Ok then, and yes perhaps I will change the percentages for each output area to population densities then.
Thank you for your advice, yes as long as I show that I've acknowledged any uncertainties surrounding my study, I think this will be ok.
And in terms of where my work fits into the bigger picture of geography, I suppose that measuring accessibility to services is important for comparing the spatial distribution of demand relative to supply, and looking at how access can vary spatially. As access to green spaces is generally considered to be associated with improvements in wellbeing, assessments into the adequacy and equality of access across cities seems important to investigate whether people have equal opportunities to yield these benefits to wellbeing, regardless of where they live. I can then use my assessments to identify areas which are potentially in greatest need of improvements to access. Hope that addresses the question.
Throughout my study I've measured distances to different types of spaces and calculated the percentages of the population for which different accessibility standards set for green spaces have been met. However I feel that these measures are all quite simplistic, since my results only really consist of average distances and percentages. So this is why I was hoping to bring in some statistical analysis by testing to see how the distributions of social groups vary with access, and whether green space are therefore well located relative to demand. But would you suggest that this isn't really worthwhile since there clearly won't be strong relationships between the variables? But if I do decide to use Pearson's to measure correlations between the variables, would you mind explaining what would be involved with transforming my data as you previously mentioned to do? You mentioned to log the percentages, rather than using the original values?