Let me tell you about something.

Distractions and amusements, with a sandwich and coffee.

Trance opera.
• Spente le Stelle

Typography geek? If you like the geometry and mathematics of these posters, you may enjoy something more lettered. Visions of type: Type Peep Show: The Private Curves of Letters posters.

Two styles of posters are available: folded paths, which show Pi on a path that maximizes adjacent prime digits, and frequency circles, which colourfully depicts the ratio of digits in groupings of 3 or 6.

Curious how these were made? Read about the method.

Sources of noise in experiments can be mitigated and assessed by nested designs. This kind of experimental design naturally models replication, which was the topic of last month's column.

Nested designs are appropriate when we want to use the data derived from experimental subjects to make general statements about populations. In this case, the subjects are *random* factors in the experiment, in contrast to *fixed* factors, such as we've seen previously.

In ANOVA analysis, random factors provide information about the amount of noise contributed by each factor. This is different from inferences made about fixed factors, which typically deal with a change in mean. Using the F-test, we can determine whether each layer of replication (e.g. animal, tissue, cell) contributes additional variation to the overall measurement.

Krzywinski, M., Altman, N. & Blainey, P. (2014) Points of Significance: Nested designs *Nature Methods* **11**:977-978.

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

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.

It's fitting that the column published just before Labor day weekend is all about how to best allocate labor.

Replication is used to decrease the impact of variability from parts of the experiment that contribute noise. For example, we might measure data from more than one mouse to attempt to generalize over all mice.

It's important to distinguish technical replicates, which attempt to capture the noise in our measuring apparatus, from biological replicates, which capture biological variation. The former give us no information about biological variation and cannot be used to directly make biological inferences. To do so is to commit *pseudoreplication*. Technical replicates are useful to reduce the noise so that we have a better chance to detect a biologically meaningful signal.

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

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.

I was commissioned by Scientific American to create an information graphic that showed how our genomes are more similar to those of the chimp and bonobo than to the gorilla.

I had about 5 x 5 inches of print space to work with. For 4 genomes? No problem. Bring out the Hilbert curve!

To accompany the piece, I will be posting to the Scientific American blog about the process of creating the figure. And to emphasize that the *genome is not a blueprint*!

As part of this project, I created some Hilbert curve art pieces. And while exploring, found thousands of Hilbertonians!

Celebrate Pi Approximation Day (July 22nd) with the art of 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.

*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.