, logarithmic), respectively displayed? Do they emphasize, diminish, distort, simplify, or clutter the information? 

What features (shapes, patterns, differences or connections) are observable, interesting or vital for understanding the chart? [1] 

Where are the largest, mid-sized and smallest values? (aka ‘stepped magnitude’ judgements). [1] 

Where lie the most/least values? Where is the average or normal? (aka ‘global comparison’ judgements)” [1] How are the values distributed? Are there any outliers present? Are they explainable? 

What features are expected or unexpected? [1] To what degree are they unexpected?  

What features are important given the subject? [1] 

What shapes and patterns strike readers as being semantically aligned with the subject? [1] 

What is the overall feeling when looking at the final result? Is the chart overcrowded? Can anything be left out/included? 

What colors were used? [1] Are the colors adequately chosen, respectively meaningful? Do they follow the general recommendations?  

What colors, patterns, forms do readers see first? What impressions come next, respectively last longer?  

Are the various elements adequately/intuitively positioned/distinguishable? What's the degree of overlapping/proximity? Do the elements respect an intuitive hierarchy? Do they match readers' expectations, respectively the best practices in scope? Are the deviations entitled? 

Is the space properly used? To what degree? Are there major gaps? 

Know Your Audience

What audience targets the visualization? Which are its characteristics (level of experience with data visualizations; authors, experts or casual attendees)? Are there any accidental attendees? How likely is the audience to pay attention? 

What is audience’s relationship with the subject matter? What knowledge do they have or, conversely, lack about the subject? What assistance might they need to interpret the meaning of the subject? Do they have the capacity to comprehend what it means to them? [1]

Why do the audience wants/needs to understand the topic? Are they familiar, respectively actively interested or more passive? Is it able to grasp the intended meaning? [1] To what degree? What kind of challenges might be involved, of what nature?

What is their motivation? Do they have a direct, expressed need or are they more passive and indifferent? Is it needed a way to persuade them or even seduce them to engage? [1] Can this be done without distorting the data and its meaning(s)?

What are their visualization literacy skill set? Do they require assistance perceiving the chart(s)? Are they sufficiently comfortable with operating features of interactivity? Do they have any visual accessibility issues (e.g. red–green color blindness)? Do they need to be (re)factored into the design? [1]

Reflections

What has been learnt? Has it reinforced or challenged existing knowledge? [1] Was new knowledge gained? How valuable is this knowledge? Can it be reused? In which contexts? 

Do the findings meet one's expectations? To what degree? Were the expectations entitled? On what basis? What's missing? What's gaps' relevance? 

What feelings have been stirred? Has the experience had an impact emotionally? [1] To what degree? Is the impact positive/negative? Is the reaction entitled/explainable? Are there any factors that distorted the reactions? Are they explainable? Do they make sense? 

What does one do with this understanding? Is it just knowledge acquired or something to inspire action (e.g. making a decision or motivating a change in behavior)? [1] How relevant/valuable is the information for us? Can it be used/misused? To what degree? 

Are the data and its representation trustworthy? [1] To what degree?

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References:
[1] Andy Kirk, "Data Visualisation: A Handbook for Data Driven Design" 2nd Ed., 2019

📊Graphical Representation: Graphics We Live By (Part XI: Comparisons Between Data Series)

Graphical Representation Series

Over the past 10-20 years it became so easy to create data visualizations just by dropping some of the data available into a tool like Excel and providing a visual depiction of it with just a few clicks. In many cases, the first draft, typically provided by default in the tool used, doesn't even need further work as the objective was reached, while in others the creator must have a minimum skillset for making the visualization useful, appealing, or whatever quality is a final requirement for the work in scope. However, the audience might judge the visualization(s) from different perspectives, and there can be a broad audience with different skills in reading, evaluating and understanding the work.

There are many depictions on the web resembling the one below, taken from a LinkedIn post:

Example Chart - Boing vs. Airbus

Even if the visualization is not perfect, it does a fair job in representing the data. Improvements can be made in the areas of labels, the title and positioning of elements, and the color palette used. At least these were the improvements made in the original post. It must be differentiated also between the environment in which the charts are made available, the print format having different characteristics than the ones in business setups. Unfortunately, the requirements of the two are widely confused, probably also because of the overlapping of the mediums used. 

Probably, it's a good idea to always start with the row data (or summaries of it) when the result consists of only a few data points that can be easily displayed in a table like the one below (the feature to round the decimals for integer values should be available soon in Power BI):

Summary Table

Of course, one can calculate more meaningful values like percentages from the total, standard deviations and other values that offer more perspectives into the data. Even if the values adequately reflect the reality, the reader can but wonder about the local and global minimal/maximal values, without talking much about the meaning of data points, which is easily identifiable in a chart. At least in the case of small data sets, using a table in combination with a chart can provide a more complete perspective and different ways of analyzing the data, especially when the navigation is interactive. 

Column and bar charts do a fair job in comparing values over time, though they do use a lot of ink in the process (see D). While they make it easy to compare neighboring values, the rectangles used tend to occupy a lot of space when they are made too wide or too high to cover the empty space within the display (e.g. when just a few values are displayed, space being wasted in the process). As the main downside, it takes a lot of scanning until the reader identifies the overall trends, and the further away the bars are from each other, the more difficult it becomes to do comparisons. 

In theory, line charts are more efficient in representing the above data points, because the marks are usually small and the line thin enough to provide a better data-ink ratio, while one can see a lot at a glance. In Power BI the creator can use different types of interpolation: linear (A), step (B) or smooth (C). In many cases, it might be a good idea to use a linear interpolation, though when there are no or minimal overlapping, it might be worthwhile to explore the other types if interpolation too (and further request feedback from the users):

Linear, Step and Smooth Line Charts

The nearness of values from different series can raise difficulties in identifying adequately the points, respectively delimiting the lines (see B).When the density of values allows it, it makes sense also to include the averages for each data series to reflect the distance between the two data sets. Unfortunately, the chart can get crowded if further data series or summaries are added to the cart(s). 

If the column chart (E) is close to the redesigned chart provided in the original redesign, the other alternatives can provide upon case more value. Stacked column charts (D) allow also to compare the overall quantity by month, area charts (F) tend to use even more color than needed, while water charts (G) allow to compare the difference between data points per time unit. Tornado charts (H) are a variation of bar charts, allowing easier comparing of the size of the bars, while ribbon charts (I) show well the stacking values. 

Alternatives to Line Charts

One should consider changing the subtitle(s) slightly to reflect the chart type when the patterns shown imply a shift in attention or meaning. Upon case, more that one of the above charts can be used within the same report when two or more perspectives are important. Using a complementary perspective can facilitate data's understanding or of identifying certain patterns that aren't easily identifiable otherwise. 

In general, the graphics creators try to use various representational means of facilitating a data set's understanding, though seldom only two series or a small subset of dimensions provide a complete description. The value of data comes when multiple perspectives are combined. Frankly, the same can be said about the above data series. Yes, there are important differences between the two series, though how do the numbers compare when one looks at the bigger picture, especially when broken down on element types (e.g. airplane size). How about plan vs. actual values, how long does it take more for production or other processes? It's one of a visualization's goals to improve the questions posed, but how efficient are visualizations that barely scratch the surface?

In what concerns the code, the following scripts can be used to prepare the data:

-- Power Query script (Boeing vs Airbus)
= let
    Source = let
    Source = #table({"Sorting", "Month Name", "Serial Date", "Boeing Deliveries", "Airbus Deliveries"},
    {
        {1, "Oct", #date(2023, 10, 31), 30, 50},
        {2, "Nov", #date(2023, 11, 30), 40, 40},
        {3, "Dec", #date(2023, 12, 31), 40, 110},
        {4, "Jan", #date(2024, 1, 31), 20, 30},
        {5, "Feb", #date(2024, 2, 29), 30, 40},  // Leap year adjustment
        {6, "Mar", #date(2024, 3, 31), 30, 60},
        {7, "Apr", #date(2024, 4, 30), 40, 60},
        {8, "May", #date(2024, 5, 31), 40, 50},
        {9, "Jun", #date(2024, 6, 30), 50, 80},
        {10, "Jul", #date(2024, 7, 31), 40, 90},
        {11, "Aug", #date(2024, 8, 31), 40, 50},
        {12, "Sep", #date(2024, 9, 30), 30, 50}
    }
    ),
    #"Changed Types" = Table.TransformColumnTypes(Source, {{"Sorting", Int64.Type}, {"Serial Date", type date}, {"Boeing Deliveries", Int64.Type}, {"Airbus Deliveries", Int64.Type}})
in
    #"Changed Types"
in
    Source

It can be useful to create the labels for the charts dynamically:

-- DAX code for labels
MaxDate = Format(Max('Boeing vs Airbus'[Serial Date]),"MMM-YYYY")
MinDate = FORMAT (Min('Boeing vs Airbus'[Serial Date]),"MMM-YYYY")
MinMaxDate = [MinDate] & " to " & [MaxDate]
Title Boing Airbus = "Boing and Airbus Deliveries " & [MinMaxDate]

Happy coding!

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📊Graphical Representation: Graphics We Live By (Part X: Pie and Donut Charts in Power BI and Excel)

Graphical Representation Series

Pie charts are loved and hated by many altogether, and there are many entitled reasons to use them and avoid them, though the most important criteria to evaluate them is whether they do the intended job in an acceptable manner, especially when compared to other representational means. The most important aspect they depict is the part to whole ratio, which even if can be depicted by other graphical tools, few tools are efficient in representing it. 

The pie chart works well as a visualization tool when it has only 3-5 values that are easily recognizable in the visualization, however as soon the size or the number of pieces vary considerably, the more difficult it is to visualize and interpret them, in case their representation has more negative than positive effects. There are many topics that form something like a long tail - the portion of the distribution having many occurrences far from the head or beginning. Displaying the items from the long tail together with the other components together can totally obscure the distribution of the items from the long tail as they become unrecognizable in the diagram. 

One approach to handle this is to group all the items from the long tail together under a piece (e.g. Other) and use a second form of representation to display them separately. For example,  Microsoft Excel offers a way to zoom in the section of a pie chart with small percentages by displaying them in a second pie chart (pie of pie) or bar chart (bar of pie), something like a "zoom in" perspective (see image below). Unfortunately, the feature seems to limit itself only to small percentages, and thus can't be used currently to offer a broader perspective. Ideally, it would be useful to zoom in on any piece of the pie, especially when the items are categorized as a hierarchy with two or even more levels. 

Unfortunately, even modern visualization tools offer limited features in displaying this kind of perspective into a flexible unitary visualization, and thus users are forced to use their creativity in providing proper solutions. In the below example the "Renewables" piece of pie is further broken down into several components of a full pie, an ensemble supposed to function as a single form of representation. With a bit of effort, the reader probably will understand the meaning behind the two pie charts, however the encoding of colors and other elements used are suboptimal in the decoding process. 

Pie Charts - Original Solution

In the above example, the arrow may suggest that in between the two donut charts exists a relationship, reflected also in the description provided, however the readers may still have difficulties in correctly interpreting the diagrams, especially when there's some kind of overlapping or other type of implied or unimplied resemblance. If the colors overlap or have other similarities, are they intentional? If the circles have the same size, does this observed resemblance have a meaning? The reader shouldn't bother himself with this type of questions, but see the resemblance and the meaning of the various elements with a minimum of effort while decoding a chart's elements. Of course, when the meaning is not clear, some guidance should be ideally provided!

Unfortunately, Power BI doesn't seem to have a similar visual like the one from Excel yet, however with a bit of effort one can obtain similar results, even if there are other minor or important limitations. For example, the lines between the two pie charts can't be drawn, so one is forced to use other encodings to show that there's a connection between the Renewable slice and the small pie chart. Moreover, the ensemble thus created isn't treated unitary and handled accordingly. Frankly, the maturity of a graphical representation environment can and should be judged also from this perspective!

The below representation built in Power BI uses a few tricks to display two pie charts together. The smaller pie chart representing the breakdown and pieces' colors are variations of parent's color, attempting to show that there's a relationship between the slice from the first chart and the pie chart with the details. Unfortunately, it wasn't possible to use similar lines like in Excel to show the relation between the two sections. 

Pie of Pie in Power BI

Instead of a pie chart, one can use a donut, like in the original representation. Even if the donut uses a smaller area for representation, in theory the pie chart offers a better basis for comparisons, at least in theory. Stacked column charts can be used as well (see C), however one loses the certainty that the pieces must add up to 100%. Further limitations can appear when one wants to achieve more with the visualizations.

Custom charts can be used as well. The pie chart coming from xViz (see D) allows to increase the size of a pie piece by using another radius, technique which could be used to highlight the piece represented in the second chart. Frankly, sunburst diagrams (see E) are better at representing the parent to child proportions, where the same color encoding has been used. Unfortunately, the more information is shown, the more loaded the visualization seems to be.

Pie of Pie Alternatives in Power BI I

A treemap can prove to be a better representation alternative because it encodes proportions in a unitary way, much like pie charts do, though it takes more space if one wants to make the labels visible. Radial charts (see G) and Aster plots (see I) can be occasionally better choices, especially because they use less space as they display only the main categories. A second diagram chart can be used to display the subcategories, much like in A and B. Sankey charts (see H) can be used as well, even if they don't allow representing any quantitative values unless one encodes them directly in the labels. 

Pie of Pie Alternatives in Power BI II

When one dives into the world of diagrams and goes behind the still limited representational choices provided by the standard tools, one can be surprised by the additional representational choices. However, their appropriateness should be considered against readers' skillset to read and interpret them! Frankly, the alternatives considered above could be a better choice when they will reach a representational maturity. 

Many thanks to Christopher Chin, who in his weekly post on data visualization blunders, suggested the examples used as basis for this post (see [1])!

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References:

[1] LinkedIn (2024) Christopher Chin's post (link)