The first blog on using R in the classroom finished with something of a challenge: could you interpret what effect the various parameters in the code below had on your chart?
![](data:image/png;base64,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)
If you tried entering the code, a much more interesting chart is generated.
R works by using set functions with parameters (called arguments) added to customise the appearance. Our bar chart is very simple, but the flexibility of the R language means sophisticated representations of multivariate data are possible. Each function has a range of parameters that can be added, with any that are not directly referenced automatically set to a default by the software. You only need to worry about the things you want to change.
The parameters explained:
|
|
main = "Favourite Colours"
|
sets the title of the chart
|
xlab = "colours"
|
sets the label on the x axis
|
ylab = "Frequency"
|
sets the label on the y axis
|
col = c("blue","green","red")
|
sets the colours of the bars in the order listed. c() is an extra function that combines the values into a list, necessary to make this parameter work.
R has a set of pre-defined colours, but it is possible to put RGB hex codes between the quotation marks for finer control of the colour palette
|
To find out more about the various parameters that can be tweaked, R has an inbuilt help() function, which opens a web page for any function in the parenthesis; e.g. help(plot). At first glance these pages can be daunting, but as you become more familiar with using R you will begin to recognise standard structures and common arguments.
Frequency charts for discrete data
If you try to use discrete data with the functions we currently have available, the chart produced will look weird and will certainly not be a frequency chart. This is due to how plot() tries to process univariate, numerical data. A new function is needed.
First, record some numerical data in a spreadsheet column, save it as a csv file called “numbers” and import into R as we did previously.
![](data:image/png;base64,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)
The data is now recorded as a list, but it needs to be converted into a frequency table in order to work with plot(). To do this, use the command below.
![](data:image/png;base64,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)
I hope that by now you are beginning to be able to interpret the commands as you read them. “frequencyTable” is a new object in which the processed data will be stored, the assignment operator is sending the output from the table() function to this new object (frequency table), which takes the list and converts it into a table with a count of each unique value.
It’s now possible to generate a frequency chart by using the plot() function on the new “frequencyTable” object, but this will create a line graph. To get a bar chart, use the barplot() function instead.
As with plot() you can add parameters to customise the appearance of the bar plot. Have a go with your own data and tweet your creations to @Cambridgemaths