🗒️Graphical Representation: Bar & Column Charts [Notes]

Disclaimer: This is work in progress intended to consolidate information from various sources and may deviate from them. Please consult the sources for the exact content!
Last updated: 15-Jun-2024

Bar & Column Charts with Variations

Bar & Column Charts (Graphs) 

• {definition} graphical representation of categorical data with rectangular figures (aka boxes) whose heights (column chart) or lengths (bar chart) are proportional to the values that they represent
• {benefit} allow to visually encode/decode quantitative information-size as magnitude and area based on the relative position of the end of the box along the common scale
• if the width of the box is the same, it's enough to compare the length
• ⇒ the basis of comparison is one-dimensional [1]
• ⇐ orient the reader to the relative magnitudes of the boxes
• area is typically encoded when the width varies
• ⇐ encoding by area is a poor encoding method as it can mislead
• can represent negative and positive values 
• one of the most useful, simple, and adaptable techniques in graphic presentation [1]
• easily understood by readers
• sometimes avoided because they are so common
• almost everything could be a bar chart
• the length of each bar is proportional to the quantity or amount of each category represented [1]
• ⇒the zero line must be shown [1]
• ⇒the scale must not be broken [1]
• {exception} an excessively long bar in a series of bars may be broken off at the end, and the amount involved shown directly beyond it [1]
• {benefit} allow to visually represent categorical data
• ⇒ occasionally represented without scales, grid lines or tick marks
• the more data elements are presented, the more difficult it becomes to navigate and/or display the data
• {benefit} allow us to easily compare magnitudes 
• sometimes without looking at the actual values
• {type} bar chart
• the box is shown horizontally
• represents magnitude by length
• allows comparing different items as of a specific time
• {type} column chart
• the box is shown vertically
• represents magnitude by height
• allows comparing different items over time
• ⇐ it still displays discrete points
• recommended for comparing similar items for different time periods [2]
• effective way to show most types of comparisons [2]
• {subtype} stacked chart
• variation of bar/column charts in which the boxes of a dimension's components are staked over each other
• {exception} spaces can be used between boxes if the values aren't cumulative [3]
• {benefit} allows encoding a further dimension where the values are staked within the same box
• {drawback} do not show data structure well
• ⇒ make it challenging to compare values across boxes
• {subtype} 100-percent chart
• variation of stacked chart in which the magnitude totals to 100%
• {benefit} allows to display part to whole relationships
• ⇐ preferable to circle chart's angle and area comparison [1]
• {subtype} clustered chart (aka grouped chart)
• variation of bar/column charts that allows encoding further quantitative information in distinct boxes tacked together which occasionally overlap
• ⇐ if there's space, it is usually kept to a minimum
• e.g. can be used to display multiple data series 
• can be used with a secondary axis
• {benefit} allows comparisons within the cluster/group as well between clusters/groups
• {drawback} more challenging to make comparisons across points
• {subtype} area chart (variable-width/variwide chart/graph) 
• variation of bar/column charts in which the height/width have significance being proportional to some measure or characteristics of the data elements represented [3]
• {benefit} allow encoding a further dimension as part of the area
• {subtype} deviation chart 
• variation of bar/column charts that display positive and negative values 
• {subtype} joined chart
• variation of bar/column charts in which the boxes are tacked together
• {benefit} allow to better use the space available 
• {subtype} paired chart 
• variation of bar/column charts in which the boxes are paired in mirror based on an axis
• e.g. the values of one data series are displayed to the left, while the values for a second data series are displayed to the right 
• {benefit} allows to study the correlation and/or other relationships between the values of two data series
• the hidden axes can have different scales 
• {subtype} circular chart (aka radial chart)
• variation of bar/column charts in which the boxes are wrapped into a circle, the various categories being uniformly spaced along the radial or category axis [3]
• the value scale can have any upper or lower value and can progress in either direction [3]
• {benefit} useful to represent data that have a circular dimension in an aesthetic form
• e.g. months, hours
• {subtype} waterfall chart (aka progressing chart)
• variation of bar/column charts in which the boxes are displayed progressively, the start of a box corresponding the end of the previous box 
• time and activity charts can be considered as variations of this subtype [3]
• {advantage} allows to determine cumulative values, respectively the increase/decrease between consecutive boxes
• {subtype}composite chart (aka mixed chart, combination chart, overlay chart)
• variation of bar/column charts in besides boxes are used other graphic types of encoding (line, area)
• ⇐ the different data graphics are overlaid on one another [3]
• {benefit} allows to improve clarity or highlight the relationships between several data series [3]
• {drawback} overlaying can result in clutter 
• used to  
• display totals, averages or frequencies
• display time series
• display the relationship between two or more items
• make a comparison among several items
• make a comparison between parts and the whole
• can be confounded with 
• [histograms]
• show distribution through the frequency of quantitative values against defined intervals of quantitative values
• used for continuous numerical data or data that can be effectively modelled as continuous
• it doesn't have spaces between bars
• ⇐ older use of bar/column charts don't use spaces
• if this aspect is ignored, histograms can be considered as a special type of area chart
• [vertical line chart] (aka price chart, bar chart)
• vertical line charts are sometimes referred as bar charts (see [3])
• things to consider
• distance between bars
• the more distant the bars, the more difficult it becomes to make comparisons and the accuracy of judgment decreases
• sorting
• sorting the bars/columns by their size facilitates comparisons, though it can impede items' search, especially when there are many categories involved
• {exception} not recommended for time series
• clutter
• displaying too many items in a cluster and/or too many labels can lead to clutter
• {recommendation} display at maximum 3-4 clustered boxes
• color
• one should follow the general recommendations 
• trend lines
• can be used especially with time series especially to represent the linear regression line
• dual axis
• {benefit} allows to compare the magnitudes of two data series by employing a secondary axis
• overlapping
• overlapping boxes can make charts easier to read
• symbols
• can be used to designate reference points of comparison for each of the bars [3]
• {alternative} pie chart
• can be used to dramatize comparisons in relation to the whole [2]
• one should consider the drawbacks 
• {alternative} choropleth maps
• more adequate for geographical dimensions
• provide minimal encoding 
• {alternative} line charts
• can be much more informative
• provides an optimal dat-ink ratio
• reduces the chart junk feeling
• {alternative} dot plots
• are closer to the original data

References:
[1] Anna C Rogers (1961) "Graphic Charts Handbook"
[2] Robert Lefferts (1981) "Elements of Graphics: How to prepare charts and graphs for effective reports"
[3] Robert L Harris (1996) "Information Graphics: A Comprehensive Illustrated Reference"

📊R Language: Visualizing the Iris Dataset

When working with a dataset that has several numeric features, it's useful to visualize it to understand the shapes of each feature, usually by category or in the case of the iris dataset by species. For this purpose one can use a combination between a boxplot and a stripchart to obtain a visualization like the one below (click on the image for a better resolution):

Iris features by species (box & jitter plots combined)

And here's the code used to obtain the above visualization:

par(mfrow = c(2,2)) #2x2 matrix display

boxplot(iris$Petal.Width ~ iris$Species) 
stripchart(iris$Petal.Width ~ iris$Species
	, method = "jitter"
	, add = TRUE
	, vertical = TRUE
	, pch = 20
	, jitter = .5
	, col = c('steelblue', 'red', 'purple'))

boxplot(iris$Petal.Length ~ iris$Species) 
stripchart(iris$Petal.Length ~ iris$Species
	, method = "jitter"
	, add = TRUE
	, vertical = TRUE
	, pch = 20
	, jitter = .5
	, col = c('steelblue', 'red', 'purple'))

boxplot(iris$Sepal.Width ~ iris$Species) 
stripchart(iris$Sepal.Width ~ iris$Species
	, method = "jitter"
	, add = TRUE
	, vertical = TRUE
	, pch = 20
	, jitter = .5
	, col = c('steelblue', 'red', 'purple'))

boxplot(iris$Sepal.Length ~ iris$Species) 
stripchart(iris$Sepal.Length ~ iris$Species
	, method = "jitter"
	, add = TRUE
	, vertical = TRUE
	, pch = 20
	, jitter = .5
	, col = c('steelblue', 'red', 'purple'))

mtext("© sql-troubles@blogspot.com 2024", side = 1, line = 4, adj = 1, col = "dodgerblue4", cex = .7)
title("Iris Features (cm) by Species", line = -2, outer = TRUE)

By contrast, one can obtain a similar visualization with just a command:

plot(iris, col = c('steelblue', 'red', 'purple'), pch = 20)

title("Iris Features (cm) by Species", line = -1, outer = TRUE)
mtext("© sql-troubles@blogspot.com 2024", side = 1, line = 4, adj = 1, col = "dodgerblue4", cex = .7)

And here's the output:

Iris features by species (general plot)

One can improve the visualization by using a bigger contrast between colors (I preferred to use the same colors as in the previous visualization).

I find the first data visualization easier to understand and it provides more information about the shape of data even it requires more work.

Histograms make it easier to understand the distribution of values, though the visualizations make sense only when done by species:

Histograms of Setosa's features

And, here's the code:

par(mfrow = c(2,2)) #2x2 matrix display

setosa = subset(iris, Species == 'setosa') #focus only on setosa
hist(setosa$Sepal.Width)
hist(setosa$Sepal.Length)
hist(setosa$Petal.Width)
hist(setosa$Petal.Length)

title("Setosa's Features (cm)", line = -1, outer = TRUE)
mtext("© sql-troubles@blogspot.com 2024", side = 1, line = 4, adj = 1, col = "dodgerblue4", cex = .7)

There's however a visual called stacked histogram that allows to delimit the data for each species:

Iris features by species (stacked histograms)

And, here's the code:

#installing plotrix & multcomp
install.packages("plotrix")
install.packages("plotrix")
library(plotrix)
library(multcomp)

par(mfrow = c(2,2)) #1x2 matrix display

histStack(iris$Sepal.Width
	, z = iris$Species
	, col = c('steelblue', 'red', 'purple')
	, main = "Sepal.Width"
	, xlab = "Width"
	, legend.pos = "topright")

histStack(iris$Sepal.Length
	, z = iris$Species
	, col = c('steelblue', 'red', 'purple')
	, main = "Sepal.Length"
	, xlab = "Length"
	, legend.pos = "topright")

histStack(iris$Petal.Width
	, z = iris$Species
	, col = c('steelblue', 'red', 'purple')
	, main = "Petal.Width"
	, xlab = "Width"
	, legend.pos = "topright")

histStack(iris$Petal.Length
	, z = iris$Species
	, col = c('steelblue', 'red', 'purple')
	, main = "Petal.Length"
	, xlab = "Length"
	, legend.pos = "topright")

title("Iris Features (cm) by Species - Histograms", line = -1, outer = TRUE)
mtext("© sql-troubles@blogspot.com 2024", side = 1, line = 4, adj = 1, col = "dodgerblue4", cex = .7)

Conversely, the standard histogram allows drawing the density curves within its boundaries:

par(mfrow = c(2,2)) #1x2 matrix display 

hist(iris$Sepal.Width
	, main = "Sepal.Width"
	, xlab = "Width"
	, las = 1, cex.axis = .8, freq = F)
eq = density(iris$Sepal.Width) # estimate density curve
lines(eq, lwd = 2) # plot density curve

hist(iris$Sepal.Length
	, main = "Sepal.Length"
	, xlab = "Length"
	, las = 1, cex.axis = .8, freq = F)
eq = density(iris$Sepal.Length) # estimate density curve
lines(eq, lwd = 2) # plot density curve

hist(iris$Petal.Width
	, main = "Petal.Width"
	, xlab = "Width"
	, las = 1, cex.axis = .8, freq = F)
eq = density(iris$Petal.Width) # estimate density curve
lines(eq, lwd = 2) # plot density curve

hist(iris$Petal.Length
	, main = "Petal.Length"
	, xlab = "Length"
	, las = 1, cex.axis = .8, freq = F)
eq = density(iris$Petal.Length) # estimate density curve
lines(eq, lwd = 2) # plot density curve

title("Iris Features (cm) by Species - Density plots", line = -1, outer = TRUE)
mtext("© sql-troubles@blogspot.com 2024", side = 1, line = 4, adj = 1, col = "dodgerblue4", cex = .7)

And, here's the diagram:

Iris features aggregated (histograms with density plots)

As final visualization, one can also compare the width and length for the sepal, respectively petal:

 

par(mfrow = c(1,2)) #1x2 matrix display

plot(iris$Sepal.Width, iris$Sepal.Length, main = "Sepal Width vs Length", col = iris$Species)
plot(iris$Petal.Width, iris$Petal.Length, main = "Petal Width vs Length", col = iris$Species)

title("Iris Features (cm) by Species - Scatter Plots", line = -1, outer = TRUE)
mtext("© sql-troubles@blogspot.com 2024", side = 1, line = 4, adj = 1, col = "dodgerblue4", cex = .7)

And, here's the output:

 

Iris features by species (scatter plots)

Happy coding!

📉Graphical Representation: Histograms (Just the Quotes)

"The histogram, with its columns of area proportional to number, like the bar graph, is one of the most classical of statistical graphs. Its combination with a fitted bell-shaped curve has been common since the days when the Gaussian curve entered statistics. Yet as a graphical technique it really performs quite poorly. Who is there among us who can look at a histogram-fitted Gaussian combination and tell us, reliably, whether the fit is excellent, neutral, or poor? Who can tell us, when the fit is poor, of what the poorness consists? Yet these are just the sort of questions that a good graphical technique should answer at least approximately." (John W Tukey, "The Future of Processes of Data Analysis", 1965)

"There is a technical difference between a bar chart and a histogram in that the number represented is proportional to the length of bar in the former and the area in the latter. This matters if non-uniform binning is used. Bar charts can be used for qualitative or quantitative data, whereas histograms can only be used for quantitative data, as no meaning can be attached to the width of the bins if the data are qualitative." (Roger J Barlow, "Statistics: A guide to the use of statistical methods in the physical sciences", 1989)

"90 percent of all problems can be solved by using the techniques of data stratification, histograms, and control charts. Among the causes of nonconformance, only one-fifth or less are attributable to the workers." (Kaoru Ishikawa, The Quality Management Journal Vol. 1, 1993)

"Averages, ranges, and histograms all obscure the time-order for the data. If the time-order for the data shows some sort of definite pattern, then the obscuring of this pattern by the use of averages, ranges, or histograms can mislead the user. Since all data occur in time, virtually all data will have a time-order. In some cases this time-order is the essential context which must be preserved in the presentation." (Donald J Wheeler," Understanding Variation: The Key to Managing Chaos" 2nd Ed., 2000)

"The ordinary histogram is constructed by binning data on a uniform grid. Although this is probably the most widely used statistical graphic, it is one of the more difficult ones to compute. Several problems arise, including choosing the number of bins (bars) and deciding where to place the cutpoints between bars." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"The plot tells us the data are granular in the data source, something we could not ascertain with the histogram. There is an important lesson here. Statistics texts and statistical packages that recommend the histogram as the graphical starting point for a data analysis are giving bad advice. The same goes for kernel density estimates. These are appropriate second stages for graphical data analysis. The best starting point for getting a sense of the distribution of a variable is a tally, stem-and-leaf, or a dot plot. A dot plot is a special case of a tally (perhaps best thought of as a delta-neighborhood tally). Once we see that the data are not granular, we may move on to a histogram or kernel density, which smooths the data more than a dot plot." (Leland Wilkinson, "The Grammar of Graphics" 2nd Ed., 2005)

"Use of a histogram should be strictly reserved for continuous numerical data or for data that can be effectively modelled as continuous […]. Unlike bar charts, therefore, the bars of a histogram corresponding to adjacent intervals should not have gaps between them, for obvious reasons." (Alan Graham, "Developing Thinking in Statistics", 2006)

"A histogram consists of the outline of bars of equal width and appropriate length next to each other. By connecting the frequency values at the position of the nominal values (the midpoints of the intervals) with straight lines, a frequency polygon is obtained. Attaching classes with frequency zero at either end makes the area (the integral) under the frequency polygon equal  to that under the histogram." (Manfred Drosg, "Dealing with Uncertainties: A Guide to Error Analysis", 2007)

"Before calculating a confidence interval for a mean, first check that one of the situations just described holds. To determine whether the data are bell-shaped or skewed, and to check for outliers, plot the data using a histogram, dotplot, or stemplot. A boxplot can reveal outliers and will sometimes reveal skewness, but it cannot be used to determine the shape otherwise. The sample mean and median can also be compared to each other. Differences between the mean and the median usually occur if the data are skewed - that is, are much more spread out in one direction than in the other." (Jessica M Utts & Robert F Heckard, "Mind on Statistics", 2007)

"Histograms are powerful in cases where meaningful class breaks can be defined and classes are used to select intervals and groups in the data. However, they often perform poorly when it comes to the visualization of a distribution." (Martin Theus & Simon Urbanek, "Interactive Graphics for Data Analysis: Principles and Examples", 2009) 

"Need to consider outliers as they can affect statistics such as means, standard deviations, and correlations. They can either be explained, deleted, or accommodated (using either robust statistics or obtaining additional data to fill-in). Can be detected by methods such as box plots, scatterplots, histograms or frequency distributions." (Randall E Schumacker & Richard G Lomax, "A Beginner’s Guide to Structural Equation Modeling" 3rd Ed., 2010)

"A histogram for discrete numerical data is a graph of the frequency or relative frequency distribution, and it is similar to the bar chart for categorical data. Each frequency or relative frequency is represented by a rectangle centered over the corresponding value (or range of values) and the area of the rectangle is proportional to the corresponding frequency or relative frequency." (Roxy Peck et al, "Introduction to Statistics and Data Analysis" 4th Ed., 2012)

"A unimodal histogram that is not symmetric is said to be skewed. If the upper tail of the histogram stretches out much farther than the lower tail, then the distribution of values is positively skewed or right skewed. If, on the other hand, the lower tail is much longer than the upper tail, the histogram is negatively skewed or left skewed." (Roxy Peck et al, "Introduction to Statistics and Data Analysis" 4th Ed., 2012)

"Histograms are often mistaken for bar charts but there are important differences. Histograms show distribution through the frequency of quantitative values (y axis) against defined intervals of quantitative values(x axis). By contrast, bar charts facilitate comparison of categorical values. One of the distinguishing features of a histogram is the lack of gaps between the bars [...]" (Andy Kirk, "Data Visualization: A successful design process", 2012)

"The use of the density scale to construct the histogram ensures that the area of each rectangle in the histogram will be proportional to the corresponding relative frequency. The formula for density can also be used when class widths are equal. However, when the intervals are of equal width, the extra arithmetic required to obtain the densities is unnecessary." (Roxy Peck et al, "Introduction to Statistics and Data Analysis" 4th Ed., 2012)

"Histograms and frequency polygons display a schematic of a numeric variable's frequency distribution. These plots can show us the center and spread of a distribution, can be used to judge the skewness, kurtosis, and modicity of a distribution, can be used to search for outliers, and can help us make decisions about the symmetry and normality of a distribution." (Forrest W Young et al, "Visual Statistics: Seeing data with dynamic interactive graphics", 2016)

"A histogram represents the frequency distribution of the data. Histograms are similar to bar charts but group numbers into ranges. Also, a histogram lets you show the frequency distribution of continuous data. This helps in analyzing the distribution (for example, normal or Gaussian), any outliers present in the data, and skewness." (Umesh R Hodeghatta & Umesha Nayak, "Business Analytics Using R: A Practical Approach", 2017)