Fun and Games with Census data

Anyone reading, watching or listening to responsible media outlets (which lets News Corp and Fox off the hook) in the last few days will have been aware that the first tranch of results from the 2011 Census of Australia have been released by the Australian Bureau of Statistics on 21 June

Since human activity has a huge impact on nature and the environment, and statistical data is a good way of demonstrating this, I have no compunction in putting up a promo for Census data on this blog.

The good folk at Flagpost were right on top of the use of Census data, publishing an interesting post on 22 June.  What particularly interested me about this post was the citation of results for two electorates, with rather different profiles.  It made me wonder which electorate was closest to the Australian average?

It seemed that use of the TableBuilder facility by ABS would be an efficient way to look at data for all electorates to sort this out, but unfortunately the databases underlying that won't be available until August 2012.  (I can quite understand the reasons for that, but now I am a user, rather than compiler, of Census data I want it NOW!)  I didn't fancy trying to hand compile several data items  for 150 Divisions so have decided to see what can be done by addressing the more restricted question:

 "Which State/Territory of Australia is closest to the Australian average?"

Depending on how I calculated this the answer appeared to be Victoria  or - surprisingly - Western Australia.  If you are interested in the methods, read on!  (If not, it has been nice having you here, and goodbye!)

The 8 States and Territories are nicely defined and it was merely necessary to come up with a set of data items to measure their closeness to the Australian average.   That is easy, if said quickly.  To really address with full rigour would be a huge job so I have just taken a sample of a few of the variables from the first release that seem to cover a fair range of attributes of society.  These variables and the values quoted in the ABS QuickStats facility are shown in the following table (note: to fit it in the width of the page this is an image, not the table per se).  Values that look 'interesting' are highlighted in yellow for high values or blue for low values.

I may return to the selection of values in a subsequent post, since there may be some correlations between them.  If I remember to do so, I may do the electorate analysis when TableBuilder data becomes available.

Method 1.
I calculated, for each variable, the percentage difference of each State's value from the Australian level (shown in the table) and then expressed those percentages as absolute values (ie 5% and -5% both show the same 'distance' from the Australian value),  Adding up those absolute values gives an index of overall distance as shown below.

Victoria wins!  (NSW would have pipped them were it not for the high level of stated religious adherence in that State - no wonder they keep electing Fred Nile!) An obvious problem with this is that NSW and Victoria comprise such a high proportion of the population of Australia that they have to be close to the Australian value.  So a second method was used.

Method 2
The method was broadly the same except that instead of using the Australian value as the origin for my measure of distance I used the arithmetic mean of the States' values.  This caused the Australian values to shift a bit (for example the average median weekly income was $1336 rather than $1234) and the sum of the percentage differences changed quite a lot as shown below.

WA wins this time, due to having most values close to the mean of State  values.  The only major difference is the low proportion of Australian born people in WA.  Queensland's second place reflects the relatively high level of religiosity in that State which boosts their 'distance' quite a bit.  Victoria and NSW score high values for proportion of old folk and dwelling ownership (possibly a manifestation of correlation right there) and the religiousness of NSW people continues to score highly.