OK, I wasn’t going to spend any more time on this, but as always once you get started with something like this, it’s hard to put it down!

This post has been inspired by very similar questions posed by Nicola Shelton and Colin MacInnes on my Facebook wall – the gist was “this is all very nice, but have you thought about religious diversity?” i.e. where are the places with the most different religions and where are the places where it’s all pretty homogeneous?

After a bit of thinking out loud on my facebook wall about how to calculate such an index, I ended up doing what most sensible people do these days – I had a bit of a Google around! Several years in academia have taught me that if you have a bit of a conundrum, chances are, most of the time, someone else will have had a very similar problem and posted an answer on the web!

So it turns out, diversity is something ecologists are pretty into – they bloody love looking at whether or not areas contain a diversity of species and have developed/plundered from other disciplines (like us geographers love to do) a plethora of indices to quantify the diversity phenomenon. One of these is the Gini-Simpson index (sometimes described as just “the Simpson Diversity index” or similar – see this Wikipedia page for a description of the difference). I could’ve also used Shannon Entropy as a measure, but much of my life for the last 2 years has been to do with Entropy maximising, so I thought I’d leave it in the bag this time!

The Gini-Simpson index is a measure of the diversity of an area. It takes into account the number of different groups in the area as well as the relative abundance of those groups. The index can be calculated using the following formula:

$latex D_{i}=1-\left(\frac{{\displaystyle \sum_{j}}\left(n_{ij}\left(n_{ij}-1\right)\right)}{N_{i}\left(N_{i}-1\right)}\right)$

where $latex D_{i}$ is the Gini-Simpson diversity for area $latex i$

$latex n_{ij}$ is the total number of people in area $latex i$ who are classified in religion $latex j$

and where $latex N_{i}$ is the total number of people across all religions $latex j$ in area $latex i$, or:

$latex N_{i}={\displaystyle \sum_{j}\left(n_{ij}\right)}$

The index ranges between 0 and 1. 1 represents an infinite diversity, 0 represents no diversity (or complete homogeneity, if you’d rather).

I calculated this index for each output area in London, and it produces some rather pretty maps. In addition, I also calculated a standardised ratio which enables you to look at the religious diversity of an output area, compared to the average diversity for the whole City. Of course, the denominator need not be London, but could easily be England and Wales, or the whole UK.

I’ve not seen anyone talk about using a standardised ratio anywhere, so in honour of Colin sparking my interest, I shall dub it the ‘Colin-Gini-Simpson or Colin-Diversity Ratio’. If you like algebra, the equation for calculating the Colin-Diversity ($latex CD$) Ratio for area $latex i$ is:

$latex CD_{i}=\frac{D_{i}}{D}$

where

$latex D={\displaystyle \frac{\sum_{j}\left(N_{j}\left(N_{j}-1\right)\right)}{T\left(T-1\right)}}$

where

$latex N_{j}={\displaystyle \sum_{i}n_{ij}}$

or the total number of people in each religious group across the whole city.

And

$latex T={\displaystyle \sum_{i}\sum_{j}n_{ij}}$

or the total number of people in the city.

Yes, yes, I know, that’s enough tedious algebra – WHAT ABOUT THE MAPS?!?!?! OK, so here we are. First up is the standard Gini-Simpson map of religious diversity. Should probably note that the reference index for the whole of London is 0.699 (remember, 1 being infinitely diverse, 0 being completely homogeneous) – so pretty diverse, as we might expect. The range of values is quite large as well, with the least diverse output area (0.19) E00004097 – which is in Bromley in South London. The most religiously diverse OA is E00010619, which is the area to the South of Canons Park in Harrow, north London.

As might be expected, with the higher LQs for most religious groups in North London, the most religiously diverse areas are in this half of the city, with much less religious diversity in the South.

The next map is the Colin index, which shows quite neatly areas which are above or below the average diversity for London:

There’s a bit of negative skew in the data, with more OAs being less religiously diverse than the Gini-Simpson score for the whole city.

And one final map, just to finish this whole thing off – this map shows the most popular religion by OA, i.e. were you in that output area, this is the religion that most people you come across will be – enjoy!

***Oops, just spotted an error (mine!) Where it says Buddhist, is should really be Hindu – will fix the map on Monday, but the pub beckons now!!!)***