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Distractions and amusements, with a sandwich and coffee.

Thoughts rearrange, familiar now strange.
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*Martin Krzywinski, Inanc Birol, Steven Jones, Marco Marra*

Presented at Biovis 2012 (Visweek 2012). Content is drawn from my book chapter Visualization Principles for Scientific Communication (Martin Krzywinski & Jonathan Corum) in the upcoming open access Cambridge Press book Visualizing biological data - a practical guide (Seán I. O'Donoghue, James B. Procter, Kate Patterson, eds.), a survey of best practices and unsolved problems in biological visualization. This book project was conceptualized and initiated at the Vizbi 2011 conference.

If you are interested in guidelines for data encoding and visualization in biology, see our Visualization Principles Vizbi 2012 Tutorial and Nature Methods Points of View column by Bang Wong.

The 20 imperatives of information design

Create legible visualizations with a strong message. Make elements large enough to be resolved comfortably. Bin dense data to avoid sacrificing clarity.

Use exploratory tools (e.g. genome browsers) to discover patterns and validate hypotheses. Avoid using screenshots from these applications for communication – they are typically too complex and cluttered with navigational elements to be an effective static figure.

Our acuity is ~50 cycles/degree or about 1/200 (0.3 pt) at 10 inches. Ensure the reader can comfortably see detail by limiting resolution to no more than 50% of acuity. Where possible, elements that require visual separation should be at least 1 pt part.

Ensure data elements are at least 1 pt on a two-column Nature figure (6.22 in), 4 pixels on a 1920 horizontal resolution display, or 2 pixels on a typical LCD projector. These restrictions become challenges for large genomes.

Data on large genomes must be downsampled. Depict variation with min/max plots and consider hiding it when it is within noise levels. Help the reader notice significant outliers.

Map size of elements onto clearly legible symbols. Legibility and clarity are more important than precise positioning and sizing. Discretize sizes and positions to facilitate making meaningful comparisons.

A strong visual message has no uncertainty in its interpretation. Focus on a single theme by aggregating unnecessary detail.

Establishing context is helpful when emergent patterns in the data provide a useful perspective on the message. When data sets are large, it is difficult to maintain detail in the context layer because the density of points can visually overwhelm the area of interest. In this case, consider showing only the outliers in the data set.

The reader’s attention can be focused by increasing the salience of interesting patterns. Other complex data sets, such as networks, are shown more effectively when context is carefully edited or even removed.

Match the visual encoding to the hypothesis. Use encodings specific and sensitive to important patterns. Dense annotations should be independent of the core data in distinct visual layers.

Choose concise encodings over elaborate ones.

Accuracy and speed in detecting differences in visual forms depends on how information is presented. We judge relative lengths more accurately than areas, particularly when elements are aligned and adjacent. Our judgment of area is poor because we use length as a proxy, which causes us to systematically underestimate.

In addition to being transparent and predictable, visualizations must be robust with respect to the data. Changes in the data set should be reflected by proportionate changes in the visualization. Be wary of force-directed network layouts, which have low spatial autocorrelation. In general, these are neither sensitive nor specific to patterns of interest.

Well-designed figures illustrate complex concepts and patterns that may be difficult to express concisely in words. Figures that are clear, concise and attractive are effective – they form a strong connection with the reader and communicate with immediacy. These qualities can be achieved with methods of graphic design, which are based on theories of how we perceive, interpret and organize visual information.

The reader does not know what is important in a figure and will assume that any spatial or color variation is meaningful. The figure’s variation should come solely from data or act to organize information.

Including details not relevant to the core message of the figure can create confusion. Encapsulation should be done to the same level of detail and to the simplest visual form. Duplication in labels should be avoided.

When the data set embodies a natural hierarchy, use an encoding that emphasizes it clearly and memorably. The use hierarchy in layout (e.g. tabular form) and encoding can significantly improve a muddled figure.

Color is a useful encoding – the eye can distinguish about 450 levels of gray, 150 hues, and 10-60 levels of saturation, depending on the color – but our ability to perceive differences varies with context. Adjacent tones with different luminance values can interfere with discrimination, in interaction known as the luminance effect.

In an audience of 8 men and 8 women, chances are 50% that at least one has some degree of color blindness. Use a palette that is color-blind safe. In the palette below the 15 colors appear as 5-color tone progressions to those with color blindness. Additional encodings can be achieved with symbols or line thickness.

I have designed 15-color palettes for color blindess for each of the three common types of color blindness.

*Residual plots can be used to validate assumptions about the regression model.*

Continuing with our series on regression, we look at how you can identify issues in your regression model.

The difference between the observed value and the model's predicted value is the residual, `r = y_i - \hat{y}_i`, a very useful quantity to identify the effects of outliers and trends in the data that might suggest your model is inadequate.

We also discuss normal probability plots (or Q-Q plots) and show how these can be used to check that the residuals are normally distributed, which is one of the assumptions of regression (constant variance being another).

Altman, N. & Krzywinski, M. (2016) Points of Significance: Analyzing outliers: Influential or nuisance? *Nature Methods* **13**:281-282.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression *Nature Methods* **12**:1103-1104.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression *Nature Methods* **12**:999-1000.

*Some outliers influence the regression fit more than others.*

This month our column addresses the effect that outliers have on linear regression.

You may be surprised, but not all outliers have the same influence on the fit (e.g. regression slope) or inference (e.g. confidence or prediction intervals). Outliers with large leverage—points that are far from the sample average—can have a very large effect. On the other hand, if the outlier is close to the sample average, it may not influence the regression slope at all.

Quantities such as Cook's distance and the so-called hat matrix, which defines leverage, are useful in assessing the effect of outliers.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression *Nature Methods* **12**:1103-1104.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple Linear Regression *Nature Methods* **12**:999-1000.

Chirp, chirp, chirp but much better looking.

If you like these, check out my other typographical art posters.

Celebrate `\\pi` Day (March 14th) with colliding digits in space. This year, I celebrate the detection of gravitational waves at the LIGO lab and simulate the effect of gravity on masses created from the digits of `\\pi`.

Some strange things can happen.

The art is featured in the Gravity of Pi article on the Scientific American SA Visual blog.

Check out art from previous years: 2013 `\\pi` Day and 2014 `\\pi` Day and 2015 `\\pi` Day.

*Use alignment and consistency to untangle complex circuit diagrams.*

This month we apply the ideas presented in our column about drawing pathways to neural circuit diagrams. Neural circuits are networks of cells or regions, typically with a large number of variables, such as cell and neurotransmitter type.

We discuss how to effectively route arrows, how to avoid pitfalls of redundant encoding and suggest ways to encorporate emphasis in the layout.

Hunnicutt, B.J. & Krzywinski, M. (2016) Points of View: Neural circuit diagrams. Nature Methods 13:189.

Hunnicutt, B.J. & Krzywinski, M. (2016) Points of Viev: Pathways. Nature Methods 13:5.

Wong, B. (2010) Points of Viev: Gestalt principles (part 1). Nature Methods 7:863.

Wong, B. (2010) Points of Viev: Gestalt principles (part 2). Nature Methods 7:941.