# Balancing a centrifuge

I saw this cute little paper on arxiv about balancing a centrifuge: Peil & Hauryliuk (2010) A new spin on spinning your samples: balancing rotors in a non-trivial manner. Let us have a look at the maths of balancing a centrifuge.

The way I think most people (including myself) balance their samples is to put them opposite of each other, just like Peil & Hauryliuk write. However, there are many more balanced configurations, some of which look really weird. The authors generate three balanced configurations with increasing oddity, show them to researchers and ask them whether they are balanced. About half, 30% and 15% of them identified each configuration as balanced. Here are the configurations:

(Drawn after their paper.)

Take a rotor in a usual bench top centrifuge. It’s a large, in itself balanced, piece of metal with holes to put microcentrifuge tubes in. We assume that all tubes have the same mass m and that the holes are equally spaced. The rotor will spin around its own axis, helping us separate samples and pellet precipitates etc. When the centrifuge is balanced, the centre of mass of the samples will be aligned with the axis of rotation. So, if we place a two-dimensional coordinate system on the axis of rotation like so,

the tubes are positioned on a circle around it:

$x_i = r \cos {\theta_i}$
$y_i = r \sin {\theta_i}$

The angle to each position in the rotor will be

$\theta(i) = \dfrac{2\pi(i - 1)}{N}$

where i is the position in question, starting at 1, and N the number of positions in the rotor. Let’s label each configuration by the numbers of the positions that are occupied. So we could talk about (1, 16)30 as the common balanced pair of tubes in a 30-position rotor. (Yeah, I know, counting from 1 is a lot more confusing than counting from zero. Let’s view it as a kind of practice for dealing with genomic coordinates.)

We express the position of each tube (treated as a point mass) as a vector. Since we put the origin on the axis of rotation, these vectors have to sum to zero for the centrifuge to be balanced.

$\sum \limits_{i} {m\mathbf{r_i}} = \mathbf{0}$

Since the masses are equal, they can be removed, as can the radius, which is constant, and we can consider the x and y coordinates separately.

$\left(\begin{array}{c} \sum \limits_{i} {\cos {\theta(i)}} \\ \sum \limits_{i} {\sin {\theta(i)}} \end{array}\right) = \left(\begin{array}{c} 0 \\ 0 \end{array}\right)$

For the (1, 16)30 configuration, the vectors are

$\left(\begin{array}{c} \cos {\theta(1)} \\ \sin {\theta(1)} \end{array}\right) + \left(\begin{array}{c} \cos {\theta(16)} \\ \sin {\theta(16)} \end{array}\right) = \left(\begin{array}{c} \cos {0} \\ \sin {0} \end{array}\right) + \left(\begin{array}{c} \cos {\pi} \\ \sin {\pi} \end{array}\right) = \left(\begin{array}{c} 1 \\ 0 \end{array}\right) + \left(\begin{array}{c} -1 \\ 0 \end{array}\right)$

So we haven’t been deluding ourselves. This configuration is balanced. That is about as much maths as I’m prepared to do in LaTex in a WordPress blog editor. So let’s implement this in R code:

library(magrittr)
theta <- function(n, N) (n - 1) * 2 * pi / N
tube <- function(theta) c(cos(theta), sin(theta))


Now, we can look at Peil & Hauryliuk’s configurations, for instance the first (1, 11, 14, 15, 21, 29, 30)30

positions <- c(1, 11, 14, 15, 21, 29, 30)
tubes <- positions %>% lapply(theta, N = 30) %>% lapply(tube)
c(sum(unlist(lapply(tubes, function(x) x[1]))),
sum(unlist(lapply(tubes, function(x) x[2]))))


The above code 1) defines the configuration; 2) turns positions into angles and then tube coordinates; and 3) sums the x and y coordinates separately. The result isn’t exactly zero (for computational reasons), but close enough. Putting in their third configuration, (4, 8, 14, 15, 21, 27, 28)30, we again get almost zero. Even this strange-looking configuration seems to be balanced.

I’m biased because I read the text first, but if someone asked me, I would have to think about the first two configurations, and there is no way I would allow a student to run with the third if I saw it in the lab. That conservative attitude, though not completely scientific, might not be the worst thing. Centrifuge accidents are serious business, and as the authors note:

Finally, non-symmetric arrangement (Fig. 1C) was recognized as balanced by 17% of researchers. Some of these were actually calculating moment of inertia, i.e. were coming to solution knowingly, the rest where basically guessing. The latter should be banished from laboratory practice, since these people are ready to make dangerous decisions without actual understanding of the case, which renders them extremely dangerous in the laboratory settings.

(Plotting code for the first figure is on Github.)

# R in genomics @ SciLifeLab, Solna

Dear diary,

I went to the Stockholm R useR group meetup on R in genomics at the Stockholm node of SciLifeLab. It was nice. If I had worked a bit closer I would attend meetups all the time. I even got to be pretentious with my notebook while waiting for the train.

The speakers were:

Jakub Orzechowski Westholm on R and genomics in general. He demonstrated genome browser-style tracks with Gviz, some GenomicRanges, and a couple of common plots of gene expression data. I have been on the fence about what package I should use for drawing genes and variants along the genome. I should play with Gviz.

Daniel Klevebring on clinical sequencing and how he uses R (not that much) in sequencing pipelines aimed at targeting the right therapy to patients based on the mutations in their cancer cells. He mentioned some getopt snippets for getting R to play nicely on the command line, which is something I should definitely try more!

Finally, Arvind Singh Mer on predictive modelling for clinical genomics (like the abovementioned ClinSeq data). He showed the caret package for machine learning, with an elastic net regression.

I don’t know the rest of the audience, so maybe the choice to gear talks towards the non-bio* person was spot on, but that made things a bit less interesting for me. For instance, in Jakub’s talk about gene expression, I would’ve preferred more about the messy stuff: how to make that nice gene-by-sample matrix in the first place, and if R can be of any help in that process; also, in the other end, what models one would use after that first pass of visualisation. But this isn’t a criticism of the presenters — time and complexity constraints apply. (If I was asked to present how I use R any demos would be toy analyses of clean datasets. That is the way these things go.)

We also heard repeated praise for and recommendations of the hadleyverse and data.table. I’m not a data.tabler myself, but I probably should be. And I completely agree about the value of dplyr — there’s this one analysis where a couple of lines with dplyr changed it from ”argh, do I have to rewrite this in C?” to being workable. I think we also saw all the three plotting systems: base graphics, ggplot2 and lattice in action.

# Finding the distance from ChIP signals to genes

I’ve had a couple of months off from blogging. Time for some computer-assisted biology! Robert Griffin asks on Stack Exchange about finding the distance between HP1 binding sites and genes in Drosophila melanogaster.  We can get a rough idea with some public chromatin immunoprecipitation data, R and the wonderful BEDTools.

### Finding some binding sites

There are indeed some ChIP-seq datasets on HP1 available. I looked up these ones from modENCODE: modENCODE_3391 and modENCODE_3392, using two different antibodies for Hp1b in 16-24 h old embroys. I’m not sure since the modENCODE site doesn’t seem to link datasets to publications, but I think this is the paper where the results are reported: A cis-regulatory map of the Drosophila genome (Nègre & al 2011).

What they’ve done, in short, is cross-linking with formaldehyde, sonicate DNA into fragments, capture fragments with either of the two antibodies and sequence those fragments. They aligned reads with Eland (Illumina’s old proprietary aligner) and called peaks (i.e. regions where there is a lot of reads, which should reflect regions bound by Hp1b) with MACS. We can download their peaks in general feature format.

I don’t know whether there is any way to make completely computation predictions of Hp1 binding sites but I doubt it.

### Some data cleaning

The files are available from ftp, and for the below analysis I’ve unzipped them and called them modENCODE_3391.gff3 and modENCODE_3392.gff3. GFF is one of all those tab separated text files that people use for genomic coordinates. If you do any bioinformatics type work you will have to convert back and forth between them and I suggest bookmarking the UCSC Genome Browser Format FAQ.

Even when we trust in their analysis, some processing of files is always required. In this case, MACS sometimes outputs peaks with negative start coordinates in the beginning of a chromosome. BEDTools will have none of that, because ”malformed GFF entry at line … Start was greater than end”. In this case, it happens only at a few lines, and I decided to set those start coordinates to 1 instead.

We need a small script to solve that. As I’ve written before, any language will do, but I like R and tend to do my utility scripting in R (and bash). If the files were incredibly huge and didn’t fit in memory, we’d have to work through the files line by line or chunk by chunk. But in this case we can just read everything at once and operate on it with vectorised R commands, and then write the table again.

modENCODE_3391 <- read.table("modENCODE_3391.gff3", stringsAsFactors=F, sep="\t")
modENCODE_3392 <- read.table("modENCODE_3392.gff3", stringsAsFactors=F, sep="\t")

fix.coord <- function(gff) {
gff$V4[which(gff$V4 < 1)] <- 1
gff
}

write.gff <- function(gff, file) {
write.table(gff, file=file, row.names=F, col.names=F,
quote=F, sep="\t")
}

write.gff(fix.coord(modENCODE_3391), file="cleaned_3391.gff3")
write.gff(fix.coord(modENCODE_3392), file="cleaned_3392.gff3")


### Flybase transcripts

To find the distance to genes, we need to know where the genes are. The best source is probably the annotation made by Flybase, which I downloaded from the Ensembl ftp in General transfer format (GTF, which is close enough to GFF that we don’t have to care about the differences right now).

This file contains a lot of different features. We extract the transcripts and find where the transcript model starts, taking into account whether the transcript is in the forward or reverse direction (this information is stored in columns 4, 5 and 7 of the GTF file). We store this in a new GTF file of transcript start positions, which is the one we will feed to BEDTools:

ensembl <- read.table("Drosophila_melanogaster.BDGP5.75.gtf",
stringsAsFactors=F, sep="\t")

transcript <- subset(ensembl, V3=="transcript")
transcript.start <- transcript
transcript.start$V3 <- "transcript_start" transcript.start$V4 <- transcript.start$V5 <- ifelse(transcript.start$V7 == "+",
transcript$V4, transcript$V5)

write.gff(transcript.start, file="ensembl_transcript_start.gtf")


### Finding distance with BEDTools

Time to find the closest feature to each transcript start! You could do this in R with GenomicRanges, but I like BEDTools. It’s a command line tool, and if you haven’t already you will need to download and compile it, which I recall being painless.

bedtools closest is the command that finds, for each feature in one file, the closest feature in the other file. The -a and -b flags tells BEDTools which files to operate on, and the -d flag that we also want it to output the distance. BEDTools writes output to standard out, so we use ”>” to capture it in a text file.

Here is the bash script. I put the above R code in clean_files.R and added it as an Rscript line at the beginning, so I could run it all with one file.

#!/bin/bash
Rscript clean_files.R

bedtools closest -d -a ensembl_transcript_start.gtf -b cleaned_3391.gff3 \
> closest_element_3391.txt
bedtools closest -d -a ensembl_transcript_start.gtf -b cleaned_3392.gff3 \
> closest_element_3392.txt


### Some results

With the resulting file we can go back to R and ggplot2 and draw cute graphs like this, which shows the distribution of distances from transcript to Hp1b peak for protein coding and noncoding transcripts separately. Note the different y-scales (there are way more protein coding genes in the annotation) and the 10-logarithm plus one transformation on the x-axis. The plus one is to show the zeroes; BEDTools returns a distance of 0 for transcripts that overlap a Hp1b site.

closest_3391 <- read.table("~/blogg/dmel_hp1/closest_element_3391.txt", header=F, sep="\t")

library(ggplot2)
qplot(x=log10(V19 + 1), data=subset(closest_3391, V2 %in% c("protein_coding", "ncRNA"))) +
facet_wrap(~V2, scale="free_y")


Or by merging the datasets from different antibodies, we can draw this strange beauty, which pretty much tells us that the antibodies do not give the same result in terms of the closest feature. To figure out how they differ, one would have to look more closely into the genomic distribution of the peaks.

closest_3392 <- read.table("~/blogg/dmel_hp1/closest_element_3392.txt", header=F, sep="\t")

combined <- merge(closest_3391, closest_3392,
by.x=c("V1", "V2","V4", "V5", "V9"),
by.y=c("V1", "V2","V4", "V5", "V9"))

qplot(x=log10(V19.x+1), y=log10(V19.y+1), data=combined)


(If you’re wondering about the points that end up below 0, those are transcripts where there are no peaks called on that chromosome in one of the datasets. BEDTools returns -1 for those that lack matching features on the same chromosome and R will helpfully transform them to -Inf.)

### About the DGRP

The question mentioned the DGRP. I don’t know that anyone has looked at ChIP in the DGRP lines, but wouldn’t that be fun? Quantitative genetics of DNA binding protein variation in DGRP and integration with eQTL … What one could do already, though, is take the interesting sites of Hp1 binding and overlap them with the genetic variants of the DGRP lines. I don’t know if that would tell you much — does anyone know what kind of variant would affect Hp1 binding?

Happy hacking!

# More fun with %.% and %>%

The %.% operator in dplyr allows one to put functions together without lots of nested parentheses. The flanking percent signs are R’s way of denoting infix operators; you might have used %in% which corresponds to the match function or %*% which is matrix multiplication. The %.% operator is also called chain, and what it does is rearrange the call to pass its left hand side on as a parameter to the right hand side function. As noted in the documentation this makes function calls read from left to right instead of inside and out. Yesterday we we took a simulated data frame, called data, and calculated some summary statistics. We could put the entire script together with %.%:

library(dplyr)
data %.%
melt(id.vars=c("treatment", "sex")) %.%
group_by(sex, treatment, variable) %.%
summarise(mean(value))


I haven’t figured out what would be the best indentation here, but I think this looks pretty okay. Of course it works for non-dplyr functions as well, but they need to take the input data as their first argument.

data %.% lm(formula=response1 ~ factor(sex)) %.% summary()


As mentioned, dplyr is not the only package that has something like this, and according to a comment from Hadley Wickham, future dplyr will use the magrittr package instead, a package that adds piping to R. So let’s look at magrittr! The magrittr %>% operator works much the same way, except it allows one to put ”.” where the data is supposed to go. This means that the data doesn’t have to be the first argument to the function. For example, we can do this, which would give an error with dplyr:

library(magrittr)
data %>% lm(response1 ~ factor(sex), .) %>% summary()


Moreover, Conrad Rudolph has used the operators %.%, %|>% and %|% in his own package for functional composition, chaining and piping. And I’m sure he is not the only one; there are several more packages that bring more new ways to define and combine functions into R. I hope I will revisit this topic when I’ve gotten used to it and decided what I like and don’t like. This might be confusing for a while with similar and rather cryptic operators that do slightly different things, but I’m sure it will turn out to be a useful development.

# Using R: quickly calculating summary statistics (with dplyr)

I know I’m on about Hadley Wickham‘s packages a lot. I’m not the president of his fanclub, but if there is one I’d certainly like to be a member. dplyr is going to be a new and improved ddply: a package that applies functions to, and does other things to, data frames. It is also faster and will work with other ways of storing data, such as R’s relational database connectors. I use plyr all the time, and obviously I want to start playing with dplyr, so I’m going to repeat yesterday’s little exercise with dplyr. Readers should be warned: this is really just me playing with dplyr, so the example will not be particularly profound. The post at the Rstudio blog that I just linked contains much more information.

So, here comes the code to do the thing we did yesterday but with dplyr:

## The code for the toy data is exactly the same
data <- data.frame(sex = c(rep(1, 1000), rep(2, 1000)),
treatment = rep(c(1, 2), 1000),
response1 = rnorm(2000, 0, 1),
response2 = rnorm(2000, 0, 1))

## reshape2 still does its thing:
library(reshape2)
melted <- melt(data, id.vars=c("sex", "treatment"))

## This part is new:
library(dplyr)
grouped <- group_by(melted, sex, treatment)
summarise(grouped, mean=mean(value), sd=sd(value))


When we used plyr yesterday all was done with one function call. Today it is two: dplyr has a separate function for splitting the data frame into groups. It is called group_by and returns the grouped data. Note that no quotation marks or concatenation were used when passing the column names. This is what it looks like if we print it:

Source: local data frame [4,000 x 4]
Groups: sex, treatment, variable

sex treatment  variable       value
1    1         1 response1 -0.15668214
2    1         2 response1 -0.40934759
3    1         1 response1  0.07103731
4    1         2 response1  0.15113270
5    1         1 response1  0.30836910
6    1         2 response1 -1.41891407
7    1         1 response1 -0.07390246
8    1         2 response1 -1.34509686
9    1         1 response1  1.97215697
10   1         2 response1 -0.08145883


The grouped data is still a data frame, but it contains a bunch of attributes that contain information about grouping.

The next function is a call to the summarise function. This is a new version of a summarise function similar to one in plyr. It will summarise the grouped data in columns given by the expressions you feed it. Here, we calculate mean and standard deviation of the values.

Source: local data frame [8 x 5]
Groups: sex, treatment

sex treatment  variable         mean        sd
1   1         1 response1  0.021856280 1.0124371
2   1         1 response2  0.045928150 1.0151670
3   1         2 response1 -0.065017971 0.9825428
4   1         2 response2  0.011512867 0.9463053
5   2         1 response1 -0.005374208 1.0095468
6   2         1 response2 -0.051699624 1.0154782
7   2         2 response1  0.046622111 0.9848043
8   2         2 response2 -0.055257295 1.0134786


Maybe the new syntax is slightly clearer. Of course, there are alternative ways of expressing it, one of which is pretty interesting. Here are two equivalent versions of the dplyr calls:

summarise(group_by(melted, sex, treatment, variable),
mean=mean(value), sd=sd(value))

melted %.% group_by(sex, treatment, variable) %.%
summarise(mean=mean(value), sd=sd(value))


The first one is nothing special: we’ve just put the group_by call into summarise. The second version, though, is a strange creature. dplyr uses the operator %.% to denote taking what is on the left and putting it into the function on the right. Reading from the beginning of the expression we take the data (melted), push it through group_by and pass it to summarise. The other arguments to the functions are given as usual. This may seem very alien if you’re used to R syntax, or you might recognize it from shell pipes. This is not the only attempt make R code less nested and full of parentheses. There doesn’t seem to be any consensus yet, but I’m looking forward to a future where we can write points-free R.

# Using R: quickly calculating summary statistics from a data frame

A colleague asked: I have a lot of data in a table and I’d like to pull out some summary statistics for different subgroups. Can R do this for me quickly?

Yes, there are several pretty convenient ways. I wrote about this in the recent post on the barplot, but as this is an important part of quickly getting something useful out of R, just like importing data, I’ll break it out into a post of its own. I will present a solution that uses the plyr and reshape2 packages. You can do the same with base R, and there’s nothing wrong with base R, but I find that plyr and reshape2 makes things convenient and easy to remember. The apply family of functions in base R does the same job as plyr, but with a slightly different interface. I strongly recommend beginners to begin with plyr or the apply functions, and not what I did initially, which was nested for loops and hard bracket indexing.

We’ll go through and see what the different parts do. First, simulate some data. Again, when you do this, you usually have a table already, and you can ignore the simulation code. Usually a well formed data frame will look something this: a table where each observation is a unit such as an individual, and each column gives the data about the individual. Here, we imagine two binary predictors (sex and treatment) and two continuous response variables.

data <- data.frame(sex = c(rep(1, 1000), rep(2, 1000)),
treatment = rep(c(1, 2), 1000),
response1 = rnorm(2000, 0, 1),
response2 = rnorm(2000, 0, 1))

  sex treatment   response1   response2
1   1         1 -0.15668214 -0.13663012
2   1         2 -0.40934759 -0.07220426
3   1         1  0.07103731 -2.60549018
4   1         2  0.15113270  1.81803178
5   1         1  0.30836910  0.32596016
6   1         2 -1.41891407  1.12561812


Now, calculating a function of the response in some group is straightforward. Most R functions are vectorised by default and will accept a vector (that is, a column of a data frame). The subset function lets us pull out rows from the data frame based on a logical expression using the column names. Say that we want mean, standard deviation and a simple standard error of the mean. I will assume that we have no missing values. If you have, you can add na.rm=T to the function calls. And again, if you’ve got a more sophisticated model, these might not be the standard errors you want. Then pull them from the fitted model instead.

mean(subset(data, sex == 1 & treatment == 1)$response1) sd(subset(data, sex == 1 & treatment == 1)$response1)

sd(subset(data, sex == 1 & treatment == 1)\$response1)/
sqrt(nrow(subset(data, sex == 1 & treatment == 1)))


Okay, but doing this for each combination of the predictors and responses is no fun and requires a lot of copying and pasting. Also, the above function calls are pretty messy with lots of repetition. There is a better way, and that’s where plyr and reshape2 come in. We load the packages. The first time you’ll have to run install.packages, as usual.

library(plyr)
library(reshape2)


First out, the melt function from rehape2. Look at the table above. It’s reasonable in many situations, but right now, it would be better if we put both the response variables in the same column. If it doesn’t seem so useful, trust me and see below. Melt will take all the columns except the ones we single out as id variables and put them in the same column. It makes sense to label each row with the sex and treatment of the individual. If we had an actual unit id column, it would go here as well:

melted <- melt(data, id.vars=c("sex", "treatment"))


The resulting ”melted” table looks like this. Instead of the response variables separately we get a column of values and a column indicating which variable the value comes from.

  sex treatment  variable       value
1   1         1 response1 -0.15668214
2   1         2 response1 -0.40934759
3   1         1 response1  0.07103731
4   1         2 response1  0.15113270
5   1         1 response1  0.30836910
6   1         2 response1 -1.41891407


Now it’s time to calculate the summary statistics again. We will use the same functions as above to do the actual calculations, but we’ll use plyr to automatically apply them to all the subsets we’re interested in. This is sometimes called the split-apply-combine approach: plyr will split the data frame into subsets, apply the function of our choice, and then collect the results for us. The first thing to notice is the function name. All the main plyr functions are called something with -ply. The letters stand for the input and return data type: ddply works on a data frame and returns a data frame. It’s probably the most important member of the family.

The arguments to ddply are the data frame to work on (melted), a vector of the column names to split on, and a function. The arguments after the function name are passed on to the function. Here we want to split in subsets for each sex, treatment and response variable. The function we apply is summarise, which makes a new data frame with named columns based on formulas, allowing us to use the column names of the input data frame in formulas. In effect it does exactly what the name says, summarises a data frame. And in this instance, we want to calculate the mean, standard deviation and standard error of the mean, so we use the above function calls, using value as the input. Run the ddply call, and we’re done!

ddply(melted, c("sex", "treatment", "variable"), summarise,
mean = mean(value), sd = sd(value),
sem = sd(value)/sqrt(length(value)))

  sex treatment  variable         mean        sd        sem
1   1         1 response1  0.021856280 1.0124371 0.04527757
2   1         1 response2  0.045928150 1.0151670 0.04539965
3   1         2 response1 -0.065017971 0.9825428 0.04394065
4   1         2 response2  0.011512867 0.9463053 0.04232006
5   2         1 response1 -0.005374208 1.0095468 0.04514830
6   2         1 response2 -0.051699624 1.0154782 0.04541357
7   2         2 response1  0.046622111 0.9848043 0.04404179
8   2         2 response2 -0.055257295 1.0134786 0.04532414


# Using R: barplot with ggplot2

Ah, the barplot. Loved by some, hated by some, the first graph you’re likely to make in your favourite office spreadsheet software, but a rather tricky one to pull off in R. Or, that depends. If you just need a barplot that displays the value of each data point as a bar — which is one situation where I like a good barplot — the barplot( ) function does just that:

some.data <- rnorm(10, 4, 1.5)
names(some.data) <- 1:10
barplot(some.data)


Done? Not really. The barplot (I know some people might not use the word plot for this type of diagram, but I will) one typically sees from a spreadsheet program has some gilding: it’s easy to get several variables (”series”) of data in the same plot, and often you’d like to see error bars. All this is very possible in R, either with base graphics, lattice or ggplot2, but it requires a little more work. As usual when it gets a bit more fancy, I prefer ggplot2 over the alternatives. Once upon a time when I started with ggplot2, I tried googling for this, and lots of people have answered this question. I was still confused, though. So, if you’re a new user and reading this, please bear with me and I’ll try to demonstrate what all the steps are good for. Whether it’s a good statistical graph or not, the barplot is actually a nice example of ggplot2 in action and will demonstrate some R principles.

Let us take an example: Say that we start with a pretty typical small dataset with two variables that we’ve measured in four groups. Now we’d like a barplot of the group means and error bars for the means.

## 0. Start a script

Making the plot will take more than a couple of lines, so it’s a good idea to put everything in a script. Below I will split the script into chunks, but the whole thing is on github. We make a new R file and load ggplot2, plyr and reshape2, the packages we will need:

library(ggplot2)
library(plyr)
library(reshape2)


## 1. Simulate some data

In the case of real barplot this is where you load your data. You will probably have it in a text file that you read with the read.table( ) family of functions or RStudios Import dataset button (which makes the read.table call for you; if you don’t feel like late nights hunched over the read.table manual page, I recommend it). Simulating data might look something like this:

n <- 10
group <- rep(1:4, n)
mass.means <- c(10, 20, 15, 30)
mass.sigma <- 4
score.means <- c(5, 5, 7, 4)
score.sigma <- 3
mass <- as.vector(model.matrix(~0+factor(group)) %*% mass.means) +
rnorm(n*4, 0, mass.sigma)
score <- as.vector(model.matrix(~0+factor(group)) %*% score.means) +
rnorm(n*4, 0, score.sigma)
data <- data.frame(id = 1:(n*4), group, mass, score)


This code is not the tersest possible, but still a bit tricky to read. If you only care about the barplot, skip over this part. We define the number of individuals per group (10), create a predictor variable (group), set the true mean and standard deviation of each variable in each group and generate values from them. The values are drawn from a normal distribution with the given mean and standard deviation. The model.matrix( ) function returns a design matrix, what is usually called X in a linear model. The %*% operator is R’s way of denoting matrix multiplication — to match the correct mean with the predictor, we multiply the design matrix by the vector of means. Now that we’ve got a data frame, we pretend that we don’t know the actual values set above.

  id group       mass    score
1  1     1  4.2367813 5.492707
2  2     2 16.4357254 1.019964
3  3     3 19.2491831 6.936894
4  4     4 23.4757636 3.845321
5  5     1  0.9533737 1.852927
6  6     2 19.9142350 5.567024

## 2. Calculate means

The secret to a good plot in ggplot2 is often to start by rearranging the data. Once the data is in the right format, mapping the columns of the data frame to the right element of the plot is the easy part. In this case, what we want to plot is not the actual data points, but a function of them — the group means. We could of course subset the data eight times (four groups times two variables), but thankfully, plyr can do that for us. Look at this piece of code:

melted <- melt(data, id.vars=c("id", "group"))
means <- ddply(melted, c("group", "variable"), summarise,
mean=mean(value))


First we use reshape2 to melt the data frame from tabular form to long form. The concept is best understood by comparing the output and input of melt( ). Compare the rows above to these rows, which are from the melted data frame:

   id group variable      value
1   1     1     mass  4.2367813
2   2     2     mass 16.4357254
3   3     3     mass 19.2491831
4   4     4     mass 23.4757636

We’ve gone from storing two values per row (mass and score) to storing one value (mass or score), keeping the identifying variables (id and group) in each row. This might seem tricky (or utterly obvious if you’ve studied database design), but you’ll soon get used to it. Trust me, if you do, it will prove useful!

The second row uses ddply (”apply from data frame to data frame”) to split up the melted data by all combinations of group and variable and calculate a function of the value, in this case the mean. The summarise function creates a new data frame from an old; the arguments are the new columns to be calculated. That is, it does exactly what it says, summarises a data frame. If you’re curious, try using it directly. It’s not very useful on its own, but very good in ddply calls.

## 3. Barplot of the means

Time to call on ggplot2! One has a choice between using qplot( ) or ggplot( ) to build up a plot, but qplot is the easier. We map the mean to y, the group indicator to x and the variable to the fill of the bar. The bar geometry defaults to counting values to make a histogram, so we need to tell use the y values provided. That’s what setting stat= to ”identity” is good for. To make the bars stand grouped next to each other instead of stacking, we tell set position=.

means.barplot <- qplot(x=group, y=mean, fill=variable,
data=means, geom="bar", stat="identity",
position="dodge")


## 4. Standard error of the mean

Some people can argue for hours about error bars. In some cases you will want other types of error bars. Maybe the inferences come from a hierarchical model where the standard errors are partially pooled. Maybe you’re dealing with some type of generalised linear model or a model made with transformed data. See my R tutorial for a simple example with anova. The point is that from the perspective of ggplot2 input to the error bars is data, just like anything else, and we can use the full arsenal of R tools to create them.

means.sem <- ddply(melted, c("group", "variable"), summarise,
mean=mean(value), sem=sd(value)/sqrt(length(value)))
means.sem <- transform(means.sem, lower=mean-sem, upper=mean+sem)


First, we add a standard error calculation to the ddply call. The transform function adds colums to a data frame; we use it to calculate the upper and lower limit to the error bars (+/- 1 SEM). Then back to ggplot2! We add a geom_errorbar layer with the addition operator. This reveals some of the underlying non-qplot syntax of ggplot2. The mappings are wrapped in the aes( ), aesthetics, function and the other settings to the layer are regular arguments. The data argument is the data frame with interval limits that we made above. The only part of this I don’t like is the position_dodge call. What it does is nudge the error bars to the side so that they line up with the bars. If you know a better way to get this behaviour without setting a constant, please write me a comment!

means.barplot + geom_errorbar(aes(ymax=upper,
ymin=lower),
position=position_dodge(0.9),
data=means.sem)


Does this seem like a lot of code? If we look at the actual script and disregard the data simulation part, I don’t think it’s actually that much. And if you make this type of barplot often, you can package this up into a function.