Are there benefits in graphing data?
March 11, 2012, 1:32 am
Filed under: Uncategorized

Are there benefits in graphing data or is it just more work, inputting data, computing and formatting a graph, just to replicate the results you have already written?

Florence Nightingale’s creative graph construction: Persuasive innovation and life-saving tool

Florence Nightingale, was the first woman admitted as a Fellow of the Royal Statistical Society in England.  When the Crimean War broke out, Nightingale directed the entire nursing operation at the war front for the British Army. Her legend began to grow as she instituted practices of basic hygiene, such as changing the bed sheets when new patients entered the hospital. She documented every change that she made so that she could identify what worked and succeeded at dramatically reducing the mortality rate.  Florence Nightingale’s response to bureaucratic resistance was statistics.  Her response began with a simple innovation: She kept systematic records of what happened to patients. Her simple act of using descriptive statistics to catalogue daily life in the hospital had huge consequences and is credited by some as having saved the British Army during the Crimean War.

                                 Figure 1

Nightingale’s careful record keeping did not accomplish her mission on its own. She needed a graph to tell the story. Florence Nightingale invented a “polar-area” diagram, often now referred to as a “cox comb” graph, so named because it resembled the shape of a rooster’s head. A recreation of this circular chart is shown in Figure 1, and it includes causes of death, numbers of deaths, and months of the year. This graph told her story more clearly and eloquently than descriptive statistics alone ever could.

They say a picture is worth a thousand words. The same thing could be said about a graph.  One major goal of statistics is to present data in a meaningful and manageable way.  Graphs are an excellent way to display information visually. Good graphs convey information quickly and easily to the user. It’s one thing to see a list of data, it’s another to understand the trends and details of the data.  Graphs highlight salient features of the data. They can show relationships that are not obvious from studying a list of numbers. Graphs can also provide a convenient way to compare different sets of data.  Different situations call for different types of graphs.

Brief summary of frequently used graphs

A boxplot is a concise graph showing the five point summary. Multiple boxplots can be drawn side by side to compare more than one data set.


  • Shows 5-point summary and outliers
  • Easily compares two or more data sets
  • Handles extremely large data sets easily


  • Not as visually appealing as other graphs
  • Exact values not retained

Bar graph
A bar graph displays discrete data in separate columns. A double bar graph can be used to compare two data sets. Categories are considered unordered and can be rearranged alphabetically, by size, etc.


  • Visually strong
  • Can easily compare two or three data sets


  • Graph categories can be reordered to emphasize certain effects
  • Use only with discrete data

A scatterplot displays the relationship between two factors of the experiment. A trend line is used to determine positive, negative, or no correlation.


  • Shows a trend in the data relationship
  • Retains exact data values and sample size
  • Shows minimum/maximum and outliers


  • Hard to visualize results in large data sets
  • Flat trend line gives inconclusive results
  • Data on both axes should be continuous

A histogram displays continuous data in ordered columns. Categories are of continuous measure such as time, inches, temperature, etc.


  • Visually strong
  • Can compare to normal curve
  • Usually vertical axis is a frequency count of items falling into each category


  • Cannot read exact values because data is grouped into categories
  • More difficult to compare two data sets
  • Use only with continuous data

Line graph
A line graph plots continuous data as points and then joins them with a line. Multiple data sets can be graphed together, but a key must be used.


  • Can compare multiple continuous data sets easily
  • Interim data can be inferred from graph line


  • Use only with continuous data

Stem and Leaf Plot
Stem and leaf plots record data values in rows, and can easily be made into a histogram. Large data sets can be accommodated by splitting stems.


  • Concise representation of data
  • Shows range, minimum & maximum, gaps & clusters, and outliers easily
  • Can handle extremely large data sets


  • Not visually appealing
  • Does not easily indicate measures of centrality for large data sets

The following examples of result for the same data set clearly demonstrate the benefits of graphing data.

A two-way independent-measures ANOVA (nationality: three levels, American, German andEnglish; age: two levels, younger and older) was performed on these data. There was a significant main effect of nationality (F 2, 30 = 21.03, p < .0001). Post-hoc tests revealed that, overall, the German tourists were faster to claim a sun-bed than were the English tourists, who in turn were faster than the Americans (Bonferroni tests, p < .05 for all tests). There was also a significant main effect of age (F1,30 = 14.88, p < .01): regardless of nationality, younger tourists were faster to claim a sun-bed than were older tourists. From fig. 1, it appears that the effects of age were more marked for the Germans and English than they were for the Americans. However, the ANOVA failed to support this interpretation, revealing no significant interaction between age and nationality (F 2, 30 = 2.34, n.s.)





4 Comments so far
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Hi 🙂 the information about Florence Nightingale in here is really interesting to read. A picture really is worth a thousand words. The speed with which you can interpret information in a graph makes it a highly beneficial tool in reporting results. In the same way an abstract is useful for telling you the important information in the minimal amount of word count. Abstracts and titles of research papers are quite often all that will get read when looking for scientific evidence so anything, be it abstract, title, graph which speeds up how we can process the information and see if it is relevant to what we are looking for is a good thing!

Comment by emcg1

I too covered Florence Nightingale’s graph in one of my blogs so I share your thinking on graphs. Although drawn in 1885 it still looks very modern and does not look out of place on a computer. Today computers are changing the way we use graphs as well, such an example is Hans Rosling and his animated graphs (example here http://www.gapminder.org/videos/crisis-narrows-china-uk-gap/). Vast quantities of data are presented in an accessible and easy to understand way. I’m sure Florence would have liked to use such tools.

One thing I did mention in my blog that applies to graphs as a whole, is that they are open to bias or misconception. For example, changing the scales on an axis can make small change look like a massively significant change (like these two images for example http://psuc5d.files.wordpress.com/2012/02/screen-shot-2012-02-05-at-17-18-23.png & http://psuc5d.files.wordpress.com/2012/02/screen-shot-2012-02-05-at-17-18-31.png). The data is exactly the same but they seem to show two different results. Error bars will help with the example I provided but if the author is not being honest then they probably won’t be used. While I don’t believe this to be a fault of graphs as it is merely a tool to be used but something to be aware of. This article (http://mediamatters.org/blog/201112120005) shows a real world example of this with Fox news displaying an incorrect unemployment rate chart. This could be a mistake but it fits in with Fox News agenda. It is worth keeping an eye out for such inaccuracies or misrepresentations.

Comment by psuc5d

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