# Graphing

Graphing visualises data to facilitate perception and interpretation of distributions and relationships. Graphs should be accompanied by descriptive statistics.
This page provides an overview of graphing steps and principles and types of graphs.
   Watch "Science is beautiful", a 5:30 minute Nature Video which explores three different visualisations: Florence Nightingale (health), genome overlaps, ocean currents.
   Watch "Is Pivot a turning point for the web?", a 6:25 minute TED talk about a Microsoft technology which enables flexible exploration and zooming in and out of visualised data. This illustrates the power of being able to visualise data as a whole in order to discover patterns and links.

## Graphing - How to

   “Visualization is any technique for creating images, diagrams, or animations to communicate a message.” - Wikipedia

### Steps

Creating effective data visualisations is not easy. Suggested basic steps are:
* Identify the purpose of the graph
* Select which type of graph to use, based on the variable(s)' level of measurement
* Draw an appropriate graph
* Modify the graph to be clear, non-distorting, and well-labelled.
* Disseminate the graph (e.g., include it in a report)

### Principles

   "Like good writing, good graphical displays of data communicate ideas with clarity, precision, and efficiency.
   Like poor writing, bad graphical displays distort or obscure the data, make it harder to understand or compare, or otherwise thwart the communicative effect which the graph should convey." Michael Friendly – Gallery of Data Visualisation
* Maximise objective display of truth. According to Tufte, the “lie factor” in graphs is size shown in graph divided by statistical size. It should be 1.
* Avoid distortion (Tufte)
* Avoid excessive use of colour - effective graphs are often monotone.
* Clearly label axes and provide a meaningful, descriptive figure caption. Use a legend and/or footnotes as appropriate to provide sufficient information for the graph to be interpretable as a whole without detailed references to accompanying text.
* Graphs are subject to the law of parsimony - i.e., they should be as simple as necessary to clearly communicate about data of interest.
* The whole of the data is more than the sum of the parts (Gary Flake, 2010)
* Show the data (Tufte)
* Reveal data at several levels (Tufte)
Graph types
The choice of graph will depend on the variables' level of measurement.
Univariate
Graphs of a single variable.
Bar chart
Also referred to as bar graphs
Used for illustrating frequencies or percentages for categories or the means of different groups or variables.
The x-axis shows the categories, groups or variables, the y-axis shows the quantity (frequency, percentage or a statistic such us a mean).
Tips for creating bar charts
Pie chart
Represents percentage data as pie slices (angles).
Generally not as effective as bar or error-bar graphs and are to be avoided.
Can be difficult to compare the relative size of similar-sized slices.
Can be difficult to label very small slices
Error-bar graph
Shows means with confidence intervals
Alternative to bar chart
Error-bar graph showing mean pulse rates and 95% confidence intervals by exercise level.
Box plot
Also known as the box and whisker plot
Plots the mean, quartiles, confidence interval and outliers
Stem and leaf plot
Displays stem (e.g., 10s) and leaves (e.g., 1s).
Each leaf represents a case
The exact data is provided in a visual display (like a histogram)
-2 | 4
-1 | 2
-0 | 3
0 | 4 6 6
1 | 6
2 | 4
3 |
4 |
5 | 7
Histogram
Displays the frequency of occurrence of data for intervals within a single variable continuous distribution.
Heights of 31 Black Cherry trees. :
Bivariate
Graphs of the relation between two variables.
Clustered bar-graph
Clustered bar-graphs are used to include an additional independent variable (e.g., gender). The separate groups are represented by different coloured bars.
Scatterplot
Plots the relation between two variables on a continuous x and y axis :