Let me tell you about something.

Distractions and amusements, with a sandwich and coffee.

Tango is a sad thought that is danced.
•
• think & dance

*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.

Celebrate Pi Approximation Day (July 22nd) with the art arm waving. This year I take the first 10,000 most accurate approximations (m/n, m=1..10,000) and look at their accuracy.

I turned to the spiral again after applying it to stack stacked ring plots of frequency distributions in Pi for the 2014 Pi Day.

Our 10th Points of Significance column! Continuing with our previous discussion about comparative experiments, we introduce ANOVA and blocking. Although this column appears to introduce two new concepts (ANOVA and blocking), you've seen both before, though under a different guise.

If you know the *t*-test you've already applied analysis of variance (ANOVA), though you probably didn't realize it. In ANOVA we ask whether the variation within our samples is compatible with the variation between our samples (sample means). If the samples don't all have the same mean then we expect the latter to be larger. The ANOVA test statistic (*F*) assigns significance to the ratio of these two quantities. When we only have two-samples and apply the *t*-test, *t*^{2} = *F*.

ANOVA naturally incorporates and partitions sources of variation—the effects of variables on the system are determined based on the amount of variation they contribute to the total variation in the data. If this contribution is large, we say that the variation can be "explained" by the variable and infer an effect.

We discuss how data collection can be organized using a randomized complete block design to account for sources of uncertainty in the experiment. This process is called blocking because we are blocking the variation from a known source of uncertainty from interfering with our measurements. You've already seen blocking in the paired *t*-test example, in which the subject (or experimental unit) was the block.

We've worked hard to bring you 20 pages of statistics primers (though it feels more like 200!). The column is taking a month off in August, as we shrink our error bars.

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

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

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — *t*-tests *Nature Methods* **11**:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, *P* values and *t*-tests *Nature Methods* **10**:1041-1042.

This month, Points of Significance begins a series of articles about experimental design. We start by returning to the two-sample and paired *t*-tests for a discussion of biological and experimental variability.

We introduce the concept of blocking using the paired *t*-test as an example and show how biological and experimental variability can be related using the correlation coefficient, *ρ*, and how its value imapacts the relative performance of the paired and two-sample *t*-tests.

We also emphasize that when reporting data analyzed with the paired t-test, differences in sample means (and their associated 95% CI error bars) should be shown—not the original samples—because the correlation in the samples (and its benefits) cannot be gleaned directly from the sample data.

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

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — *t*-tests *Nature Methods* **11**:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, *P* values and *t*-tests *Nature Methods* **10**:1041-1042.

Our May Points of Significance Nature Methods column jumps straight into dealing with skewed data with Non Parametric Tests.

We introduce non-parametric tests and simulate data scenarios to compare their performance to the *t*-test. You might be surprised—the *t*-test is extraordinarily robust to distribution shape, as we've discussed before. When data is highly skewed, non-parametric tests perform better and with higher power. However, if sample sizes are small they are limited to a small number of possible *P* values, of which none may be less than 0.05!

Krzywinski, M. & Altman, N. (2014) Points of Significance: Non Parametric Testing *Nature Methods* **11**:467-468.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part I — *t*-tests *Nature Methods* **11**:215-216.

Krzywinski, M. & Altman, N. (2013) Points of Significance: Significance, *P* values and *t*-tests *Nature Methods* **10**:1041-1042.

In the April Points of Significance Nature Methods column, we continue our and consider what happens when we run a large number of tests.

Observing statistically rare test outcomes is expected if we run enough tests. These are statistically, not biologically, significant. For example, if we run *N* tests, the smallest *P* value that we have a 50% chance of observing is 1–exp(–ln2/*N*). For *N* = 10^{k} this *P* value is *P*_{k}=10^{–k}ln2 (e.g. for 10^{4}=10,000 tests, *P*_{4}=6.9×10^{–5}).

We discuss common correction schemes such as Bonferroni, Holm, Benjamini & Hochberg and Storey's *q* and show how they impact the false positive rate (FPR), false discovery rate (FDR) and power of a batch of tests.

Krzywinski, M. & Altman, N. (2014) Points of Significance: Comparing Samples — Part II — Multiple Testing *Nature Methods* **11**:215-216.

*t*-tests *Nature Methods* **11**:215-216.

*P* values and *t*-tests *Nature Methods* **10**:1041-1042.