📉Graphical Representation: Curves (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)

"A more important case is where the divisions are laid off to a logarithmic scale. Paper ready ruled in this way may now be had from dealers in mathematical instruments and is valuable for many purposes. On it many problems which would have to be solved by tediously drawn curves, may be worked with ease by straight lines." (John B Peddle, "The Construction of Graphical Charts", 1910)

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

"For a curve the vertical scale, whenever practicable, should be so selected that the zero line will appear on the diagram. [...] If the zero line of the vertical scale will not normally appear on the curve diagram, the zero line should be shown by the use of a horizontal break in the diagram." (Joint Committee on Standards for Graphic Presentation, "Publications of the American Statistical Association" Vol.14" (112), 1915)

"Co-ordinate ruling does not appear prominently on most original charts because the ruling is usually printed in some color of ink distinct from the curve itself. When, however, a chart is reproduced in a line engraving the co-ordinate lines come out the same color as the curve or other important data, and there may be too little contrast to assist the reader." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"Graphic representation by means of charts depends upon the super-position of special lines or curves upon base lines drawn or ruled in a standard manner. For the economic construction of these charts as well as their correct use it is necessary that the standard rulings be correctly designed." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"It should be a strict rule for all kinds of curve plotting that the horizontal scale must be used. for the independent variable and the vertical scale for the dependent variable. When the curves are plotted by this rule the reader can instantly select a set of conditions from the horizontal scale and read the information from the vertical scale. If there were no rule relating to the arrangement of scales for the independent and dependent variables, the reader would never be able to tell whether he should approach a chart from the vertical scale and read the information from the horizontal scale, or the reverse." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

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

"The practice of drawing several curves on the same sheet is not to be commended except in cases where the curves will not intersect. A crowded chart on which the curves frequently intersect resembles a Chinese puzzle more than a graphic record, and a report submitted in figures is to be preferred to a chart of this kind. Even when the curves do not intersect, they should be made in different colors in order that they may be readily distinguished, one from the other." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

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

"A graph is a pictorial representation or statement of a series of values all drawn to scale. It gives a mental picture of the results of statistical examination in one case while in another it enables calculations to be made by drawing straight lines or it indicates a change in quantity together with the rate of that change. A graph then is a picture representing some happenings and so designed as to bring out all points of significance in connection with those happenings. When the curve has been plotted delineating these happenings a general inspection of it shows the essential character of the table or formula from which it was derived." (William C Marshall, "Graphical methods for schools, colleges, statisticians, engineers and executives", 1921)

"A curve cannot, however, always be used in the place of a bar-chart, for the line which connects the various points implies that the data itself can be considered connected. Much data can not be so considered. A careful inspection of the data will soon show whether it is connected or not, for the stubs of connected data always form a variable." (Karl G Karsten, "Charts and Graphs", 1925)

"Multiple curves are far better than multiple bar charts. A number of curves wiggling across the page at the tops of invisible bars are eminently more satisfactory than actual bars interlarded. In the first place, comparison of several series of data is greatly facilitated in curves - because each set has been condensed and simplified into a single line. There is no difficulty in comparing values of each series with each other. In the second place, such a comparison is more accurate in curves because all similar points on various sets or series have been brought together upon a single vertical line." (Karl G Karsten, "Charts and Graphs", 1925)

"There is a magic in graphs. The profile of a curve reveals in a flash a whole situation - the life history of an epidemic, a panic, or an era of prosperity. The curve informs the mind, awakens the imagination, convinces." (Henry D Hubbard [in William Brinton's "Graphic Presentation", 1939])

"[….] double-scale charts are likely to be misleading unless the two zero values coincide" (either on or off the chart). To insure an accurate comparison of growth the scale intervals should be so chosen that both curves meet at some point. This treatment produces the effect of percentage relatives or simple index numbers with the point of juncture serving as the base point. The principal advantage of this form of presentation is that it is a short-cut method of comparing the relative change of two or more series without computation. It is especially useful for bringing together series that either vary widely in magnitude or are measured in different units and hence cannot be compared conveniently on a chart having only one absolute-amount scale. In general, the double scale treatment should not be used for presenting growth comparisons to the general reader." (Kenneth W Haemer, "Double Scales Are Dangerous", The American Statistician Vol. 2" (3) , 1948)

"[…] many readers are confused by the presence of two scales, and either use the wrong one or simply disregard both. Also, the general reader has the disconcerting habit of believing that because one curve is higher than another, it is also larger in magnitude. This leads to all sorts of misconceptions." (Kenneth W Haemer, "Double Scales Are Dangerous", The American Statistician Vol. 2" (3) , 1948)

"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)

"If a chart contains a number of series which vary widely in individual magnitude, optical distortion may result from the necessarily sharp changes in the angle of the curves. The space between steeply rising or falling curves always appears narrower than the vertical distance between the plotting points." (Rufus R Lutz, "Graphic Presentation Simplified", 1949)

"The grid lines should be lighter than the curves, with the base line somewhat heavier than the others. All vertical lines should be of equal weight, unless the time scale is subdivided in quarters or other time periods, indicated by heavier rules. Very wide base lines, sometimes employed for pictorial effect, distort the graphic impression by making the base line the most prominent feature of the chart." (Rufus R Lutz, "Graphic Presentation Simplified", 1949)

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

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

"The histogram, with its columns of area proportional to number, like the bar graph, is one of the most classical of statistical graphs. Its combination with a fitted bell-shaped curve has been common since the days when the Gaussian curve entered statistics. Yet as a graphical technique it really performs quite poorly. Who is there among us who can look at a histogram-fitted Gaussian combination and tell us, reliably, whether the fit is excellent, neutral, or poor? Who can tell us, when the fit is poor, of what the poorness consists? Yet these are just the sort of questions that a good graphical technique should answer at least approximately." (John W Tukey, "The Future of Processes of Data Analysis", 1965)

"Probably one of the most common misuses (intentional or otherwise) of a graph is the choice of the wrong scale - wrong, that is, from the standpoint of accurate representation of the facts. Even though not deliberate, selection of a scale that magnifies or reduces - even distorts - the appearance of a curve can mislead the viewer." (Peter H Selby, "Interpreting Graphs and Tables", 1976)

"As a general rule, plotted points and graph lines should be given more 'weight' than the axes. In this way the 'meat' will be easily distinguishable from the 'bones'. Furthermore, an illustration composed of lines of unequal weights is always more attractive than one in which all the lines are of uniform thickness. It may not always be possible to emphasise the data in this way however. In a scattergram, for example, the more plotted points there are, the smaller they may need to be and this will give them a lighter appearance. Similarly, the more curves there are on a graph, the thinner the lines may need to be. In both cases, the axes may look better if they are drawn with a somewhat bolder line so that they are easily distinguishable from the data." (Linda Reynolds & Doig Simmonds, "Presentation of Data in Science" 4th Ed, 1984)

"Exploratory regression methods attempt to reveal unexpected patterns, so they are ideal for a first look at the data. Unlike other regression techniques, they do not require that we specify a particular model beforehand. Thus exploratory techniques warn against mistakenly fitting a linear model when the relation is curved, a waxing curve when the relation is S-shaped, and so forth." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"Skewness is a measure of symmetry. For example, it's zero for the bell-shaped normal curve, which is perfectly symmetric about its mean. Kurtosis is a measure of the peakedness, or fat-tailedness, of a distribution. Thus, it measures the likelihood of extreme values." (John L Casti, "Reality Rules: Picturing the world in mathematics", 1992)

"As a general rule, the fewer the time intervals used in the averaging process, the more closely the moving average curve resembles the curve of the actual data. Conversely, the greater the number of intervals, the smoother the moving average curve. […] Moving average curves tend to have a delayed reaction to changes." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"As a general rule, the fewer the time intervals used in the averaging process, the more closely the moving average curve resembles the curve of the actual data. Conversely, the greater the number of intervals, the smoother the moving average curve. […] Moving average curves tend to have a delayed reaction to changes." (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)

"When approximations are all that are needed, stacked area graphs are usually adequate. When accuracy is desired, this type of graph is generally not used, particularly when the values fluctuate significantly and/or the slopes of the curves are steep." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"It is important to pay heed to the following detail: a disadvantage of logarithmic diagrams is that a graphical integration is not possible, i.e., the area under the curve" (the integral) is of no relevance." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Sometimes bar charts are avoided because they are common. This is a mistake. Rather, bar charts should be leveraged because they are common, as this means less of a learning curve for your audience." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"With time series though, there is absolutely no substitute for plotting. The pertinent pattern might end up being a sharp spike followed by a gentle taper down. Or, maybe there are weird plateaus. There could be noisy spikes that have to be filtered out. A good way to look at it is this: means and standard deviations are based on the naïve assumption that data follows pretty bell curves, but there is no corresponding 'default' assumption for time series data" (at least, not one that works well with any frequency), so you always have to look at the data to get a sense of what’s normal. [...] Along the lines of figuring out what patterns to expect, when you are exploring time series data, it is immensely useful to be able to zoom in and out." (Field Cady, "The Data Science Handbook", 2017)

"Skewed data means data that is shifted in one direction or the other. Skewness can cause machine learning models to underperform. Many machine learning models assume normally distributed data or data structures to follow the Gaussian structure. Any deviation from the assumed Gaussian structure, which is the popular bell curve, can affect model performance. A very effective area where we can apply feature engineering is by looking at the skewness of data and then correcting the skewness through normalization of the data." (Anthony So et al, "The Data Science Workshop" 2nd Ed., 2020)

"Standard graphs, like bar and line charts, are so common because they are perceptually more accurate, familiar to people, and easy to create. Nonstandard graphs - those that use circles or curves, for instance - may not allow the reader to most accurately perceive the exact data values. But perceptual accuracy is not always the goal. And sometimes it's not a goal at all. Spurring readers to engage with a graph is sometimes just as important. Sometimes, it's more important. And nonstandard chart types may do just that. In some cases, nonstandard graphs may help show underlying patterns and trends in better ways that standard graphs. In other cases, the fact that these nonstandard graphs are different may make them more engaging, which we may sometimes need to first attract attention to the visualization."  (Jonathan Schwabish, "Better Data Visualizations: A guide for scholars, researchers, and wonks", 2021)

📉Graphical Representation: Accuracy (Just the Quotes)

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

"In fitting an equation to a given set of observations the first step is to draw through the plotted points a smooth curve. If the experimental work has been carefully and accurately done the curve may be made to pass through, or close to, almost all the points. If not, the curve must be drawn in such a way as to represent a good probable average; that is, so as to lea:ve about an equal number of points at about equal distances on either side of it, these distances, of course, being kept as small as possible. Such a curve is assumed to represent the most probable values of the observations, and we then attempt to get its equation." (John B Peddle, "The Construction of Graphical Charts", 1910)

"In getting an algebraic expression to show the relations between the components of a given set of data there may be two entirely distinct objects in view, one being to determine the physical law controlling the results and the other to get a mathematical expression, which may or may not have a physical basis, but which will enable us to calculate in a more or less accurate manner other results of a nature similar to those of the observations." (John B Peddle, "The Construction of Graphical Charts", 1910)

"In all chart-making, the material to be shown must be accurately compiled before it can be charted. For an understanding of the classification chart, we must delve somewhat into the mysteries of the various methods of classification and indexing. The art of classifying calls into play the power of visualizing a 'whole' together with all its 'parts'. Even in the most exact science, it is not always easy to break up a whole into a complete set of the distinct, mutually exclusive parts which together exactly compose it." (Karl G Karsten, "Charts and Graphs", 1925)

"In short, the rule that no more dimensions or axes should be used in the chart than the data calls for, is fundamental. Violate this rule and you bring down upon your head a host of penalties. In the first place, you complicate your computing processes, or else achieve a grossly deceptive chart. If your chart becomes deceptive, it has defeated its purpose, which was to represent accurately. Unless, of course, you intended to deceive, in which case we are through with you and leave you to Mark Twain’s mercies. If you make your chart accurate, at the cost of considerable square or cube root calculating, you still have no hope, for the chart is not clear; your reader is more than likely to misunderstand it. Confusion, inaccuracy and deception always lie in wait for you down the path departing from the principle we have discussed - and one of them is sure to catch you." (Karl G Karsten, "Charts and Graphs", 1925)

"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)

"Of course increased bias does not necessarily imply less overall accuracy. The reasoning, however, is that the mechanism leading to bias might well lead to other types of inaccuracy as well." (William S Cleveland & Robert McGill, "Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods", Journal of the American Statistical Association Vol. 79(387), 1984)

"The aim of good data graphics is to display data accurately and clearly. Let us use this definition as a starting point for categorizing methods of bad data display. The definition has three parts. These are (a) showing data, (b) showing data accurately, and (c) showing data clearly." (Howard Wainer, "How to Display Data Badly", The American Statistician Vol. 38(2), 1984)

"One must be careful not to fall into a conceptual trap by adopting accuracy as a criterion. We are not saying that the primary purpose of a graph is to convey numbers with as many decimal places as possible. […] The power of a graph is its ability to enable one to take in the quantitative information, organize it, and see patterns and structure not readily revealed by other means of studying the data." (William S Cleveland & Robert McGill, "Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods", Journal of the American Statistical Association Vol. 79(387), 1984)

"For every rule in data visualization, there is a scenario where that rule should be broken. This means that choosing the best chart or the best design is always a trade-off between several conflicting goals. Our imperfect perception means that data visualization has a larger subjective dimension than a data table. Sometimes we only need this subjective, impressionist dimension and other times we need to translate it into hard figures. Striving for accuracy is important, but it’s more important to provide those insights that only a visual display can reveal." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

📉Graphical Representation: Fluctuations (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)

"In any chart where index numbers are used the greatest care should be taken to select as unity a set of conditions thoroughly typical and representative. It is frequently best to take as unity the average of a series of years immediately preceding the years for which a study is to be made. The series of years averaged to represent unity should, if possible, be so selected that they will include one full cycle or wave of fluctuation. If one complete cycle involves too many years, the years selected as unity should be taken in equal number on either side of a year which represents most nearly the normal condition." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"Under certain conditions, however, the ordinary form of graphic chart is slightly misleading. It will be conceded that its true function is to portray comparative fluctuations. This result is practically secured when the factors or quantities compared are nearly of the same value or volume, but analysis will show that this is not accomplished when the amounts compared differ greatly in value or volume. [...] The same criticism applies to charts which employ or more scales for various curve. If the different scale are in proper proportion, the result is the same as with one scale, but when two or more scales are used which are not proportional an indication may be given with respect to comparative fluctuations which is absolutely false." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"When dealing with very large quantities it is not always practicable to use a scale which starts at zero, and is carried up by even steps to a figure representing the highest peak on the curve. Such a chart would either be too large for convenient handling, or else the scale would have to be condensed so that only very large fluctuations would be indicated on the curve. In a ease of this kind the best practice is to start the at zero, and just above this point draw a wavy line across the sheet to indicate that the scale is broken at this point. This line can be very easily drawn with an ordinary serrated edge ruler as used by many accountants. The scale starts again on the upper side of the wavy line at a figure a little lower than the lowest point on the curve, and is carried up by even steps to a figure a little above the highest point to be shown on the curve." (Allan C Haskell, "How to Make and Use Graphic Charts", 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)

"In short, the scales on which a curve is drawn can affect very much our impressions of the data by magnifying or minimizing the apparent movements of the curve itself. Of course, this does not mean that the relative height from the base-line of the various points on the curve have been altered. If you have been careful to show the base-line always, the base-line itself will approach nearer to the curve as the vertical scale is reduced and the wiggles are flattened out, and will recede farther from the curve as the vertical scale is enlarged and the wiggles are exaggerated. But it means that the oscillation or fluctuation of the curve will have been made to appear more violent or milder according as either of the scales is changed. And it therefore behooves us to give serious thought to the matter of scales before’ we determine upon them finally for any particular chart. As a matter of fact, we may have to try out several combinations of scales before we find one which gives just the right amount of emphasis to curve fluctuations to suit us." (Karl G Karsten, "Charts and Graphs", 1925)

"This practice of omitting the zero line is all too common, but it is not for that reason excusable. The amputated chart is a deceptive one, tempting the average reader to compare the heights of points on the curve from the false bottom of the amputated chart-field, rather than from the true zero line, far below and invisible. A curve-chart without a zero line is in general no whit less of a printed lie, than a vertical bar-chart in which the lower part of the bars themselves are cut away. The representation of comparative sizes has been distorted and the fluctuations (changes in value) exaggerated." (Karl G Karsten, "Charts and Graphs", 1925)

"A connected graph is appropriate when the time series is smooth, so that perceiving individual values is not important. A vertical line graph is appropriate when it is important to see individual values, when we need to see short-term fluctuations, and when the time series has a large number of values; the use of vertical lines allows us to pack the series tightly along the horizontal axis. The vertical line graph, however, usually works best when the vertical lines emanate from a horizontal line through the center of the data and when there are no long-term trends in the data." (William S Cleveland, "The Elements of Graphing Data", 1985)

📉Graphical Representation: Trends (Just the Quotes)

"Wherever unusual peaks or valleys occur on a curve it is a good plan to mark these points with a small figure inside a circle. This figure should refer to a note on the back of the chart explaining the reason for the unusual condition. It is not always sufficient to show that a certain item is unusually high or low; the executive will want to know why it is that way." (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)

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

"In line charts with an arithmetic scale, it is essential to set the base line at zero in order that the correct perspective of the general movement may not be lost. Breaking or leaving off part of the scale leads to misinterpretation, because the trend then shows a disproportionate degree of variation in movement." (Mary E Spear, "Charting Statistics", 1952)

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

"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)

"Since bars represent magnitude by their length, the zero line must be shown and the arithmetic scale must not be broken. Occasionally an excessively long bar in a series of bars may be broken off at the end, and the amount involved shown directly beyond it, without distorting the general trend of the other bars, but this practice applies solely when only one bar exceeds the scale." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"Charts not only tell what was, they tell what is; and a trend from was to is" (projected linearly into the will be) contains better percentages than clumsy guessing." (Robert A Levy, "The Relative Strength Concept of Common Stock Forecasting", 1968)

"In certain respects, line graphs are uniquely applicable to particular graphic requirements for which a bar or circle chart could not be substituted. Strictly speaking, the line graph must be used to portray changes in a continuous variable, since technically such a variable must be represented by a line and not by 'points' or 'bars'. Line graphs are often uniquely applicable to problems of analysis, particularly when it is essential to visualize a trend, observe the behavior of a set of variables through time, or portray the same variable in differing time periods." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

"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)

"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)

"Graphic forms help us to perform and influence two critical functions of the mind: the gathering of information and the processing of that information. Graphs and charts are ways to increase the effectiveness and the efficiency of transmitting information in a way that enhances the reader's ability to process that information. Graphics are tools to help give meaning to information because they go beyond the provision of information and show relationships, trends, and comparisons. They help to distinguish which numbers and which ideas are more important than others in a presentation." (Robert Lefferts, "Elements of Graphics: How to prepare charts and graphs for effective reports", 1981)

"There are several uses for which the line graph is particularly relevant. One is for a series of data covering a long period of time. Another is for comparing several series on the same graph. A third is for emphasizing the movement of data rather than the amount of the data. It also can be used with two scales on the vertical axis, one on the right and another on the left, allowing different series to use different scales, and it can be used to present trends and forecasts." (Anker V Andersen, "Graphing Financial Information: How accountants can use graphs to communicate", 1983)

"A connected graph is appropriate when the time series is smooth, so that perceiving individual values is not important. A vertical line graph is appropriate when it is important to see individual values, when we need to see short-term fluctuations, and when the time series has a large number of values; the use of vertical lines allows us to pack the series tightly along the horizontal axis. The vertical line graph, however, usually works best when the vertical lines emanate from a horizontal line through the center of the data and when there are no long-term trends in the data." (William S Cleveland, "The Elements of Graphing Data", 1985)

"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) 

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

"Stacked bar graphs do not show data structure well. A trend in one of the stacked variables has to be deduced by scanning along the vertical bars. This becomes especially difficult when the categories do not move in the same direction." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"Dashboards and visualization are cognitive tools that improve your 'span of control' over a lot of business data. These tools help people visually identify trends, patterns and anomalies, reason about what they see and help guide them toward effective decisions. As such, these tools need to leverage people's visual capabilities. With the prevalence of scorecards, dashboards and other visualization tools now widely available for business users to review their data, the issue of visual information design is more important than ever." (Richard Brath & Michael Peters, "Dashboard Design: Why Design is Important," DM Direct, 2004)

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

"Sparklines are compact line graphs that do not have a quantitative scale. They are meant to provide a quick sense of a metric's movement or trend, usually over time. They are more expressive than arrows, which only indicate change from the prior period and do not qualify the degree of change. Sparklines are significantly more compact than normal line graphs but are precise." (Wayne W Eckerson, "Performance Dashboards: Measuring, Monitoring, and Managing Your Business", 2010)

"Line graphs that show more than one line can be useful for making comparisons, but sometimes it is important to discuss each individual line. By using sparklines evaluators can call attention to and discuss individual cases. Sparklines can be embedded within a sentence to illustrate a trend and help stakeholders better understand the data. Evaluators can use this simple visualization when creating reports." (Christopher Lysy, "Developments in Quantitative Data Display and Their Implications for Evaluation", 2013) 

"What is good visualization? It is a representation of data that helps you see what you otherwise would have been blind to if you looked only at the naked source. It enables you to see trends, patterns, and outliers that tell you about yourself and what surrounds you. The best visualization evokes that moment of bliss when seeing something for the first time, knowing that what you see has been right in front of you, just slightly hidden. Sometimes it is a simple bar graph, and other times the visualization is complex because the data requires it." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

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

"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)

"As presenters of data visualizations, often we just want our audience to understand something about their environment – a trend, a pattern, a breakdown, a way in which things have been progressing. If we ask ourselves what we want our audience to do with that information, we might have a hard time coming up with a clear answer sometimes. We might just want them to know something." (Ben Jones, "Avoiding Data Pitfalls: How to Steer Clear of Common Blunders When Working with Data and Presenting Analysis and Visualizations", 2020)

"[...] scatterplots had advantages over earlier graphic forms: the ability to see clusters, patterns, trends, and relations in a cloud of points. Perhaps most importantly, it allowed the addition of visual annotations (point symbols, lines, curves, enclosing contours, etc.) to make those relationships more coherent and tell more nuanced stories." (Michael Friendly & Howard Wainer, "A History of Data Visualization and Graphic Communication", 2021)

"Data storytelling is a method of communicating information that is custom-fit for a specific audience and offers a compelling narrative to prove a point, highlight a trend, make a sale, or all of the above. [...] Data storytelling combines three critical components, storytelling, data science, and visualizations, to create not just a colorful chart or graph, but a work of art that carries forth a narrative complete with a beginning, middle, and end." (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

"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: Pitfalls (Just the Quotes)

Disclaimer: the following quotes are intended as a list of the things to avoid in Graphical Representation. For the full quotes see the previous post

"[...] avoid complicating the diagram by including too much data." (Armand Julin, "Summary for a Course of Statistics, General and Applied", 1910) 

"In general, the comparison of two circles of different size should be strictly avoided." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"Try telling the story in words different from those on the charts. […] If the chart shows a picture, describe the picture. Tell what it shows and why it is shown. If it is a diagram, explain it. Don't leave the audience to figure it out." (Edward J Hegarty, "How to Use a Set of Display Charts", The American Statistician Vol. 2" (5), 1948)

"It is not enough to avoid outright falsehood; one must be on the alert to detect possible distortion of truth." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"[...] avoid distortion or misrepresentation." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"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)

"There are two kinds of misrepresentation. In one, the numerical data do not agree with the data in the graph, or certain relevant data are omitted. This kind of misleading presentation, while perhaps hard to determine, clearly is wrong and can be avoided. In the second kind of misrepresentation, the meaning of the data is different to the preparer and to the user." (Anker V Andersen, "Graphing Financial Information: How accountants can use graphs to communicate", 1983)

"Do not allow data labels in the data region to interfere with the quantitative data or to clutter the graph. […] Avoid putting notes, keys, and markers in the data region. Put keys and markers just outside the data region and put notes in the legend or in the text." (William S Cleveland, "The Elements of Graphing Data", 1985)

"Make the data stand out and avoid superfluity are two broad strategies that serve as an overall guide to the specific principles. " (William S Cleveland, "The Elements of Graphing Data", 1985)

"Shorten long labels; avoid abbreviations unless they are universally understood; avoid repetition on the same graph." (Mary H Briscoe, "Preparing Scientific Illustrations: A guide to better posters, presentations, and publications" 2nd ed., 1995) 

"[...] avoid those graphical features that are purely decorative [...]" (Phillip I Good & James W Hardin, "Common Errors in Statistics" (and How to Avoid Them)", 2003)

"[...] avoid useless graphics." (Jacques Bertin [interview], 2003)

"If a break cannot be avoided, use a full scale break." (Naomi B Robbins, "Creating More effective Graphs", 2005)

"[...] when labels abandon the data points, then a code is often needed to relink names to numbers. Such codes, keys, and legends are impediments to learning, causing the reader's brow to furrow." (Edward R Tufte, "Beautiful Evidence", 2006) [argumentation against Cleveland's recommendation of not using words on data plots]

"Generally pie charts are to be avoided, as they can be difficult to interpret particularly when the number of categories is greater than five." (Jenny Freeman et al, "How to Display Data", 2008)

"Spurious precision should be avoided although when certain measures are to be used for further calculations or when presenting the results of analyses, greater precision may sometimes be appropriate." (Jenny Freeman et al, "How to Display Data", 2008)

"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." (Dennis K Lieu & Sheryl Sorby, "Visualization, Modeling, and Graphics for Engineering Design", 2009)

"[...] it is often best to avoid round charts and graphs." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"Avoid countering conventions where possible in order to avoid creating cognitive dissonance, a clash of habitual interpretation with the underlying message you are sending." (Noah Iliinsky & Julie Steel, "Designing Data Visualizations", 2011)

"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)

"Highlighting one aspect can make other things harder to see one word of warning in using preattentive attributes: when you highlight one point in your story, it can actually make other points harder to see. When you’re doing exploratory analysis, you should mostly avoid the use of preattentive attributes for this reason." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"Collecting data through sampling therefore becomes a never-ending battle to avoid sources of bias. [...] While trying to obtain a random sample, researchers sometimes make errors in judgment about whether every person or thing is equally likely to be sampled." (Daniel J Levitin, "Weaponized Lies", 2017)

"[...] avoid pure colors that are bright and saturated." (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

📉Graphical Representation: Taboos (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)

"Comparison between circles of different size should be absolutely avoided. It is inexcusable when we have available simple methods of charting so good and so convenient from every point of view as the horizontal bar." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"In general, the comparison of two circles of different size should be strictly avoided. Many excellent works on statistics approve the comparison of circles of different size, and state that the circles should always be drawn to represent the facts on an area basis rather than on a diameter basis. The rule, however, is not always followed and the reader has no way of telling whether the circles compared have been drawn on a diameter basis or on an area basis, unless the actual figures for the data are given so that the dimensions may be verified." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"Judgment must be used in the showing of figures in any chart or numerical presentation, so that the figures may not give an appearance of greater accuracy than their method of collection would warrant. Too many otherwise excellent reports contain figures which give the impression of great accuracy when in reality the figures may be only the crudest approximations. Except in financial statements, it is a safe rule to use ciphers whenever possible at the right of all numbers of great size. The use of the ciphers greatly simplifies the grasping of the figures by the reader, and, at the same time, it helps to avoid the impression of an accuracy which is not warranted by the methods of collecting the data." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"Many people use statistics as a drunkard uses a street lamp - for support rather than illumination. It is not enough to avoid outright falsehood; one must be on the alert to detect possible distortion of truth. One can hardly pick up a newspaper without seeing some sensational headline based on scanty or doubtful data." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"Simplicity, accuracy, appropriate size, proper proportion, correct emphasis, and skilled execution - these are the factors that produce the effective chart. To achieve simplicity your chart must be designed with a definite audience in mind, show only essential information. Technical terms should be absent as far as possible. And in case of doubt it is wiser to oversimplify than to make matters unduly complex. Be careful to avoid distortion or misrepresentation. Accuracy in graphics is more a matter of portraying a clear reliable picture than reiterating exact values. Selecting the right scales and employing authoritative titles and legends are as important as precision plotting. The right size of a chart depends on its probable use, its importance, and the amount of detail involved." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"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)

"There are two kinds of misrepresentation. In one, the numerical data do not agree with the data in the graph, or certain relevant data are omitted. This kind of misleading presentation, while perhaps hard to determine, clearly is wrong and can be avoided. In the second kind of misrepresentation, the meaning of the data is different to the preparer and to the user." (Anker V Andersen, "Graphing Financial Information: How accountants can use graphs to communicate", 1983)

"Do not allow data labels in the data region to interfere with the quantitative data or to clutter the graph. […] Avoid putting notes, keys, and markers in the data region. Put keys and markers just outside the data region and put notes in the legend or in the text." (William S Cleveland, "The Elements of Graphing Data", 1985)

"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)

"Labels should be complete but succinct. Long and complicated labels will defeat the viewer and therefore the purpose of the graph. Treat a label as a cue to jog the memory or to complete comprehension. Shorten long labels; avoid abbreviations unless they are universally understood; avoid repetition on the same graph. A title, for instance, should not repeat what is already in the axis labels. Be consistent in terminology." (Mary H Briscoe, "Preparing Scientific Illustrations: A guide to better posters, presentations, and publications" 2nd ed., 1995)

"Principal components and factor analysis are methods for data reduction. They seek a few underlying dimensions that account for patterns of variation among the observed variables underlying dimensions imply ways to combine variables, simplifying subsequent analysis. For example, a few combined variables could replace many original variables in a regression. Advantages of this approach include more parsimonious models, improved measurement of indirectly observed concepts, new graphical displays, and the avoidance of multicollinearity." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"Graphical illustrations should be simple and pleasing to the eye, but the presentation must remain scientific. In other words, we want to avoid those graphical features that are purely decorative while keeping a critical eye open for opportunities to enhance the scientific inference we expect from the reader. A good graphical design should maximize the proportion of the ink used for communicating scientific information in the overall display." (Phillip I Good & James W Hardin, "Common Errors in Statistics" (and How to Avoid Them)", 2003)

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

"Use a scale break only when necessary. If a break cannot be avoided, use a full scale break. Taking logs can cure the need for a break." (Naomi B Robbins, "Creating More effective Graphs", 2005)

"Conflicting with the idea of integrating evidence regardless of its these guidelines provoke several issues: First, labels are data. even intriguing data. [...] Second, when labels abandon the data points, then a code is often needed to relink names to numbers. Such codes, keys, and legends are impediments to learning, causing the reader's brow to furrow. Third, segregating nouns from data-dots breaks up evidence on the basis of mode" (verbal vs. nonverbal), a distinction lacking substantive relevance. Such separation is uncartographic; contradicting the methods of map design often causes trouble for any type of graphical display. Fourth, design strategies that reduce data-resolution take evidence displays in the wrong direction. Fifth, what clutter? Even this supposedly cluttered graph clearly shows the main ideas: brain and body mass are roughly linear in logarithms, and as both variables increase, this linearity becomes less tight." (Edward R Tufte, "Beautiful Evidence", 2006) [argumentation against Cleveland's recommendation of not using words on data plots]

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

"Numerical precision should be consistent throughout and summary statistics such as means and standard deviations should not have more than one extra decimal place" (or significant digit) compared to the raw data. Spurious precision should be avoided although when certain measures are to be used for further calculations or when presenting the results of analyses, greater precision may sometimes be appropriate." (Jenny Freeman et al, "How to Display Data", 2008)

"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)

"Dealing with a circular visualization and trying to compare its radial portions is always problematic. When designing with data, the story should always be told as clearly as possible. To do so, it is often best to avoid round charts and graphs." (Brian Suda, "A Practical Guide to Designing with Data", 2010)

"[...] you should not rely on social or cultural conventions to convey information. However, these conventions can be very powerful, and you should be aware that your reader brings them to the table. Making use of them, when possible, to reinforce your message will help you convey information efficiently. Avoid countering conventions where possible in order to avoid creating cognitive dissonance, a clash of habitual interpretation with the underlying message you are sending." (Noah Iliinsky & Julie Steel, "Designing Data Visualizations", 2011)

"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)

"Highlighting one aspect can make other things harder to see one word of warning in using preattentive attributes: when you highlight one point in your story, it can actually make other points harder to see. When you’re doing exploratory analysis, you should mostly avoid the use of preattentive attributes for this reason. When it comes to explanatory analysis, however, you should have a specific story you are communicating to your audience. Leverage preattentive attributes to help make that story visually clear." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"My base color is grey, not black, to allow for greater contrast since color stands out more against grey than black. For my attention-grabbing color, I often use blue for a number of reasons: (1) I like it, (2) you avoid issues of colorblindness that we’ll discuss momentarily, and (3) it prints well in black-and-white. That said, blue is certainly not your only option (and you’ll see many examples where I deviate from my typical blue for various reasons)." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"Sometimes bar charts are avoided because they are common. This is a mistake. Rather, bar charts should be leveraged because they are common, as this means less of a learning curve for your audience." (Cole N Knaflic, "Storytelling with Data: A Data Visualization Guide for Business Professionals", 2015)

"Effective data scientists know that they are trying to convey accurate information in an easily understood way. We have never seen a pie chart that was an improvement over a simple table. Even worse, the creative addition of pictures, colors, shading, blots, and splotches may produce chartjunk that confuses the reader and strains the eyes." (Gary Smith & Jay Cordes, "The 9 Pitfalls of Data Science", 2019)

"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)

"One tip to keep an audience focused on your story without overwhelming them is to reduce the saturation of the colors [...] When you lower the brightness and intensity, you are reducing the cognitive load that your audience has to bear. [...] Regardless of what combinations you decide on, you need to avoid pure colors that are bright and saturated." (Kate Strachnyi, "ColorWise: A Data Storyteller’s Guide to the Intentional Use of Color", 2023)

📉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)

"Statistics has its own basic suite of domain-specific visualization tools. These statistical graphics can best be classified by the kind of data that they depict. Statistical data are usually characterized by their scale: nominal, ordinal (which are both categorical) or numerical (which is usually regarded as continuous). What is most important in distinguishing statistical graphics from other graphics is their universality: statistical graphics are not tailored towards only one specific application but are valid for any data measured on the appropriate scales." (Antony Unwin et al [in "Graphics of Large Datasets: Visualizing a Million"], 2006)

"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)

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

"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)

"Mosaic plots […] are designed to show the dependencies and interactions between multiple categorical variables in one plot. […] A spineplot can be regarded as a kind of one-dimensional mosaic plot. […] In contrast with a barchart, where the bars are aligned to an axis, the mosaic plot uses a rectangular region, which is subdivided into tiles according to the numbers of observations falling into the different classes. This subdivision is done recursively, or in statistical terms conditionally, as more variables are included." (Antony Unwin et al [in "Graphics of Large Datasets: Visualizing a Million"], 2006)

"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 rectangular treemap, sometimes called the mosaic graph, is a space-filling visualization model used for displaying hierarchical data by means of nested rectangles. Each major branch of the tree is depicted as a rectangle, which is then sequentially tiled with smaller rectangles representing its subbranches. The area of each individual cell generally corresponds to a given quantity or data attri bute, for example size, length, price, time, or temperature. Color can indicate an additional quality, such as type, class, gender, or category." (Manuel Lima, "The Book of Trees: Visualizing Branches of Knowledge", 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)