The Points of Significance column was launched in September 2013 as an educational resource to authors and to provide practical suggestions about best practices in statistical analysis and reporting.
This month we launch a new column "Points of Significance" devoted to statistics, a topic of profound importance for biological research, but one that often doesn’t receive the attention it deserves.
The "aura of exactitude" that often surrounds statistics is one of the main notions that the Points of Significance column will attempt to dispel, while providing useful pointers on using and evaluating statistical measures.
—Dan Evanko, Let's Give Statistics the Attention it Deserves in Biological Research
In February 2015, Nature Methods announced that the entire Points of Significance collection will be free.
When Nature Methods launched the Points of Significance column over a year ago we were hopeful that those biologists with a limited background in statistics, or who just needed a refresher, would find it accessible and useful for helping them improve the statistical rigor of their research. We have since received comments from researchers and educators in fields ranging from biology to meteorology who say they read the column regularly and use it in their courses. Hearing that the column has had a wider impact than we anticipated has been very encouraging and we hope the column continues for quite some time.
—Dan Evanko, Points of Significance now free access
The pieces range from comments, to advice on very specific experimental approaches, to the entire collection of the Points of Significance columns that address basic concepts in statistics in an experimental biology context. These columns, originally published in Nature Methods thanks to Martin Krzywinski and guest editor Naomi Altman, have already proven very popular with readers and teachers. Finally, the collection presents a web tool to create box plots among other resources.
—Veronique Kiermer, Statistics for biologists—A free Nature Collection
Each column is written with continuity and consistency in mind. Our goal is to never rely on concepts that we have not previously discussed. We do not assume previous statistical knowledge—only basic math. Concepts are illustrated using practical examples that embody the ideas without extraneous complicated details. All of the figures are designed with the same approach—as simple and self-contained as possible.
Apply visual grouping principles to add clarity to information flow in pathway diagrams.
We draw on the Gestalt principles of connection, grouping and enclosure to construct practical guidelines for drawing pathways with a clear layout that maintains hierarchy.
We include tips about how to use negative space and align nodes to emphasizxe groups and how to effectively draw curved arrows to clearly show paths.
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.
When multiple variables are associated with a response, the interpretation of a prediction equation is seldom simple.
This month we continue with the topic of regression and expand the discussion of simple linear regression to include more than one variable. As it turns out, although the analysis and presentation of results builds naturally on the case with a single variable, the interpretation of the results is confounded by the presence of correlation between the variables.
By extending the example of the relationship of weight and height—we now include jump height as a second variable that influences weight—we show that the regression coefficient estimates can be very inaccurate and even have the wrong sign when the predictors are correlated and only one is considered in the model.
Care must be taken! Accurate prediction of the response is not an indication that regression slopes reflect the true relationship between the predictors and the response.
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.
Students generated images published in Fast Diploidization in Close Mesopolyploid Relatives of Arabidopsis.
Students also learned how to use hive plots to show synteny.
Mandakova, T. et al. Fast Diploidization in Close Mesopolyploid Relatives of Arabidopsis The Plant Cell, Vol. 22: 2277-2290, July 2010
Choose your own dust adventure!
Nobody likes dusting but everyone should find dust interesting.
Working with Jeannie Hunnicutt and with Jen Christiansen's art direction, I created this month's Scientific American Graphic Science visualization based on a recent paper The Ecology of microscopic life in household dust.
We have also written about the making of the graphic, for those interested in how these things come together.
Barberan A et al. (2015) The ecology of microscopic life in household dust. Proc. R. Soc. B 282: 20151139.
A very large list of named colors generated from combining some of the many lists that already exist (X11, Crayola, Raveling, Resene, wikipedia, xkcd, etc).
For each color, coordinates in RGB, HSV, XYZ, Lab and LCH space are given along with the 5 nearest, as measured with ΔE, named neighbours.
I also provide a web service. Simply call this URL with an RGB string.
It is possible to predict the values of unsampled data by using linear regression on correlated sample data.
This month, we begin our column with a quote, shown here in its full context from Box's paper Science and Statistics.
In applying mathematics to subjects such as physics or statistics we make tentative assumptions about the real world which we know are false but which we believe may be useful nonetheless. The physicist knows that particles have mass and yet certain results, approximating what really happens, may be derived from the assumption that they do not. Equally, the statistician knows, for example, that in nature there never was a normal distribution, there never was a straight line, yet with normal and linear assumptions, known to be false, he can often derive results which match, to a useful approximation, those found in the real world.
—Box, G. J. Am. Stat. Assoc. 71, 791–799 (1976).
This column is our first in the series about regression. We show that regression and correlation are related concepts—they both quantify trends—and that the calculations for simple linear regression are essentially the same as for one-way ANOVA.
While correlation provides a measure of a specific kind of association between variables, regression allows us to fit correlated sample data to a model, which can be used to predict the values of unsampled data.
Altman, N. & Krzywinski, M. (2015) Points of Significance: Simple Linear Regression Nature Methods 12:999-1000.
Altman, N. & Krzywinski, M. (2015) Points of significance: Association, correlation and causation Nature Methods 12:899-900.
Krzywinski, M. & Altman, N. (2014) Points of significance: Analysis of variance (ANOVA) and blocking. Nature Methods 11:699-700.
Correlation implies association, but not causation. Conversely, causation implies association, but not correlation.
This month, we distinguish between association, correlation and causation.
Association, also called dependence, is a very general relationship: one variable provides information about the other. Correlation, on the other hand, is a specific kind of association: an increasing or decreasing trend. Not all associations are correlations. Moreover, causality can be connected only to association.
We discuss how correlation can be quantified using correlation coefficients (Pearson, Spearman) and show how spurious corrlations can arise in random data as well as very large independent data sets. For example, per capita cheese consumption is correlated with the number of people who died by becoming tangled in bedsheets.
Altman, N. & Krzywinski, M. (2015) Points of Significance: Association, correlation and causation Nature Methods 12:899-900.
For making probabilistic inferences, a graph is worth a thousand words.
This month we continue with the theme of Bayesian statistics and look at Bayesian networks, which combine network analysis with Bayesian statistics.
In a Bayesian network, nodes represent entities, such as genes, and the influence that one gene has over another is represented by a edge and probability table (or function). Bayes' Theorem is used to calculate the probability of a state for any entity.
In our previous columns about Bayesian statistics, we saw how new information (likelihood) can be incorporated into the probability model (prior) to update our belief of the state of the system (posterior). In the context of a Bayesian network, relationships called conditional dependencies can arise between nodes when information is added to the network. Using a small gene regulation network we show how these dependencies may connect nodes along different paths.
Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayesian Statistics Nature Methods 12:277-278.
Puga, J.L, Krzywinski, M. & Altman, N. (2015) Points of Significance: Bayes' Theorem Nature Methods 12:277-278.