In the A level syllabus, the deprivation issue is said to arise from movement of populations. Where more attractive, modern development has taken place, the more affluent and more mobile members of society tend to move towards them. Those who are unable to move are said to be 'stranded' so to speak and unable to move, leaving poorer sections of society in areas such as inner cities; these areas tend to be more deprived. There is a cycle of deprivation since jobs move away with the better skilled areas of society, people are left unemployed, they do not pay tax and councils tend not to invest in services there.
But this is all just theory. What you have to try and experiment upon is whether this theory is true.
What you would need to do first is identify the main parts of city - inner city( generally terraced homes, flats and factories), the inner city (1930-70 semi detached homes), outer city ('Brookside' style cul-de-sacs) and the rural urban fringe (the most modern homes close to out of town shopping centres). I would say to select one 'site' - unsure about size - that you can continue to use whenever you talk about/research 'the outer city' for example.
Once this is done (and this will be part of a preliminary research task that you can write about, show photos of and, best of all, get marks for) you can talk about these areas directly in your hypotheses etc without the examiner thinking you are making assumptions.
Hypotheses:
The inner city will be deprived of recreational areas and transport provisions.
You would expect this because of the lack of local authority investment.
You could test this by recording number of buses that pass within one hour at each of your sites across the city or retrieving secondary data from Arriva or local bus service websites.
You may conclude that the inner city is well provided by buses but only because it is enroute to the CBD and therefore cannot be relied upon as evidence but you still suspect the city is deprived (this is a completely valid conclusion) - you may also find that the inner city is actually the most advanced area and least deprived due to regeneration of the inner city - this has occurred in Newcastle and may well have happened beside the bay barrage (however i do apologise but dont know which section of the city that the barrage is located).
You could pick a school in each of the areas and compare GCSE results for evidence too.
2nd hypothesis: There are better employment opportunities as you move out of the city.
using a sample approach in each area, record the land use - business/residential etc and record the type of business and estimate the salary of the average resident of that section of the city. I could see some nice graphs here.
Car registration plates should get newer as you move out of the city.
There should be fewer minorities outside of the inner city.
Air quality - indicating poor quality of life - will improve as you move out of the city - if you could find equipment or source of info.
Look for council housing and councils will certainly have statistics as well as the DSS about the number of people claiming unemployment benefits.
Overall, you want to get enough information so that you are able to make an informed decision as to whether certain areas of the city are more deprived than others - conclude with a heirarchy and compare with the expectation you had (ie. more deprived as you approach centre with older buildings etc - i would leave regeneration out of your expectations and leave that as a thoughtful ending "the inner city did not meet my expectations since the local authorities have recently undergone redevelopment in order to improve the quality of life in the area" - then what would be really good is if you went on to question whether the tactic works - will the poorer sections of the community not just be forced out into other areas, remaining deprived, whilst more affluent members of society become tenants in the attractive new apartments?
Hope ive helped - ive tried to think through the project myself and say the path i would take but obviously not thought about it for too long - this will have certainly given direction. I was confused this time last year but just picked something and went for it and got very frustrated at times thinking - but where is this going to go? it will come together in end!!