16 November 2011

📉Graphical Representation: Composition (Just the Quotes)

"Nothing is so illuminating as a set of properly proportioned diagrams. [...] In addition to the significance of graphics in analytical work, it is likewise a valuable aid to the memory. A picture is manifestly more readily retained in mind than a description of the same subject, no matter how vividly it may have been expressed. A pictorial or diagrammatic illustration usually produces a firmer and more lasting impression than any composition of words or tabulation of figures, however well they may be arranged or set forth." (Allan C Haskell, "How to Make and Use Graphic Charts", 1919)

"Without adequate planning, it is seldom possible to achieve either proper emphasis of each component element within the chart or a presentation that is pleasing in its entirely. Too often charts are developed around a single detail without sufficient regard for the work as a whole. Good chart design requires consideration of these four major factors:" (1) size," (2) proportion," (3) position and margins, and" (4) composition." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"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)

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

"While visuals are an essential part of data storytelling, data visualizations can serve a variety of purposes from analysis to communication to even art. Most data charts are designed to disseminate information in a visual manner. Only a subset of data compositions is focused on presenting specific insights as opposed to just general information. When most data compositions combine both visualizations and text, it can be difficult to discern whether a particular scenario falls into the realm of data storytelling or not." (Brent Dykes, "Effective Data Storytelling: How to Drive Change with Data, Narrative and Visuals", 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)

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

"Beyond basic charts, practitioners must also learn to compose visualizations together elegantly. The perceptual stage focuses on making the literal charts more precise as well as working to de-emphasize the entire piece. Design choices start to consider distractions, reducing visual clutter and centering on the message. Minimalism is espoused as a core value with an emphasis on shifting toward precision as accuracy. This is the most common next step for practitioners. Minimalism is also a key stage in maturation. It is experimentation at one extreme that helps practitioners distill down to core, shared practices." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"Chart choices can also create weight within the entire composition. Presenting information as a comprehensive visualization, such as in a dashboard, requires thinking beyond individual charts. In writing, we not only craft sentences, but write the composition as an entire piece. Certain sentences may drive the writing more, but all sentences play a role in conveying the message." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"Visualizations are abstractions, relying on primary graphicacy skills to fully understand the composition." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

15 November 2011

📉Graphical Representation: Distribution (Just the Quotes)

"Some distributions [...] are symmetrical about their central value. Other distributions have marked asymmetry and are said to be skew. Skew distributions are divided into two types. If the 'tail' of the distribution reaches out into the larger values of the variate, the distribution is said to show positive skewness; if the tail extends towards the smaller values of the variate, the distribution is called negatively skew." (Michael J Moroney, "Facts from Figures", 1951)

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

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

"Plotting on power-transformed scales (either cube roots or logs) is recommended only in those cases where the distribution is very asymmetric and the reference configuration for the untransformed plot would be a straight line through the origin." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"Boxplots provide information at a glance about center (median), spread (interquartile range), symmetry, and outliers. With practice they are easy to read and are especially useful for quick comparisons of two or more distributions. Sometimes unexpected features such as outliers, skew, or differences in spread are made obvious by boxplots but might otherwise go unnoticed." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"Comparing normal distributions reduces to comparing only means and standard deviations. If standard deviations are the same, the task even simpler: just compare means. On the other hand, means and standard deviations may be incomplete or misleading as summaries for nonnormal distributions." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"If a distribution were perfectly symmetrical, all symmetry-plot points would be on the diagonal line. Off-line points indicate asymmetry. Points fall above the line when distance above the median is greater than corresponding distance below the median. A consistent run of above-the-line points indicates positive skew; a run of below-the-line points indicates negative skew." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"Remember that normality and symmetry are not the same thing. All normal distributions are symmetrical, but not all symmetrical distributions are normal. With water use we were able to transform the distribution to be approximately symmetrical and normal, but often symmetry is the most we can hope for. For practical purposes, symmetry (with no severe outliers) may be sufficient. Transformations are not a magic wand, however. Many distributions cannot even be made symmetrical." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"Many good things happen when data distributions are well approximated by the normal. First, the question of whether the shifts among the distributions are additive becomes the question of whether the distributions have the same standard deviation; if so, the shifts are additive. […] A second good happening is that methods of fitting and methods of probabilistic inference, to be taken up shortly, are typically simple and on well understood ground. […] A third good thing is that the description of the data distribution is more parsimonious." (William S Cleveland, "Visualizing Data", 1993)

"The quantile plot is a good general display since it is fairly easy to construct and does a good job of portraying many aspects of a distribution. Three convenient features of the plot are the following: First, in constructing it, we do not make any arbitrary choices of parameter values or cell boundaries [...] and no models for the data are fitted or assumed. Second, like a table, it is not a summary but a display of all the data. Third, on the quantile plot every point is plotted at a distinct location, even if there are duplicates in the data. The number of points that can be portrayed without overlap is limited only by the resolution of the plotting device. For a high resolution device several hundred points distinguished." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"Boxplots provide information at a glance about center (median), spread (interquartile range), symmetry, and outliers. With practice they are easy to read and are especially useful for quick comparisons of two or more distributions. Sometimes unexpected features such as outliers, skew, or differences in spread are made obvious by boxplots but might otherwise go unnoticed." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

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

"Histograms use area to represent counts of a distribution. This makes them somewhat related to barcharts and mosaic plots, although the number or the width of the bins of a histogram is not determined a priori and the bins are drawn without gaps between them reflecting the continuous scale of the data. Whereas barcharts and mosaic plots show the exact distribution of the sample, a histogram is always just one approximation to the distribution of the data. Sometimes histograms are also used as crude density estimators for some 'true', but usually unknown, underlying distribution for the data. There are much better density estimation methods that produce smooth distribution displays." (Antony Unwin et al [in "Graphics of Large Datasets: Visualizing a Million"], 2006)

"How would a million be visualized today? If you have ever drawn a histogram or a scatterplot of a million cases, you know that it is possible, but that there are problems. The screen resolution of a computer cannot be high enough to show very small bars in the histogram, and in regions of high density the scatterplots look like black blobs with huge numbers of points piled on top of one another. (It is noteworthy - and useful - that the weaknesses of the two kinds of plot arise at opposite extremes of the distributional densities.) So what should be visualized? If the distributional form of the bulk of the data is of interest, then the histogram will be fine for one-dimensional views (and it may give some information about outliers too). If individual outliers are of interest, then the scatterplot will be pretty good (and it will give a fair bit of distributional information as well). One aim might be described as global, attempting to summarise the main structure, and the other as local, attempting to identify individual features. Ideally, both kinds of plot are needed to satisfy both aims." (Antony Unwin et al [in "Graphics of Large Datasets: Visualizing a Million"], 2006)

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

"'Distribution' refers to how the vof a variable are placed along an axis, keeping the proportional distances taken from the values in the table. In descriptive statistics, there are two complementary ways to study a distribution: searching for what is common (the measures of central tendency) and searching for what is different along with how much different it is (measures of dispersion)." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

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

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

📉Graphical Representation: Simplification (Just the Quotes)

"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) 

"The great difference between the graphic representation of yesterday, which was poorly dissociated from the figurative image, and the graphics of tomorrow, is the disappearance of the congential fixity of the image. […] When one can superimpose, juxtapose, transpose, and permute graphic images in ways that lead to groupings and classings, the graphic image passes from the dead image, the 'illustration,' to the living image, the widely accessible research instrument it is now becoming. The graphic is no longer only the 'representation' of a final simplification, it is a point of departure for the discovery of these simplifications and the means for their justification. The graphic has become, by its manageability, an instrument for information processing." (Jacques Bertin, "Semiology of graphics" ["Semiologie Graphique"], 1967)

"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)

"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)

"An axis is the ruler that establishes regular intervals for measuring information. Because it is such a widely accepted convention, it is often taken for granted and its importance overlooked. Axes may emphasize, diminish, distort, simplify, or clutter the information. They must be used carefully and accurately." (Mary H Briscoe, "Preparing Scientific Illustrations: A guide to better posters, presentations, and publications" 2nd ed., 1995)

"Good ideas do not communicate themselves. Ideas must be organized. Highly complex ideas need to be clarified and simplified whereas diffuse data may benefit from being combined. Ideas and data must be made interesting and comprehensible to those not familiar with them." (Mary H Briscoe, "Preparing Scientific Illustrations:  guide to better posters, presentations, and publications" 2nd ed., 1995)

"Mathematical models are continually invoking ideas of infinitely smooth surfaces, weightless strings, weightless beams, perfectly spherical balls, projectiles flying through airless space, gases which are perfectly compressible and liquids which are perfectly incompressible, and so on. The purpose of such simplifications is, in theory, to understand the world better despite the oversimplification, which you hope either will not matter or will be corrected when you construct a second (better) model." (David Wells, "You Are a Mathematician: A wise and witty introduction to the joy of numbers", 1995)

"Charts are used to represent quantitative data in a graphic format. A chart visually illustrates relationships between numbers. When creating a chart, keep in mind that the goal is to represent the data in a simplified and appealing way so as not to muddle the message the chart is meant to convey." (Dennis K Lieu & Sheryl Sorby, "Visualization, Modeling, and Graphics for Engineering Design", 2009)

"Information graphics are an essential component of technical communication. Very few technical documents or presentations can be considered complete without graphical elements to present some essential data. Because engineers are visually oriented, graphic aids allow their thoughts and ideas to be better understood by other engineers. Information graphics are essential in presenting data because they simplify the content, offer a visually pleasing alternative to gray text in a proposal or an article, and thereby invite interest." (Dennis K Lieu & Sheryl Sorby, "Visualization, Modeling, and Graphics for Engineering Design", 2009)

"The data is a simplification - an abstraction - of the real world. So when you visualize data, you visualize an abstraction of the world, or at least some tiny facet of it. Visualization is an abstraction of data, so in the end, you end up with an abstraction of an abstraction, which creates an interesting challenge. […] Just like what it represents, data can be complex with variability and uncertainty, but consider it all in the right context, and it starts to make sense." (Nathan Yau, "Data Points: Visualization That Means Something", 2013)

"Form simplification means simplifying relationships among the components of the whole, emphasizing the whole and reducing the relevance of individual components by standardizing and generalizing relationships. This results in an increased weight of useful information (signal) against useless information (noise)." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"GIGO is a famous saying coined by early computer scientists: garbage in, garbage out. At the time, people would blindly put their trust into anything a computer output indicated because the output had the illusion of precision and certainty. If a statistic is composed of a series of poorly defined measures, guesses, misunderstandings, oversimplifications, mismeasurements, or flawed estimates, the resulting conclusion will be flawed." (Daniel J Levitin, "Weaponized Lies", 2017)

"Any chart is a simplification of reality, and it reveals as much as it hides. Therefore, it’s always worth asking ourselves: What other patterns or trends may be hidden behind the data displayed on the chart?" (Alberto Cairo, "How Charts Lie", 2019)

"No chart can ever capture reality in all its richness. However, a chart can be made worse or better depending on its ability to strike a balance between oversimplifying that reality and obscuring it with too much detail."  (Alberto Cairo, "How Charts Lie", 2019)

🔭Data Science: Centrality (Just the Quotes)

"An average value is a single value within the range of the data that is used to represent all of the values in the series. Since an average is somewhere within the range of the data, it is sometimes called a measure of central value." (Frederick E Croxton & Dudley J Cowden,Practical Business Statistics", 1937)

"Some distributions [...] are symmetrical about their central value. Other distributions have marked asymmetry and are said to be skew. Skew distributions are divided into two types. If the 'tail' of the distribution reaches out into the larger values of the variate, the distribution is said to show positive skewness; if the tail extends towards the smaller values of the variate, the distribution is called negatively skew." (Michael J Moroney,Facts from Figures", 1951)

"Numerical data, which have been recorded at intervals of time, form what is generally described as a time series. [...] The purpose of analyzing time series is not always the determination of the trend by itself. Interest may be centered on the seasonal movement displayed by the series and, in such a case, the determination of the trend is merely a stage in the process of measuring and analyzing the seasonal variation. If a regular basic or under- lying seasonal movement can be clearly established, forecasting of future movements becomes rather less a matter of guesswork and more a matter of intelligent forecasting." (Alfred R Ilersic, "Statistics", 1959)

"Dispersion or spread is the degree of the scatter or variation of the variables about a central value." (Bertram C Brookes & W F L Dick,Introduction to Statistical Method", 1969)

"Equal variability is not always achieved in plots. For instance, if the theoretical distribution for a probability plot has a density that drops off gradually to zero in the tails" (as the normal density does), then the variability of the data in the tails of the probability plot is greater than in the center. Another example is provided by the histogram. Since the height of any one bar has a binomial distribution, the standard deviation of the height is approximately proportional to the square root of the expected height; hence, the variability of the longer bars is greater." (John M Chambers et al,Graphical Methods for Data Analysis", 1983)

"There are several reasons why symmetry is an important concept in data analysis. First, the most important single summary of a set of data is the location of the center, and when data meaning of 'center' is unambiguous. We can take center to mean any of the following things, since they all coincide exactly for symmetric data, and they are together for nearly symmetric data: (l) the center of symmetry. (2) the arithmetic average or center of gravity, (3) the median or 50%. Furthermore, if data a single point of highest concentration instead of several" (that is, they are unimodal), then we can add to the list (4) point of highest concentration. When data are far from symmetric, we may have trouble even agreeing on what we mean by center; in fact, the center may become an inappropriate summary for the data." (John M Chambers et al,Graphical Methods for Data Analysis", 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)

"If the sample is not representative of the population because the sample is small or biased, not selected at random, or its constituents are not independent of one another, then the bootstrap will fail. […] For a given size sample, bootstrap estimates of percentiles in the tails will always be less accurate than estimates of more centrally located percentiles. Similarly, bootstrap interval estimates for the variance of a distribution will always be less accurate than estimates of central location such as the mean or median because the variance depends strongly upon extreme values in the population." (Phillip I Good & James W Hardin,Common Errors in Statistics" (and How to Avoid Them)", 2003)

"Central tendency is the formal expression for the notion of where data is centered, best understood by most readers as 'average'. There is no one way of measuring where data are centered, and different measures provide different insights." (Charles Livingston & Paul Voakes,Working with Numbers and Statistics: A handbook for journalists", 2005)

"Mean-averages can be highly misleading when the raw data do not form a symmetric pattern around a central value but instead are skewed towards one side [...], typically with a large group of standard cases but with a tail of a few either very high" (for example, income) or low" (for example, legs) values." (David Spiegelhalter,The Art of Statistics: Learning from Data", 2019)

"The elements of this cloud of uncertainty (the set of all possible errors) can be described in terms of probability. The center of the cloud is the number zero, and elements of the cloud that are close to zero are more probable than elements that are far away from that center. We can be more precise in this definition by defining the cloud of uncertainty in terms of a mathematical function, called the probability distribution." (David S Salsburg,Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Two clouds of uncertainty may have the same center, but one may be much more dispersed than the other. We need a way of looking at the scatter about the center. We need a measure of the scatter. One such measure is the variance. We take each of the possible values of error and calculate the squared difference between that value and the center of the distribution. The mean of those squared differences is the variance." (David S Salsburg,Errors, Blunders, and Lies: How to Tell the Difference", 2017)

📉Graphical Representation: Rulings (Just the Quotes)

"A warning seems justifiable that the background of a chart should not be made any more prominent than actually necessary. Many charts have such heavy coordinate ruling and such relatively narrow lines for curves or other data that the real facts the chart is intended to portray do not stand out clearly from the background. No more coordinate lines should be used than are absolutely necessary to guide the eye of the reader and to permit an easy reading of the curves." (Willard C Brinton, "Graphic Methods for Presenting Facts", 1919)

"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)

"Admittedly a chart is primarily a picture, and for presentation purposes should be treated as such; but in most charts it is desirable to be able to read the approximate magnitudes by reference to the scales. Such reference is almost out of the question without some rulings to guide the eye. Second, the picture itself may be misleading without enough rulings to keep the eye 'honest'. Although sight is the most reliable of our senses for measuring" (and most other) purposes, the unaided eye is easily deceived; and there are numerous optical illusions to prove it. A third reason, not vital, but still of some importance, is that charts without rulings may appear weak and empty and may lack the structural unity desirable in any illustration." (Kenneth W Haemer, "Hold That Line. A Plea for the Preservation of Chart Scale Ruling", The American Statistician Vol. 1" (1) 1947)

"The grid with the vertical ruling carrying the logarithmic scale and the horizontal ruling carrying the arithmetic scale denoting time is the most common. The reverse may be used, and the horizontal ruling may carry the log scale. Charts of this type are frequently referred to as 'semilog charts'. [...] The full or double log scale (with the log grid carried on both horizontal and vertical rulings) is used mostly for statistical study and economic analysis and is not a good tool for popular presentation of data." (Mary E Spear, "Charting Statistics", 1952)

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

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

"The ratio chart not only correctly represents relative changes but also indicates absolute amounts at the same time. Because of its distinctive structure, it is referred to as a semilogarithmic chart. The vertical axis is ruled logarithmically and the horizontal axis arithmetically. The continued narrowing of the spacings of the scale divisions on the vertical axis is characteristic of logarithmic rulings; the equal intervals on the horizontal axis are indicative of arithmetic rulings." (Anna C Rogers, "Graphic Charts Handbook", 1961)

"The scales used are important; contracting or expanding the vertical or horizontal scales will change the visual picture. The trend lines need enough grid lines to obviate difficulty in reading the results properly. One must be careful in the use of cross-hatching and shading, both of which can create illusions. Horizontal rulings tend to reduce the appearance. while vertical lines enlarge it. In summary, graphs must be reliable, and reliability depends not only on what is presented but also on how it is presented." (Anker V Andersen, "Graphing Financial Information: How accountants can use graphs to communicate", 1983)


14 November 2011

📉Graphical Representation: Boxplots (Just the Quotes)

"Boxplots provide information at a glance about center (median), spread (interquartile range), symmetry, and outliers. With practice they are easy to read and are especially useful for quick comparisons of two or more distributions. Sometimes unexpected features such as outliers, skew, or differences in spread are made obvious by boxplots but might otherwise go unnoticed." (Lawrence C Hamilton, "Regression with Graphics: A second course in applied statistics", 1991)

"A bar graph typically presents either averages or frequencies. It is relatively simple to present raw data" (in the form of dot plots or box plots). Such plots provide much more information. and they are closer to the original data. If the bar graph categories are linked in some way - for example, doses of treatments - then a line graph will be much more informative. Very complicated bar graphs containing adjacent bars are very difficult to grasp. If the bar graph represents frequencies. and the abscissa values can be ordered, then a line graph will be much more informative and will have substantially reduced chart junk." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"Before calculating a confidence interval for a mean, first check that one of the situations just described holds. To determine whether the data are bell-shaped or skewed, and to check for outliers, plot the data using a histogram, dotplot, or stemplot. A boxplot can reveal outliers and will sometimes reveal skewness, but it cannot be used to determine the shape otherwise. The sample mean and median can also be compared to each other. Differences between the mean and the median usually occur if the data are skewed - that is, are much more spread out in one direction than in the other." (Jessica M Utts & Robert F Heckard, "Mind on Statistics", 2007)

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

"Sorting data is one of the most efficient actions to derive different views of data in order to see the variables from many angles. Sorting is usually not applied to the data itself, but to statistical objects of a plot. We might want to sort the bars in a barchart, the variables in a parallel boxplot or the categories in a boxplot y by x." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)

"Need to consider outliers as they can affect statistics such as means, standard deviations, and correlations. They can either be explained, deleted, or accommodated (using either robust statistics or obtaining additional data to fill-in). Can be detected by methods such as box plots, scatterplots, histograms or frequency distributions." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"A boxplot is similar in spirit to an individual bar in a bar chart in that only a single spatial axis is used to visually encode data, but boxplots show five numbers through the use of a glyph rather than the single number encoded by the linear mark in a bar chart. A boxplot chart features multiple boxplots within a single shared frame to contrast different attribute distributions, just as bar charts show multiple bars along the second axis." (Tamara Munzner, "Visualization Analysis and Design", 2014)

"Boxplots directly show the spread, namely, the degree of dispersion, with the extent of the box. They show the skew of the distribution compared with a normal distribution with the peak at the center by the asymmetry between the top and bottom sections of the box. Standard boxplots are designed to handle unimodal data, where there is only one value that occurs the most frequently. There are many variants of boxplots that augment the basic visual encoding with more information." (Tamara Munzner, "Visualization Analysis and Design", 2014)

"A boxplot is a dotplot enhanced with a schematic that provides information about the center and spread of the data, including the median, quartiles, and so on. This is a very useful way of summarizing a variable's distribution. The dotplot can also be enhanced with a diamond-shaped schematic portraying the mean and standard deviation" (or the standard error of the mean)." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"Visual clutter is one of the most serious issues with bar charts. Using a bar to represent a simple data point is clearly overkill that results in no room for more data. At times, this may make us overlook less obvious things. The population pyramids offer a glaring example of this. But dot plots are not only about reducing clutter and avoiding overstimulation. Because we don’t compare heights, dot plots actually allow us to break the scale to improve resolution, and that’s a big plus over bar charts." (Jorge Camões, "Data at Work: Best practices for creating effective charts and information graphics in Microsoft Excel", 2016)

"[boxplots] allow you to assess variability both between and within the groups. [...] Each box shows the within-group variability, as measured by the interquartile range of the numerical variable (SAT score) for all cases in that category. The middle line within each box is the median of that category, and the differences between these medians give you a sense of the between-group variability. In this boxplot, the whiskers extend outside the box no further than 1.5 times the interquartile range. Points outside this interval are shown as individual dots." (James G Scott, "Statistical Modeling: A Gentle Introduction", 2017)

"[…] the drawback of the box plot is that it tends to hide the values due to its design." (Andy Kriebel & Eva Murray, "#MakeoverMonday: Improving How We Visualize and Analyze Data, One Chart at a Time", 2018)

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

"Side-by-side box plots is a simpler approach that can give a crude understanding of the relationship between one quantitative variable and two or more qualitative variables. When we have many subgroups, side-by-side box-and-whisker plots can be very useful for comparing basic features of a distribution." (Deborah Nolan & Sara Stoudt, "Communicating with Data: The Art of Writing for Data Science", 2021)

"Side-by-side box plots offer a similar comparison of distributions across groups. The box plot offers a simpler approach that can give a crude understanding of a distribution. Likewise, violin plots sketch density curves along an axis for each group. The curve is flipped to create a symmetric 'violin' shape. The violin plot aims to bridge the gap between the density curve and box plot." (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)

"The principle of symmetry states that objects that are symmetrical, or have a balanced appearance, tend to be perceived as a group or a pattern. Some data visualization graphs that can be used to explore this principle are the boxplot with boxes symmetrically placed around the median (Q2), the radar chart displaying multivariate data as a bidimensional chart with quantitative variables, and the mirrored bar chart with two sets of bars with mirrored values displayed." (Leandro N de Castro, "Exploratory Data Analysis: Descriptive Analysis, Visualization, and Dashboard Design", 2025)

📉Graphical Representation: Extremes (Just the Quotes)

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

"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)

"If the underlying pattern of the data has gentle curvature with no local maxima and minima, then locally linear fitting is usually sufficient. But if there are local maxima or minima, then locally quadratic fitting typically does a better job of following the pattern of the data and maintaining local smoothness." (William S Cleveland, "Visualizing Data", 1993)

"Variance and its square root, the standard deviation, summarize the amount of spread around the mean, or how much a variable varies. Outliers influence these statistics too, even more than they influence the mean. On the other hand. the variance and standard deviation have important mathematical advantages that make them (together with the mean) the foundation of classical statistics. If a distribution appears reasonably symmetrical, with no extreme outliers, then the mean and standard deviation or variance are the summaries most analysts would use." (Lawrence C Hamilton, "Data Analysis for Social Scientists: A first course in applied statistics", 1995)

"Clearly, the mean is greatly influenced by extreme values, but it can be appropriate for many situations where extreme values do not arise. To avoid misuse, it is essential to know which summary measure best reflects the data and to use it carefully. Understanding the situation is necessary for making the right choice. Know the subject!" (Herbert F Spirer et al, "Misused Statistics" 2nd Ed, 1998)

"A feature shared by both the range and the interquartile range is that they are each calculated on the basis of just two values - the range uses the maximum and the minimum values, while the IQR uses the two quartiles. The standard deviation, on the other hand, has the distinction of using, directly, every value in the set as part of its calculation. In terms of representativeness, this is a great strength. But the chief drawback of the standard deviation is that, conceptually, it is harder to grasp than other more intuitive measures of spread." (Alan Graham, "Developing Thinking in Statistics", 2006)

"Many scientists who work not just with noise but with probability make a common mistake: They assume that a bell curve is automatically Gauss's bell curve. Empirical tests with real data can often show that such an assumption is false. The result can be a noise model that grossly misrepresents the real noise pattern. It also favors a limited view of what counts as normal versus non-normal or abnormal behavior. This assumption is especially troubling when applied to human behavior. It can also lead one to dismiss extreme data as error when in fact the data is part of a pattern." (Bart Kosko, "Noise", 2006)

"Standard quantile graphs offer certain advantages over cumulative percent frequency graphs. Among these advantages are ease of construction, actual data points are shown as opposed to summaries of class intervals, no decisions are required as to what the best size class interval might be, the same curve functions as a less-than and greater-than curve, and the actual maximum and minimum values are shown on the graph." (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"[…] 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 is a mistake - maybe due to a measuring or recording error." (Alan Graham, "Developing Thinking in Statistics", 2006)

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

📉Graphical Representation: Improvement (Just the Quotes)

"Graphical methodology provides powerful diagnostic tools for conveying properties of the fitted regression, for assessing the adequacy of the fit, and for suggesting improvements. There is seldom any prior guarantee that a hypothesized regression model will provide a good description of the mechanism that generated the data. Standard regression models carry with them many specific assumptions about the relationship between the response and explanatory variables and about the variation in the response that is not accounted for by the explanatory variables. In many applications of regression there is a substantial amount of prior knowledge that makes the assumptions plausible; in many other applications the assumptions are made as a starting point simply to get the analysis off the ground. But whatever the amount of prior knowledge, fitting regression equations is not complete until the assumptions have been examined." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"The illusion of randomness gradually disappears as the skill in chart reading improves." (John W. Murphy, "Technical Analysis of the Financial Markets", 1999)

"Always bear in mind that the purposes of any chart are (1) to help gather, organize or visualize the facts; (2) to aid in analyzing them; (3) to help in developing the better method and evaluating it; (4) to assist in convincing management of the improvement’s value." (Ben B Graham, "Detail Process Charting: Speaking the Language of Process", 2004)

"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)

"The Sixth Principle for the analysis and display of data: 'Analytical presentations ultimately stand or fall depending on the quality, relevance, and integrity of their content.' This suggests that the most effective way to improve a presentation is to get better content. It also suggests that design devices and gimmicks cannot salvage failed content." (Edward R Tufte, "Beautiful Evidence", 2006)

"Exploring data generates hypotheses about patterns in our data. The visualizations and tools of dynamic interactive graphics ease and improve the exploration, helping us to 'see what our data seem to say'." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"A performance dashboard is a practical tool to improve management effectiveness and efficiency, not just a pretty retrospective picture in an annual report." (Pearl Zhu, "Performance Master: Take a Holistic Approach to Unlock Digital Performance", 2017)

"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)

"Good design serves a more important function than simply pleasing you: It helps you access ideas. It improves your comprehension and makes the ideas more persuasive. Good design makes lesser charts good and good charts transcendent." (Scott Berinato, "Good Charts : the HBR guide to making smarter, more persuasive data visualizations", 2023)

📉Graphical Representation: Appropriateness (Just the Quotes)

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

"First, color has identity value. In other words, it serves to distinguish one thing from another. In many cases it does this much better and much quicker than black and white coding by different types of shading or lines. […] Second, color has suggestion value. […] Red is usually taken to mean a danger signal or an unfavorable condition. But since it is one of the most visible of colors it is excellent for adding emphasis, regardless of connotation. […] Green has no such unfavorable implication, and is usually appropriate for suggesting a green light" condition. […] Similarly, every color carries its own connotations; and although they seldom make a vital difference one way or the other, it seems logical to try to make them work for you rather than against you." (Kenneth W Haemer, "Color in Chart Presentation", The American Statistician Vol. 4 (2) , 1950)

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

"The bar chart is one of the most useful, simple, adaptable, and popular techniques in graphic presentation. The simple bar chart. with its many variations, is particularly appropriate for comparing the magnitude, or size, of coordinate items or of parts of a total. The basis of comparison in the bar chart is linear or one-dimensional. The length of each bar or of its components is proportional to the quantity or amount of each category' represented. " (Calvin F Schmid, "Handbook of Graphic Presentation", 1954)

"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)

"The common bar chart is particularly appropriate for comparing magnitude or size of coordinate items or parts of a total. It is one of the most useful, simple, and adaptable techniques in graphic presentation. The basis of comparison in the bar chart is linear or one-dimensional. The length of each bar or of its components is proportional to the quantity or amount of each category represented." (Anna C Rogers, "Graphic Charts Handbook", 1961)

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

"Data should not be forced into an uncomfortable or improper mold. For example, data that is appropriate for line graphs is not usually appropriate for circle charts and in any case not without some arithmetic transformation. Only graphs that are designed to fit the data can be used profitably." (Cecil H Meyers, "Handbook of Basic Graphs: A modern approach", 1970)

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

"There are several reasons why symmetry is an important concept in data analysis. First, the most important single summary of a set of data is the location of the center, and when data meaning of 'center' is unambiguous. We can take center to mean any of the following things, since they all coincide exactly for symmetric data, and they are together for nearly symmetric data: (l) the center of symmetry. (2) the arithmetic average or center of gravity, (3) the median or 50%. Furthermore, if data a single point of highest concentration instead of several (that is, they are unimodal), then we can add to the list (4) point of highest concentration. When data are far from symmetric, we may have trouble even agreeing on what we mean by center; in fact, the center may become an inappropriate summary for the data." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

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

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

"[…] the partial scale break is a weak indicator that the reader can fail to appreciate fully; visually the graph is still a single panel that invites the viewer to see, inappropriately, patterns between the two scales. […] The partial scale break also invites authors to connect points across the break, a poor practice indeed; […]" (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38 (4) 1984) 

"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)

"Visual displays rich with data are not only an appropriate and proper complement to human capabilities, but also such designs are frequently optimal. If the visual task is contrast, comparison, and choice - as so often it is - then the more relevant information within eyespan, the better. Vacant, low-density displays, the dreaded posterization of data spread over pages and pages, require viewers to rely on visual memory - a weak skill - to make a contrast, a comparison, a choice." (Edward R Tufte, "Envisioning Information", 1990)

"We analyze numbers in order to know when a change has occurred in our processes or systems. We want to know about such changes in a timely manner so that we can respond appropriately. While this sounds rather straightforward, there is a complication - the numbers can change even when our process does not. So, in our analysis of numbers, we need to have a way to distinguish those changes in the numbers that represent changes in our process from those that are essentially noise." (Donald J Wheeler, "Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"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)

"The content and context of the numerical data determines the most appropriate mode of presentation. A few numbers can be listed, many numbers require a table. Relationships among numbers can be displayed by statistics. However, statistics, of necessity, are summary quantities so they cannot fully display the relationships, so a graph can be used to demonstrate them visually. The attractiveness of the form of the presentation is determined by word layout, data structure, and design." (Gerald van Belle, "Statistical Rules of Thumb", 2002)

"The plot tells us the data are granular in the data source, something we could not ascertain with the histogram. There is an important lesson here. Statistics texts and statistical packages that recommend the histogram as the graphical starting point for a data analysis are giving bad advice. The same goes for kernel density estimates. These are appropriate second stages for graphical data analysis. The best starting point for getting a sense of the distribution of a variable is a tally, stem-and-leaf, or a dot plot. A dot plot is a special case of a tally" (perhaps best thought of as a delta-neighborhood tally). Once we see that the data are not granular, we may move on to a histogram or kernel density, which smooths the data more than a dot plot." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

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

"A histogram consists of the outline of bars of equal width and appropriate length next to each other. By connecting the frequency values at the position of the nominal values" (the midpoints of the intervals) with straight lines, a frequency polygon is obtained. Attaching classes with frequency zero at either end makes the area" (the integral) under the frequency polygon equal to that under the histogram." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"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)

"There are two main reasons for using graphic displays of datasets: either to present or to explore data. Presenting data involves deciding what information you want to convey and drawing a display appropriate for the content and for the intended audience. [...] Exploring data is a much more individual matter, using graphics to find information and to generate ideas. Many displays may be drawn. They can be changed at will or discarded and new versions prepared, so generally no one plot is especially important, and they all have a short life span." (Antony Unwin, "Good Graphics?" [in "Handbook of Data Visualization"], 2008)

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

"The problem of overplotting can be as severe that (smaller) groups can disappear completely, which will not only lead to quantitatively biased inferences, but even to qualitatively inappropriate conclusions." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009) 

"In order to be effective a descriptive statistic has to make sense - it has to distill some essential characteristic of the data into a value that is both appropriate and understandable. […] the justification for computing any given statistic must come from the nature of the data themselves - it cannot come from the arithmetic, nor can it come from the statistic. If the data are a meaningless collection of values, then the summary statistics will also be meaningless - no arithmetic operation can magically create meaning out of nonsense. Therefore, the meaning of any statistic has to come from the context for the data, while the appropriateness of any statistic will depend upon the use we intend to make of that statistic." (Donald J Wheeler, "Myths About Data Analysis", International Lean & Six Sigma Conference, 2012) 

"Visualization ethics relates to the potential deception that can be created, intentionally or otherwise, from an ineffective and inappropriate representation of data. Sometimes it can be through a simple lack of understanding of visual perception." (Andy Kirk, "Data Visualization: A successful design process", 2012)

"There are two kinds of mistakes that an inappropriate inductive bias can lead to: underfitting and overfitting. Underfitting occurs when the prediction model selected by the algorithm is too simplistic to represent the underlying relationship in the dataset between the descriptive features and the target feature. Overfitting, by contrast, occurs when the prediction model selected by the algorithm is so complex that the model fits to the dataset too closely and becomes sensitive to noise in the data."(John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, Worked Examples, and Case Studies", 2015)

"When using indexes in a data set, using an average aggregation is appropriate as long as you only use it at the individual region, month, and visitor type level (i.e., the lowest granularity of the data). You cannot use an average of the average to represent the total."  (Andy Kriebel & Eva Murray, "#MakeoverMonday: Improving How We Visualize and Analyze Data, One Chart at a Time", 2018)

"The second rule of communication is to know what you want to achieve. Hopefully the aim is to encourage open debate, and informed decision-making. But there seems no harm in repeating yet again that numbers do not speak for themselves; the context, language and graphic design all contribute to the way the communication is received. We have to acknowledge we are telling a story, and it is inevitable that people will make comparisons and judgements, no matter how much we only want to inform and not persuade. All we can do is try to pre-empt inappropriate gut reactions by design or warning." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"For numbers to be transparent, they must be placed in an appropriate context. Numbers must presented in a way that allows for fair comparisons." (Carl T Bergstrom & Jevin D West, "Calling Bullshit: The Art of Skepticism in a Data-Driven World", 2020)

"To tell an honest story, it is not enough for numbers to be correct. They need to be placed in an appropriate context so that a reader or listener can properly interpret them." (Carl T Bergstrom & Jevin D West, "Calling Bullshit: The Art of Skepticism in a Data-Driven World", 2020)

"Raw data without appropriate visualization is like dumped construction raw materials at a building construction site. The finished house is the actual visuals created from those data like raw materials." (Bill Inmon et al, "Building the Data Lakehouse", 2021)

"[...] to support a conversation, charts need to provide cohesive and relevant responses to a user's intent. Sometimes the interface needs to respond by changing the visual encoding of existing charts, while in other cases, it is necessary to create a new chart to support the analytical conversation. In addition to appropriate visualization responses, it is critical to help the user understand how the system has interpreted their intent by producing appropriate feedback and allowing them to clarify if necessary." (Vidya Setlur & Bridget Cogley, "Functional Aesthetics for data visualization", 2022)

"If an organization had a single overall data quality key performance indicator (KPI), then it might be appropriate to put a greater weighting on those rules which would impact regulatory compliance. A lack of regulatory compliance is a risk to the very existence of organizations like these, and therefore, a greater weighting might be needed." (Robert Hawker, "Practical Data Quality", 2023)

13 November 2011

📉Graphical Representation: Density (Just the Quotes)

"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) 

"Equal variability is not always achieved in plots. For instance, if the theoretical distribution for a probability plot has a density that drops off gradually to zero in the tails (as the normal density does), then the variability of the data in the tails of the probability plot is greater than in the center. Another example is provided by the histogram. Since the height of any one bar has a binomial distribution, the standard deviation of the height is approximately proportional to the square root of the expected height; hence, the variability of the longer bars is greater." (John M Chambers et al, "Graphical Methods for Data Analysis", 1983)

"[…] the only worse design than a pie chart is several of them, for then the viewer is asked to compare quantities located in spatial disarray both within and between pies. […] Given their low data-density and failure to order numbers along a visual dimension, pie charts should never be used." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"Maximizing data ink (within reason) is but a single dimension of a complex and multivariate design task. The principle helps conduct experiments in graphical design. Some of those experiments will succeed. There remain, however, many other considerations in the design of statistical graphics - not only of efficiency, but also of complexity, structure, density, and even beauty." (Edward R Tufte, "Data-Ink Maximization and Graphical Design", Oikos Vol. 58 (2), 1990)

"Visual displays rich with data are not only an appropriate and proper complement to human capabilities, but also such designs are frequently optimal. If the visual task is contrast, comparison, and choice - as so often it is - then the more relevant information within eyespan, the better. Vacant, low-density displays, the dreaded posterization of data spread over pages and pages, require viewers to rely on visual memory - a weak skill - to make a contrast, a comparison, a choice." (Edward R Tufte, "Envisioning Information", 1990)

"We envision information in order to reason about, communicate, document, and preserve that knowledge - activities nearly always carried out on two-dimensional paper and computer screen. Escaping this flatland and enriching the density of data displays are the essential tasks of information design." (Edward R Tufte, "Envisioning Information", 1990)

"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)

"The use of the density scale to construct the histogram ensures that the area of each rectangle in the histogram will be proportional to the corresponding relative frequency. The formula for density can also be used when class widths are equal. However, when the intervals are of equal width, the extra arithmetic required to obtain the densities is unnecessary." (Roxy Peck et al, "Introduction to Statistics and Data Analysis" 4th Ed., 2012)

"Occlusion can be a major readability problem with scatterplots, because many dots could be overplotted on the same location. Size coding exacerbates the problem, as does the use of text labels. Continuous scatterplots use color coding at each pixel to indicate the density of overplotting, often in conjunction with transparency. Conceptually, this approach uses a derived attribute, overplot density, which can be calculated after the layout is computed. Practically, many hardware acceleration techniques sidestep the need to do this calculation explicitly." (Tamara Munzner, "Visualization Analysis and Design", 2014)

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

"When there are few data points, place the data labels directly on the data. Data density refers to the amount of data shown in a visualization through encodings (points, bars, lines, etc.). A common mistake is presenting too much data in a single data graph. The data itself can obscure the insight. It can make the chart unreadable because the data values are not discernible. Examples include: overlapping data points, too many lines in a line chart, or too many slices in a pie chart. Selecting the appropriate amount of data requires a delicate balance. It is your job to determine how much detail is necessary." (Kristen Sosulski, "Data Visualization Made Simple: Insights into Becoming Visual", 2018)

"Researchers have studied how accurately people can read information displayed in different types of plots. They have found the following ordering, from most to leasta ccurately judged (•) Positions along a common scale, like in a rug plot, strip plot, or dot plot (•) Positions on identical, nonaligned scales, like in a bar plot (•) Length, like in a stacked bar plot (•) Angle and slope, like in a pie chart (•) Area, like in a stacked line plot or bubble chart (•) Volume and density, like in a three-dimensional bar plot (•) Color saturation and hue, like when overplotting with semitransparent points."  (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)

"Smoothing and aggregating can help us see important features and relationships, but when we have only a handful of observations, smoothing techniques can be misleading. With just a few observations, we prefer rug plots over histograms, box plots, and density curves, and we use scatterplots rather than smooth curves and density contours. This may seem obvious, but when we have a large amount of data, the amount of data in a subgroup can quickly dwindle. This phenomenon is an example of the curse of dimensionality." (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)

"The preattentive processing of density occurs automatically and rapidly, without conscious effort or attention, and can be used in visual communication to create contrast and emphasize importance or relevance. This feature can be swiftly detected by the presence of varying numbers of objects (e.g., data points or shapes) in a given region of the space, rep‑resenting different quantities or values. For instance, in a chart or graph, a higher density of data points can be used to represent a larger quantity, a more significant trend, or a more exciting or energetic area. By making use of the preattentive processing of density, design‑ers can create effective visual designs that convey information quickly and efficiently to the viewer." (Leandro N de Castro, "Exploratory Data Analysis: Descriptive Analysis, Visualization, and Dashboard Design", 2025)

📉Graphical Representation: Missing Data (Just the Quotes)

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

"We often think, naïvely, that missing data are the primary impediments to intellectual progress - just find the right facts and all problems will dissipate. But barriers are often deeper and more abstract in thought. We must have access to the right metaphor, not only to the requisite information. Revolutionary thinkers are not, primarily, gatherers of facts, but weavers of new intellectual structures." (Stephen J Gould, "The Flamingo's Smile: Reflections in Natural History", 1985)

"Statistics depend on collecting information. If questions go unasked, or if they are asked in ways that limit responses, or if measures count some cases but exclude others, information goes ungathered, and missing numbers result. Nevertheless, choices regarding which data to collect and how to go about collecting the information are inevitable." (Joel Best, "More Damned Lies and Statistics: How numbers confuse public issues", 2004)

"People tend to give greater weight to the data that they have just been exposed to than other relevant data. […] This phenomenon, where people give greater attention to recent or easily available data, is often referred to as an availability error." (Alan Graham, "Developing Thinking in Statistics", 2006)

"There are many reasons for the existence of missing values: the failure of a sensor, different recording standards for different parts of a sample, or structural differences of the objects observed that make it impossible to record all attributes for all observed instances." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009)

"There are several key issues in the field of statistics that impact our analyses once data have been imported into a software program. These data issues are commonly referred to as the measurement scale of variables, restriction in the range of data, missing data values, outliers, linearity, and nonnormality." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"[…] events will always occur that cannot be foreseen by following a chain of logical deductive reasoning. Successful prediction requires intuitive leaps and/or information that is not part of the original data available." (John L Casti, "X-Events: The Collapse of Everything", 2012)

"Missing data is the blind spot of statisticians. If they are not paying full attention, they lose track of these little details. Even when they notice, many unwittingly sway things our way. Most ranking systems ignore missing values." (Kaiser Fung, "Numbersense: How To Use Big Data To Your Advantage", 2013)

"Having NUMBERSENSE means: (•) Not taking published data at face value; (•) Knowing which questions to ask; (•) Having a nose for doctored statistics. [...] NUMBERSENSE is that bit of skepticism, urge to probe, and desire to verify. It’s having the truffle hog’s nose to hunt the delicacies. Developing NUMBERSENSE takes training and patience. It is essential to know a few basic statistical concepts. Understanding the nature of means, medians, and percentile ranks is important. Breaking down ratios into components facilitates clear thinking. Ratios can also be interpreted as weighted averages, with those weights arranged by rules of inclusion and exclusion. Missing data must be carefully vetted, especially when they are substituted with statistical estimates. Blatant fraud, while difficult to detect, is often exposed by inconsistency." (Kaiser Fung, "Numbersense: How To Use Big Data To Your Advantage", 2013)

"Accuracy and coherence are related concepts pertaining to data quality. Accuracy refers to the comprehensiveness or extent of missing data, performance of error edits, and other quality assurance strategies. Coherence is the degree to which data - item value and meaning are consistent over time and are comparable to similar variables from other routinely used data sources." (Aileen Rothbard, "Quality Issues in the Use of Administrative Data Records", 2015)

"There are several key issues in the field of statistics that impact our analyses once data have been imported into a software program. These data issues are commonly referred to as the measurement scale of variables, restriction in the range of data, missing data values, outliers, linearity, and nonnormality." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"[…] people attempt to use highly flexible mathematical structures with large numbers of parameters that can be adjusted to fit the data, the result often being models that fit the data well but lack structural representation of the phenomena and thus are not predictive outside the range of the data. The situation is exacerbated by uncertainty regarding model parameters on account of insufficient data relative to model complexity, which in fact means uncertainty regarding the models themselves. More importantly from the standpoint of epistemology, the amount of available data is often miniscule in comparison to the amount needed for validation. The desire for knowledge has far outstripped experimental/observational capability. We are starved for data." (Edward R Dougherty, "The Evolution of Scientific Knowledge: From certainty to uncertainty", 2016)

"There are other problems with Big Data. In any large data set, there are bound to be inconsistencies, misclassifications, missing data - in other words, errors, blunders, and possibly lies. These problems with individual items occur in any data set, but they are often hidden in a large mass of numbers even when these numbers are generated out of computer interactions." (David S Salsburg, "Errors, Blunders, and Lies: How to Tell the Difference", 2017)

"Before progressing to analysis and visualization of the data, examine the data for inconsistencies and missing values. Data that fall outside an expected range, values that are missing or null, or have a different encoding or data type need to be addressed." (Gerald Benoît,"Introduction to Information Visualization: Transforming Data into Meaningful Information", 2019)

"Unless we’re collecting data ourselves, there’s a limit to how much we can do to combat the problem of missing data. But we can and should remember to ask who or what might be missing from the data we’re being told about. Some missing numbers are obvious […]. Other omissions show up only when we take a close look at the claim in question." (Tim Harford, "The Data Detective: Ten easy rules to make sense of statistics", 2020)

"Correlation does not imply causation: often some other missing third variable is influencing both of the variables you are correlating. […] The need for a scatterplot arose when scientists had to examine bivariate relations between distinct variables directly. As opposed to other graphic forms - pie charts, line graphs, and bar charts - the scatterplot offered a unique advantage: the possibility to discover regularity in empirical data (shown as points) by adding smoothed lines or curves designed to pass 'not through, but among them', so as to pass from raw data to a theory-based description, analysis, and understanding." (Michael Friendly & Howard Wainer, "A History of Data Visualization and Graphic Communication", 2021)

📉Graphical Representation: Views (Just the Quotes)

"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)

"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)

"The prevailing style of management must undergo transformation. A system cannot understand itself. The transformation requires a view from outside. The aim [...] is to provide an outside view - a lens - that I call a system of profound knowledge. It provides a map of theory by which to understand the organizations that we work in." (Dr. W. Edwards Deming, "The New Economics for Industry, Government, Education", 1994)

"Good numeric representation is a key to effective thinking that is not limited to understanding risks. Natural languages show the traces of various attempts at finding a proper representation of numbers. [...] The key role of representation in thinking is often downplayed because of an ideal of rationality that dictates that whenever two statements are mathematically or logically the same, representing them in different forms should not matter. Evidence that it does matter is regarded as a sign of human irrationality. This view ignores the fact that finding a good representation is an indispensable part of problem solving and that playing with different representations is a tool of creative thinking." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 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)

"Making a presentation is a moral act as well as an intellectual activity. The use of corrupt manipulations and blatant rhetorical ploys in a report or presentation - outright lying, flagwaving, personal attacks, setting up phony alternatives, misdirection, jargon-mongering, evading key issues, feigning disinterested objectivity, willful misunderstanding of other points of view - suggests that the presenter lacks both credibility and evidence. To maintain standards of quality, relevance, and integrity for evidence, consumers of presentations should insist that presenters be held intellectually and ethically responsible for what they show and tell. Thus consuming a presentation is also an intellectual and a moral activity." (Edward R Tufte, "Beautiful Evidence", 2006)

"Heat maps offer a good way to systematically identify risks, but from our point of view they have one problem - they focus on risk reduction, not risk leverage. [...] The point of the inverse heat map is to highlight opportunities that might be discarded out-of-hand because they are a gamble. If something is very unlikely" (the left-hand side of the heat map), it is not worth pursuing, but opportunities that are somewhat unlikely but would have a high payoff are attractive" (top right portion of the heat map)." (John W Boudreau et al, "Transformative HR: How Great Companies Use Evidence-Based Change for Sustainable Advantage", 2011)

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

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

"There's a strand of the data viz world that argues that everything could be a bar chart. That’s possibly true but also possibly a world without joy." (Amanda Cox, [interview in" ( Scott Berinato's "The Power of Visualization’s 'Aha!' Moments, Harvard Business Review] 2013)

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

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

"It’s the 'message' that decides the presentation. The numbers, visual, or text or a combination of these are to only support the way of putting the message across. This also changes the way one conceptualizes a graphic. The thought starts with the message and then gets into putting other related information together to support it instead of starting with the data and thinking of what to make of it [...] The advantage of taking this route is also that you are not just restricted by topics or numbers or just presenting “news.” You can go a step further and air your “views,” too, to make a point." (Raj Kamal, "Everyday Visuals as News", 2014)

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

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IT Professional with more than 25 years experience in IT in the area of full life-cycle of Web/Desktop/Database Applications Development, Software Engineering, Consultancy, Data Management, Data Quality, Data Migrations, Reporting, ERP implementations & support, Team/Project/IT Management, etc.