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I understand the critiques of pie charts as referenced here: Problems with pie charts

However, the above response (and the R manual) always cite dot plots from Cleveland as an alternative. My question is why are dot plots considered an alternative? It seems to be that dot plots only apply when:

  1. the data set is relatively small (so that you can perhaps even by eye count dots in the plot, each dot corresponding to a data point, and

  2. they are not intended to display percentages / density estimates of data.

It seems to me like the main goal of the pie chart is (even if it does so badly) to highlight the fact that the categories must sum to 1 or 100%. with the dot plots you can show the cardinal value of each category, but it will not be obvious what fraction of all the categories a particular value is. Also, with a pie chart it doesn't matter if you have 10 data points or 1,000,000, where as a dot plot with a million points (even if the number of categories is small) seems odd and might just collapse to a bar graph.

Could someone explain why dots plots are seen as an alternative and maybe provide a few examples of dot plots to other quantitative alternatives to pie charts (like bar plots?)

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  • $\begingroup$ There are some nice discussions about this in Andrew Gelman's blog: "Please stop me before I barf again", "Why tables are really much better than graphs", "A data visualization manifesto". $\endgroup$ – user10525 Aug 15 '12 at 15:25
  • $\begingroup$ See mbq's answer to the question you linked to, you certainly can not effectively display 1 million pie slices in a pie chart and the chart still be intelligible. $\endgroup$ – Andy W Aug 15 '12 at 15:26
  • $\begingroup$ I agree that dot plots don't substitute for pie charts. They are like bar charts. In my comments about pie charts on another post I mentioned that sometimes they can be useful. I think the main complaint is that the eye cannot discern proportions based on looking at slices especially thin ones. But 90 degree and 45 degree slices are discernable I think. At least in a pie chart you can tell whether a particular category has a slice that is large or small relative to the complete pie. $\endgroup$ – Michael Chernick Aug 15 '12 at 15:47
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    $\begingroup$ @user248237 Yeah, but the question is too subjective/broad to get a convincing answer in the general case, so I just wanted to point those references. $\endgroup$ – user10525 Aug 15 '12 at 16:29
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    $\begingroup$ @user248237, that comparison doesn't make sense. If you summarize the information in a pie chart you can summarize that same information into a dot plot or a bar chart (what we are talking about here is the number of pie slices or bars in a bar chart, not the number of disaggregated items used to make the chart). I would suggest to read Cleveland's work, as it should illuminate how human perception is better at identifying points along a common axis, as opposed to identifying the angles within slices in a pie chart. $\endgroup$ – Andy W Aug 15 '12 at 16:35
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There are two different types of chart that that are referred to as 'dotplots' and I think that you are getting the two confused. The type of dotplot that it looks like you are thinking about is really a variation on a histogram and does not convey the same type of information that a pie chart would.

The type of dotplot from Cleveland is essentially a bar chart with a dot placed at the end of each bar, then the bar is removed. So even with millions of data points, they would be tabled the same as for creating a pie chart, then a single dot is plotted for each category. The summary preparing for the plot is the same in a pie chart and a dotplot: the difference is in a pie chart you are trying to compare non-aligned angles or areas (and the temptation to add chartjunk or otherwise distort the perception of the values is much higher) and in the dotplot you are comparing points on an aligned scale.

If you want the viewer to be able to easily judge percentage of the whole then just make sure that the axis for the dot positions goes from 0 to the total count. You can also easily add another axis (or replace the main one) that shows the percentage rather than the counts, then the percentage can be read off that axis much more accurately than estimating angles and areas in pie charts.

Here are a couple of examples using R:

This is the type of dotplot that I think you are thinking of, and this would not replace a pie chart:

library(TeachingDemos)
dots(round( rnorm(100),0 ) )

enter image description here

But this is the type of dotplot being referred to in Cleveland as a replacement for pie charts:

# steal data from ?pie
pie.sales <- c(0.12, 0.3, 0.26, 0.16, 0.04, 0.12)
names(pie.sales) <- c("Blueberry", "Cherry",
    "Apple", "Boston Cream", "Other", "Vanilla Cream")
par(mfrow=c(2,1))
dotchart(pie.sales*100)
# or
par(xaxs='i')
dotchart( pie.sales*100, xlim=c(0,100) )

enter image description here

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  • $\begingroup$ Thanks for the clarification. The two types of dot plots are very different. I guess I can read the proportions off the dot plot and have the numbers clear. But the same could be done with a pie chart putting the percentage inside each slice or if the slice is too narrow it could be given pointing to the appropriate slice. I actually think that would give me a better sense of how the pecentages are distributed than this dot plot. $\endgroup$ – Michael Chernick Aug 15 '12 at 17:59
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    $\begingroup$ Adding percentages (or counts) to a pie chart (or at the ends of the bars in a bar chart, or at the dots in a dot plot) accomplishes 2 things: 1. Serves as an admission that the plot cannot convey the information by itself; 2. Converts the plot into a poorly laid out table (with colorful background). And in the case of the bar chart it also 3. distorts the lengths of the bars (what effect this has in the bar and dot plots is less clear). $\endgroup$ – Greg Snow Aug 15 '12 at 18:18
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    $\begingroup$ To note in addition to this (+1), if you want the percentages in the dot plots (the usual Cleveland dot plots, not the what I will call Wilkinson Dot plots (why did he pick that name!?!) all you have to do is change the X axis labels, the "dots" all stay in the same location. This should also reinforce why dot plots can really replace pie charts (in the vast majority of instances). The extra information in knowing "proportion" of whole is really trivial, and starting from the dot plot allows more flexibility. $\endgroup$ – Andy W Aug 15 '12 at 18:34
  • $\begingroup$ The pie chart can look very nice either using a legend or well placed percentages. I agree with Greg that the fact that these numbers are needed conveys the point that none of these types of graphs convey the proportion information without the addition of the numbers. $\endgroup$ – Michael Chernick Aug 15 '12 at 19:56
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Greg Snow's response has covered much about dot plot. I'd just like to suggest an alternative which you can compress the dimension further:

enter image description here

Sorry the legend is missing but the idea is pretty much here. Instead of displaying the four pieces of data on four horizontal lines, we can put them in one line with accumulative percentage as the scale. This way, the difference between dots will allow quantitative comparison just like usual dot plots do. In addition, it can overcome the difficulty of comparing multiple pie charts: if we need to show data from another entity, we could just add one more horizontal line in the illustration.

Reference code:

library(lattice)
perc <- c(100, 60, 30, 10)
setnum <- rep(1,4)
category <- c("A", "B", "C", "D")
dotplot(setnum ~ perc, group=category, xlim=c(-5,105),ylab="", xlab="Cumulative %", pch=16)
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  • $\begingroup$ Hi @Penguin_Knight - do you mind elaborating on how this answers the question? $\endgroup$ – Macro Aug 15 '12 at 17:53
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    $\begingroup$ @Macro Thanks, I am just merely suggesting an alternative to what Greg Snow has shown. As how this answers the question, because the questions asks "Could someone explain why dots plots are seen as an alternative and maybe provide a few examples of dot plots to other quantitative alternatives to pie charts." $\endgroup$ – Penguin_Knight Aug 15 '12 at 17:58
  • $\begingroup$ @Macro Thanks for the comment. I just quickly put this together. Will expand. Regards. $\endgroup$ – Penguin_Knight Aug 15 '12 at 18:07
  • $\begingroup$ I like this plot (I've never seen this type of 'dot plot' before), as it does convey the exact same information as a pie chart, except using the length of the interval to denote the proportion, rather than the area of a slice of pie. Some expansion of this answer will be good to see. In some ways this is more intuitively appealing than the Cleveland dot plot, but I can see that it would become unwieldy more quickly that the Cleveland dot plot as the number of categories increases. $\endgroup$ – Macro Aug 15 '12 at 18:09
  • $\begingroup$ @Macro this is synonymous with a stacked bar chart (I'm sure you've seen one of those) in which you replace the bar ends with a dot. Hence any complaints about stacked bar charts apply to this as well. $\endgroup$ – Andy W Aug 15 '12 at 18:32

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