📉Graphical Representation: Large Values (Just the Quotes)

"Huge numbers are commonplace in our culture, but oddly enough the larger the number the less meaningful it seems to be." (Albert Sukoff, "Lotsa Hamburgers", Saturday Review of the Society, 1973)

"We know the laws of trial and error, of large numbers and probabilities. We know that these laws are part of the mathematical and mechanical fabric of the universe, and that they are also at play in biological processes. But, in the name of the experimental method and out of our poor knowledge, are we really entitled to claim that everything happens by chance, to the exclusion of all other possibilities?" (Albert Claude, [Nobel Prize Lecture], 1974)

"A graph presents a limited number of figures in a bold and forceful manner. To do this it usually must omit a large number of figures available on the subject. The choice of what graphic format to use is largely a matter of deciding what figures have the greatest significance to the intended reader and what figures he can best afford to skip." (Peter H Selby, "Interpreting Graphs and Tables", 1976)

"The logarithm is an extremely powerful and useful tool for graphical data presentation. One reason is that logarithms turn ratios into differences, and for many sets of data, it is natural to think in terms of ratios. […] Another reason for the power of logarithms is resolution. Data that are amounts or counts are often very skewed to the right; on graphs of such data, there are a few large values that take up most of the scale and the majority of the points are squashed into a small region of the scale with no resolution." (William S. Cleveland, "Graphical Methods for Data Presentation: Full Scale Breaks, Dot Charts, and Multibased Logging", The American Statistician Vol. 38 (4) 1984)

"The trouble with integers is that we have examined only the small ones. Maybe all the exciting stuff happens at really big numbers, ones we can’t get our hand on or even begin to think about in any very definite way. So maybe all the action is really inaccessible and we’re just fiddling around. Our brains have evolved to get us out of the rain, find where the berries are, and keep us from getting killed. Our brains did not evolve to help us grasp really large numbers or to look at things in a hundred thousand dimensions." (Paul Hauffman, "The Man Who Loves Only Numbers", The Atlantic Magazine, Vol 260, No 5, 1987)

"The law of truly large numbers states: With a large enough sample, any outrageous thing is likely to happen." (Frederick Mosteller, "Methods for Studying Coincidences Journal of the American Statistical Association, Volume 84, 1989)

"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)

"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)

"Data that are skewed toward large values occur commonly. Any set of positive measurements is a candidate. Nature just works like that. In fact, if data consisting of positive numbers range over several powers of ten, it is almost a guarantee that they will be skewed. Skewness creates many problems. There are visualization problems. A large fraction of the data are squashed into small regions of graphs, and visual assessment of the data degrades. There are characterization problems. Skewed distributions tend to be more complicated than symmetric ones; for example, there is no unique notion of location and the median and mean measure different aspects of the distribution. There are problems in carrying out probabilistic methods. The distribution of skewed data is not well approximated by the normal, so the many probabilistic methods based on an assumption of a normal distribution cannot be applied." (William S Cleveland, "Visualizing Data", 1993)

"The logarithm is one of many transformations that we can apply to univariate measurements. The square root is another. Transformation is a critical tool for visualization or for any other mode of data analysis because it can substantially simplify the structure of a set of data. For example, transformation can remove skewness toward large values, and it can remove monotone increasing spread. And often, it is the logarithm that achieves this removal." (William S Cleveland, "Visualizing Data", 1993)

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

"Comparisons are the lifeblood of empirical studies. We can’t determine if a medicine, treatment, policy, or strategy is effective unless we compare it to some alternative. But watch out for superficial comparisons: comparisons of percentage changes in big numbers and small numbers, comparisons of things that have nothing in common except that they increase over time, comparisons of irrelevant data. All of these are like comparing apples to prunes." (Gary Smith, "Standard Deviations", 2014)