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pi day: beautiful

Visualization Tour, Melbourne, October 9–20, 2014

visualization + design

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.

Pi Approximation Day Art Posters — July 22, 2014

The never-repeating digits of π can be approximated by 22/7 = 3.142857 to within 0.04%.

This 22/7 ratio is celebrated each year on July 22nd. If you like hand waving or back-of-envelope mathematics, this day is for you.

These pages artistically and mathematically explore rational approximations to π .

Want more math + art? Discover the Accidental Similarity Number and this year's Pi Day Art. Find humor in my poster of the first 2,000 4s of Pi.

getting it mostly right

Curiously, this rational approximation of π is more accurate than using the first three digits 3.14 which are accurate within 0.05% and are celebrated on π Day on March 14th. The Approximation Day is 20% more accurate!

art of Pi rational approximation

The poster shows the accuracy of 10,000 rational approximations of π for each m/n and m=1..10,000. The details behind the method are below.

Pi Approximation Day Art Poster | July 22nd is Pi Approximation Day. Celebrate with this post-modern poster. (PNG, BUY ARTWORK)

Nested Designs—Assessing Sources of Noise

Mon 29-09-2014

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.

Nature Methods Points of Significance column: Nested designs. (read)

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.

Replication—Quality over Quantity

Tue 02-09-2014

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.

Nature Methods Points of Significance column: Replication. (read)

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.

Monkeys on a Hilbert Curve—Scientific American Graphic

Tue 19-08-2014

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!

Our genomes are much more similar to the chimp and bonobo than to the gorilla. And, we're practically still Denisovans. (details)

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!

Happy Pi Approximation Day— π, roughly speaking 10,000 times

Wed 13-08-2014

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.

Accuracy of the first 10,000 m/n approximations of Pi. (details)

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

Frequency distribution of digits of Pi in groups of 4 up to digit 4,988. (details)

Analysis of Variance (ANOVA) and Blocking—Accounting for Variability in Multi-factor Experiments

Mon 07-07-2014

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.

Nature Methods Points of Significance column: Analysis of variance (ANOVA) and blocking. (read)

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, t2 = 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.

Designing Experiments—Coping with Biological and Experimental Variation

Thu 29-05-2014

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.

Nature Methods Points of Significance column: Designing Comparative Experiments. (read)

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.