4.1: Bar (column) charts

Introduction

Bar or column charts are used to compare counts among two or more categories, i.e., an alternative to pie charts (Fig. \(\PageIndex{1}\)).

Figure \(\PageIndex{1}\): Single-nucleotide variants for human gene ACTB by DNA and functional element.

Although bar charts are common in the literature (Cumming et al 2007; Streit and Gehlenborg 2014), bar charts may not be a good choice for comparisons of ratio scale data (Streit and Gehlenbor 2014). Bar charts for ratio data are misleading. Parts of the range implied by the bar may never have been observed: the bars of the chart always start at zero. Box (whisker) plots are better for comparisons of ratio scale data and are presented in the next section of this chapter. That said, I will go ahead and present how to create bar chars for both count, generally considered acceptable, and ratio scale data, for which their use is controversial.

Purpose of the bar chart

Like all graphics, a bar chart should tell a story. The purpose of displaying data is to give your readers a quick impression of the general differences among two or more groups of the data. For counts, that’s where the bar chart comes in. The bar chart is preferred over the pie chart because differences are represented by lengths of the bars in the bar chart. Differences among categories in a pie chart are reflected by angles, and it seems that humans are much better at judging lengths than angles.

Figure \(\PageIndex{2}\): A simple bar chart.

myCombo <- seq(0,10, by=1) 
myCounts <- choose(10, myCombo)    #combinations
barplot(myCounts, names.arg = myCombo, xlab = "Number correct", ylab = "Count",col = "darkblue")

A stacked bar chart is used to compare how different categories are further divided into subcategories shared among all the groups. For example, passengers on the Titanic at the time of its sinking can be grouped based on their passage class (first, second, or third), but if we want to compare the count of those who died or survived in each class, we can use a stacked bar chart.

Figure \(\PageIndex{3}\): The luxury ship RMS Titanic, which sunk 15 April 1912, More than 1500 souls were lost. Public domain image, Wikipedia.

Stacked bar chart, data set TitanicSurvival in package carData.

Figure \(\PageIndex{4}\): A stacked bar chart of survival rates on the Titanic by passenger class.

Barplot(passengerClass, by=survived, style="divided", legend.pos="above", xlab="passengerClass", ylab="Frequency")

Bar charts with error bars

Although many data visualization specialists argue against the bar chart, their use is well established. For the familiar bar chart with ratio scale data, the X (horizontal) axis displays the categories of one variable (e.g., location, or treatment group). You plot groups to emphasize comparisons. The Y (vertical) axis then is the mean for each group.

You need error bars. If the mean is displayed, some measure of precision should be (must be?) displayed (Cumming et al 2007). And, as you should recall by now, your choices are standard deviation (Chapter 3.2), standard error of the mean (SEM) (Chapters 3.2, 3.5), or confidence interval (see Chapter 3.5). It is strongly advised that without a representation of precision, one should not interpret trends or group differences from representations of means (i.e., height of bars) alone.

The bar charts on this page are means plus or minus the standard error of the mean, \(\pm\) SEM. We’ll discuss which choice to make.

Examples

The Copper_rats_PMID3357063 dataset will be used for the next series of graphs (Data set). Refer to Mike’s Workbook for Biostatistics Part 07 to review how to import the data.

A portion of the data set is shown below

head(Copper)
         Diet     Body    Heart    Liver
1 Adequate-Cu 320.1381 1.125037 10.259657
2 Adequate-Cu 329.6879 1.158982 9.843295
3 Adequate-Cu 327.9838 1.090374 9.855975
4 Adequate-Cu 334.6669 1.118183 9.942997
5 Adequate-Cu 338.3134 1.172636 9.860971
6 Adequate-Cu 345.4608 1.056183 8.885820

The data set consists of organ weights (heart, liver) from rats fed a diet adequate in copper, deficient in copper, and then a third group who received the adequate diet from perspective of amount of copper, but calorie restricted to match the decreased feeding rates of the rats fed the copper deficient diet. Copper is an essential trace element in our diet. The data set was simulated from descriptive statistics (means, standard deviation, number of subjects) of published data by sampling from a normal distribution. (Table 1, Ovecka et al 1988).

On we go with some graphs.

Note:

R has many options to create bar charts, and especially ggplot2 can be used to great advantage, but there is a learning curve. One of the great things about R is that folks help each other by sharing code. For example, http://www.cookbook-r.com/Graphs/Plotting_means_and_error_bars_(ggplot2)/

But, I’m still learning about R graphics, and for bar charts with error bars, I find other packages more straight-forward. So, I’ll use this moment to point out that making a good graph is more about the end product then the particular tools. I have been using other tools for years to make my graphics, so I tend to default on these options first. Graphs presented here are mostly from Veusz software program (pronounced “views”). I like it because the software allows me to edit any of the elements of the graph.

Here’s a typical looking bar chart with ratio scale data: means ± SEM. Let’s look at them more critically.

Figure \(\PageIndex{5}\): A bar chart with error bars (standard error of the mean).

Figure \(\PageIndex{6}\): Another bar chart with error bars (standard errors of mean).

When making comparisons, make sure the axes have the same scale, or consider putting the graphs together.

Figure \(\PageIndex{7}\): Bar chart that allows for a comparison among levels of a a factor (organs, liver vs. heart).

Analysis Note:

For variables that covary with body size (for example, on average, tall people generally are heavier too), a major consideration is how to present (and analyze) the data in such a way that body size is accounted for. Here, the solution was to express organ weight as the ratio of organ weight to body weight for the mice. This may or may not be a good solution, and the answer is too complicated for us now (has to do with a thing called allometric scaling), but I wanted to at least present the issue and show how the graphics can be improved to handle some of these concerns.

Here are the organ weights again, but taken as ratio of body mass.

Figure \(\PageIndex{8}\): Same chart as in Figure \(\PageIndex{7}\), but in ratio form.

Note:

Let’s be clear about expectations of you for statistics class. Now, R (and Rcmdr) do lots of graphics, pretty much anything you want, but it is not as friendly as it could be. For BI311 homework, the default graphics available via Rcmdr will generally be adequate for assignments. R and Rcmdr have many bar chart options, but there isn’t a straightforward way to get the error bars, unless you are willing to enter some code to the command line or learn a particular package (like gplots or ggplot2).

How to make a bar chart with error bars in R

Option 1. First, let’s try a work-around. Instead of an error bar option for the bar chart menu, Rcmdr provides a plot of means that allows you to plot with error bars. These are equivalent graphs, the “bar chart” and the “plot of means”, though you should favor the bar chart format for publishing.

Rcmdr: Graphs → Plot of means…

Figure \(\PageIndex{9}\): Rcmdr menu popup for Plot Means.

Here, Rcmdr takes the data and calculates the mean and your choice of standard errors or deviations, confidence intervals, or no error bars. The resulting graph is below.

Figure \(\PageIndex{10}\): Plot of means, default settings.

That’s an ugly graph (Fig. \(\PageIndex{10}\)). Functional, good enough for data exploration and preliminary results, and certainly good enough for a Biostatistics homework or report. Additionally, connecting the dots here is a no-no. It implies that if we had measured categories between “adequate copper” and “deficient copper,” then the points would fall on those lines. That would be a complete guess. So, why did I include the connecting lines? That was the default setting for the command, and it makes the point — think before you click. One argument for connecting points in a graph is that it makes it easier for the reader to visualize trends.

This graph (Fig. \(\PageIndex{10}\)) is fine for exploring data, but you will want to do better for publication.

Let’s make some better graphs with R

Once you are ready to go beyond the default settings available in Rcmdr, there is tremendous functionality in R for graphics. To access R’s potential, you’ll need to get into the commands a bit. I’m going to continue to try and shield you from the programming aspects of R, but from time to time you really need to see what is possible with R. Graphics is one such area. I use the package gplots, with 23 different graphing functions (type at R prompt ?gplots to call up the manual pages).

gplots should be among the packages on your R installation; if not, then install the package and run library(gplots) to complete the installation. We’ll try the barchart2 function.

But first, we need to get means for each of our groups.

At the R command prompt:

hrtWt <- tapply(Dataset$HeartWt, list(Group=Dataset$Group), mean, na.rm=TRUE) 

This code extracts means from our HeartWt variable for each Group, then stores the three (in this case, because our data set has 3 groups) in the place holder I had called hrtWt. To verify that the three means are there, type “hrtWt” without the quotes, then enter.

You should see

hrtWt Group Cu adequate Cu deficient Pair-fed 
               1.200000     1.566667 0.900000

R functions used: tapply, list, mean; na.rm was not needed but would be used to remove all missing values (recall during our import phase we were asked how missing observations were noted in our file; the default is NA).

Next, I want to apply standard error bars

stdDEV <- tapply(Dataset$HeartWt, list(Group=Dataset$Group), sd, na.rm=TRUE)
cil <- hrtWt-(stdDEV/sqrt(3))
ciu <- hrtWt+(stdDEV/sqrt(3))

I used cil and ciu to designate the lower cil and upper ciu values for my ± SEM (standard error of the mean).

ciu stands for “confidence interval lower;” ciu stands for “confidence interval upper.”

Finally, here’s the plot command

barplot2(hrtWt, beside = TRUE, main=c("Mice fed different amounts of copper in diet"), col = c("blue", "red", "green"), xlab="Copper in diet", ylab="Heart mass (g)", ylim = c(0, 2), plot.ci=TRUE, ci.l=cil, ci.u=ciu)

Now, draw a box around the graphic

box()

Whew!

What does your new graph look like? My graph is below (Fig. 11).

Figure \(\PageIndex{11}\): A bar chart made using barplot2.

This works, and the point is that once the script is written it easy to make small changes as you need in the future to make nice graphs.

If you are impatient like me, I like a GUI option, at least to start crafting the graph. The Rcmdr plugin KMggplot2 provides a good set of tools to make bar charts with error bars. An even better option I think is to use a software package that is designed for graphics, at least simple graphics like a bar chart. I use SciDAVis and Veusz for simple graphs like pie charts and bar charts; much easier to control.

ggplot2 bar charts with error bars

Nevertheless, here’s how to make a bar chart with error bars using ggplot2 (Fig. \(\PageIndex{11}\)). First, we need to create a statistics summary. The script printed here was modified from scripts at R Graph Cookbook website.

require(plyr)
summarySE <- function(data=NULL, measurevar, groupvars=NULL, na.rm=FALSE,
     conf.interval=.95, .drop=TRUE) {
length2 <- function (x, na.rm=FALSE) {
     if (na.rm) sum(!is.na(x))
     else length(x)
}

#returns a vector with N, mean, and sd
datac <- ddply(data,groupvars, .drop=.drop,
    .fun = function(xx,col){
      c(N=length2(xx[[col]],na.rm=na.rm),
      mean=mean(xx[[col]],na.rm=na.rm),
      sd=sd(xx[[col]],na.rm=na.rm)
     )
    },
    measurevar
   )

#Rename the "mean" column
datac <- rename(datac,c("mean"=measurevar))

#Calculate the standard error of the mean
datac$se <- datac$sd/sqrt(datac$N)

#Get confidence interval
ciMult <- qt(conf.interval/2 + .5, datac$N-1)
datac$ci <- datac$se*ciMult

return(datac)
}

Applying this function to the BMI dataset yields the following output.

sumBMI <- summarySE(BMI, measurevar="BMI", groupvars=c("Sex", "Smoke"));sumBMI

   Sex Smoke   N      BMI       sd        se       ci 
1    F    No  23 26.83567 7.610271 1.5868511 3.290928 
2    F   Yes  14 25.76133 4.658625 1.2450698 2.689810 
3    M    No  10 26.35731 3.363575 1.0636557 2.406156 
4    M   Yes  27 26.71879 4.675631 0.8998256 1.849618

Now we are ready to make the bar chart with error bars

ggplot(tgc,aes(x=Smoke,y=BMI,fill=Sex)) + 
 geom_bar(position=position_dodge(),stat="identity",color="black") + 
 geom_errorbar(aes(ymin=BMI,ymax=BMI+se),width=.2,position=position_dodge(.9))

Figure \(\PageIndex{12}\): A barchart from ggplot2.

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Questions

1. Why should you use box plots and not bar charts to display comparisons for a ratio scale variable between categories? Obtain a copy of the article by Streit and Gehlenbor 2014 — it’s free! After reading, summarize the pro and cons for box plots over bar charts with error bars.

2. Enter the following data into R. The data are sulfate levels in water, parts per million.

type = c("Palolo Stream","Chaminade tap water", "Aquafina","Dasani") 
sulfateppm =c(11, 14, 5, 12)
try = data.frame(type,sulfateppm) 
byWater = tapply(try$sulfateppm,list(Group=try$type),mean)

Make a simple bar chart using the boxplot2 function in gplots package.

3. Change the range of values on the vertical axis to 0, 20

4. Change the color of the bars from gray to blue

5. Add a label to the vertical axis, “Sulfates, ppm” (without the quotes)

6. Add a box around the graph.

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Data set

Diet	Body	Heart	Liver
Adequate-Cu	320.1381	1.125037	10.259657
Adequate-Cu	329.6879	1.158982	9.843295
Adequate-Cu	327.9838	1.090374	9.855975
Adequate-Cu	334.6669	1.118183	9.942997
Adequate-Cu	338.3134	1.172636	9.860971
Adequate-Cu	345.4608	1.056183	8.88582
Adequate-Cu	343.089	1.081261	10.166647
Adequate-Cu	328.3403	1.111278	10.124185
Adequate-Cu	324.9723	1.189194	10.158402
Adequate-Cu	325.2378	1.14715	9.939521
Deficient-Cu	195.5052	1.90973	7.907565
Deficient-Cu	182.7809	1.823672	8.430167
Deficient-Cu	184.3701	1.632249	7.619104
Deficient-Cu	193.7867	1.831765	8.742489
Deficient-Cu	180.0417	1.710367	7.975879
Deficient-Cu	208.5349	2.495623	8.652445
Deficient-Cu	182.3048	1.262053	7.257726
Deficient-Cu	203.0413	2.153639	8.081782
Deficient-Cu	193.3829	1.986028	7.807328
Deficient-Cu	195.0523	1.76975	8.297611
Pair-fed	211.0858	0.6911343	6.251177
Pair-fed	210.4041	0.6928067	7.696669
Pair-fed	208.5969	0.6911901	6.973803
Pair-fed	209.3333	0.7039211	6.629303
Pair-fed	208.8889	0.7077486	6.038704
Pair-fed	208.2994	0.7004535	6.606877
Pair-fed	209.4524	0.6915543	6.228888
Pair-fed	210.2699	0.6984497	6.638466
Pair-fed	208.8142	0.7214847	6.353705
Pair-fed	209.2977	0.6848656	6.536642