📉Graphical Representation: Variation (Just the Quotes)

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

"Graphical integrity is more likely to result if these six principles are followed:

The representation of numbers, as physically measured on the surface of the graphic itself, should be directly proportional to the numerical quantities represented.

Clear, detailed, and thorough labeling should be used to defeat graphical distortion and ambiguity. Write out explanations of the data on the graphic itself. Label important events in the data.

Show data variations, not design variations. 

In time-series displays of money, deflated and standardized units of monetary measurements are nearly always better than nominal units.

The number of information-carrying (variable) dimensions depicted should not exceed the number of dimensions in the data.

Graphics must not quote data out of context." (Edward R Tufte, "The Visual Display of Quantitative Information", 1983)

"One can hide data in a variety of ways. One method that occurs with some regularity is hiding the data in the grid. The grid is useful for plotting the points, but only rarely afterwards. Thus to display data badly, use a fine grid and plot the points dimly [...] A second way to hide the data is in the scale. This corresponds to blowing up the scale (i.e., looking at the data from far away) so that any variation in the data is obscured by the magnitude of the scale. One can justify this practice by appealing to 'honesty requires that we start the scale at zero', or other sorts of sophistry." (Howard Wainer, "How to Display Data Badly", The American Statistician Vol. 38(2), 1984)

"A good description of the data summarizes the systematic variation and leaves residuals that look structureless. That is, the residuals exhibit no patterns and have no exceptionally large values, or outliers. Any structure present in the residuals indicates an inadequate fit. Looking at the residuals laid out in an overlay helps to spot patterns and outliers and to associate them with their source in the data." (Christopher H Schrnid, "Value Splitting: Taking the Data Apart", 1991)

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

"Comparing series visually can be misleading […]. Local variation is hidden when scaling the trends. We first need to make the series stationary (removing trend and/or seasonal components and/or differences in variability) and then compare changes over time. To do this, we log the series (to equalize variability) and difference each of them by subtracting last year’s value from this year’s value." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"In general. statistical graphics should be moderately greater in length than in height. And, as William Cleveland discovered, for judging slopes and velocities up and down the hills in time-series, best is an aspect ratio that yields hill - slopes averaging 45°, over every cycle in the time-series. Variations in slopes are best detected when the slopes are around 45°, uphill or downhill." (Edward R Tufte, "Beautiful Evidence", 2006)

"Graphical displays are often constructed to place principal focus on the individual observations in a dataset, and this is particularly helpful in identifying both the typical positions of datapoints and unusual or influential cases. However, in many investigations, principal interest lies in identifying the nature of underlying trends and relationships between variables, and so it is often helpful to enhance graphical displays in ways which give deeper insight into these features. This can be very beneficial both for small datasets, where variation can obscure underlying patterns, and large datasets, where the volume of data is so large that effective representation inevitably involves suitable summaries." (Adrian W Bowman, "Smoothing Techniques for Visualisation" [in "Handbook of Data Visualization"], 2008)

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

"A signal is a useful message that resides in data. Data that isn’t useful is noise. […] When data is expressed visually, noise can exist not only as data that doesn’t inform but also as meaningless non-data elements of the display (e.g. irrelevant attributes, such as a third dimension of depth in bars, color variation that has no significance, and artificial light and shadow effects)." (Stephen Few, "Signal: Understanding What Matters in a World of Noise", 2015)

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

"Another word of caution for dot plots that show changes over time. The dot plot is, by definition, a summary chart. It does not show all of the data in the intervening years. If the data between the two dots generally move in the same direction, a dot plot is sufficient. But if the data contain sharp variations year by year, a dot plot will obscure that pattern (as it also does for bar charts)." (Jonathan Schwabish, "Better Data Visualizations: A guide for scholars, researchers, and wonks", 2021)

"The urn model is a simple abstraction that can be helpful for understanding variation.This model sets up a container (an urn, which is like a vase or a bucket) full of identical marbles that have been labeled, and we use the simple action of drawing marbles from the urn to reason about sampling schemes, randomized controlled experiments, and measurement error. For each of these types of variation, the urn model helps us estimate the size of the variation using either probability or simulation." (Sam Lau et al, "Learning Data Science: Data Wrangling, Exploration, Visualization, and Modeling with Python", 2023)

"Index number shows by its variations the changes in a magnitude which is not susceptible either of accurate measurement in itself or of direct valuation in practice." (Francis Y Edgeworth)