For my dissertation I have a dataset of postcodes of 9984 that I am converting to coordinates atm.
I looking to find whether this dataset has a 'typical or 'atypical' spatial distribution compared to the whole of the UK Postcodes spatial distribution.
Well I can think of the following approach. I assume that you don't have access to the whole dataset of the entire postcodes. In general spatial distribution of postcodes will be similar to the population density or to the density of buildings. You can easily get most of the buildings of the UK from the OpenStreetMap. Converth them to points. Create a kernel density map for the buildings using for example spatstat package for R (density() function). Divide it by the number of buildings. Do the same for the postcodes you have - create a kernel density map and divide it by the number of postcodes. Then subtract values of one image from the other or divide one by the other to get the difference map. Compute summary statistics on the difference map and make a conclusion whether your postcodes distribution is typical or not.
A remark. As you are working on the dissertation you should use scientific approach. You should have checked scientific literature on approaches to point pattern evaluation first. Then pick up the method that fits your goals the best and only after that ask here how to implement that method if there is no clear software implementation. [as a scientist] I'm not sure that my approach is good enough for the scientific work.
The UK government provides a dataset on all UK postcodes under a modified UK OGL license.
http://opendatacommunities.org/data/postcodes
Some factors you may want to consider in your analysis:
Distribution Reference: Population or Occupied Housing Units
Variables:
Land Use/Zoning
Gross Domestic Product (GDP) per capita
