Here we are now at the middle of the fourth large part of this talk.
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• get nowhere

*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.

Building on last month's column about Bayes' Theorem, we introduce Bayesian inference and contrast it to frequentist inference.

Given a hypothesis and a model, the frequentist calculates the probability of different data generated by the model, *P*(data|model). When this probability to obtain the observed data from the model is small (e.g. `alpha` = 0.05), the frequentist rejects the hypothesis.

In contrast, the Bayesian makes direct probability statements about the model by calculating P(model|data). In other words, given the observed data, the probability that the model is correct. With this approach it is possible to relate the probability of different models to identify one that is most compatible with the data.

The Bayesian approach is actually more intuitive. From the frequentist point of view, the probability used to assess the veracity of a hypothesis, P(data|model), commonly referred to as the *P* value, does not help us determine the probability that the model is correct. In fact, the *P* value is commonly misinterpreted as the probability that the hypothesis is right. This is the so-called "prosecutor's fallacy", which confuses the two conditional probabilities *P*(data|model) for *P*(model|data). It is the latter quantity that is more directly useful and calculated by the Bayesian.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem *Nature Methods* **12**:277-278.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem *Nature Methods* **12**:277-278.

In our first column on Bayesian statistics, we introduce conditional probabilities and Bayes' theorem

*P*(B|A) = *P*(A|B) × *P*(B) / *P*(A)

This relationship between conditional probabilities *P*(B|A) and *P*(A|B) is central in Bayesian statistics. We illustrate how Bayes' theorem can be used to quickly calculate useful probabilities that are more difficult to conceptualize within a frequentist framework.

Using Bayes' theorem, we can incorporate our beliefs and prior experience about a system and update it when data are collected.

Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem *Nature Methods* **12**:277-278.

Oldford, R.W. & Cherry, W.H. Picturing probability: the poverty of Venn diagrams, the richness of eikosograms. (University of Waterloo, 2006)

Celebrate `pi` Day (March 14th) with splitting its digit endlessly. This year I use a treemap approach to encode the digits in the style of Piet Mondrian.

The art has been featured in Ana Swanson's Wonkblog article at the Washington Post—10 Stunning Images Show The Beauty Hidden in `pi`.

I also have art from 2013 `pi` Day and 2014 `pi` Day.

The split plot design originated in agriculture, where applying some factors on a small scale is more difficult than others. For example, it's harder to cost-effectively irrigate a small piece of land than a large one. These differences are also present in biological experiments. For example, temperature and housing conditions are easier to vary for groups of animals than for individuals.

The split plot design is an expansion on the concept of blocking—all split plot designs include at least one randomized complete block design. The split plot design is also useful for cases where one wants to increase the sensitivity in one factor (sub-plot) more than another (whole plot).

Altman, N. & Krzywinski, M. (2015) Points of Significance: Split Plot Design *Nature Methods* **12**:165-166.

1. Krzywinski, M. & Altman, N. (2014) Points of Significance: Designing Comparative Experiments *Nature Methods* **11**:597-598.

2. Krzywinski, M. & Altman, N. (2014) Points of Significance: Analysis of variance (ANOVA) and blocking *Nature Methods* **11**:699-700.

3. Blainey, P., Krzywinski, M. & Altman, N. (2014) Points of Significance: Replication *Nature Methods* **11**:879-880.

In an audience of 8 men and 8 women, chances are 50% that at least one has some degree of color blindness^{1}. When encoding information or designing content, use colors that is color-blind safe.