Methodology DETR
Percentages were calculated based on numerator and denominator relationships between the census variables in order to capture the intensity of inequality, rather than the number of inequality within the households. This process was subjective in that we wished to identify the proportion of households that fell within a high range of socioeconomic inequality rather than the raw number of households that fell within the same range. This resulted in the analysis of deprivation through percentages rather than through raw numbers.

Re-scaling the datasets was necessary to allow us to convert the indicators into a common metric so that they can be combined (Senior, 2002). Due to the lack of information regarding the weighting of the original 32 sub-variables from the DETR index we based our aggregation methods on the Z score. This process has been utilized by previous deprivation index authors such as Jarman (1983), Townsend (1988), Carstairs and Morris (1991). Z scores were seen as advantageous when working with data within different distributions as it is often difficult to combine multiple factors into a meaningful result without first standardizing the dataset. Typical fields used inserted into this process included varying percentage ratios; multiple numerator and denominator tables; and the inclusion of 20% sample data with 100% sampled data.

Z score =

Where:

Xi = the observed value

 = median reference value, or mean of Xi 

SD = standard deviation of the sum of the observed value Xi 

           

Assigning Weights to the sub-variables

             The only information available pertaining to the original weighting of the DETR Index of Multiple Deprivation at the time of our original analysis were those pertaining to the 6 factors of deprivation. Little information could be retrieved pertaining to influence of the variables within the weighting criteria. It was considered highly unfavorable to weight each of the factor variables equally as this would imply that all variables affected population health in the same fashion. Instead, we decided to assign weights with regard to their importance within the actual data table. This was done in order to treat all variables with the level of importance that they exhibited within each factor calculation. Consequently, it was necessary to use the raw values of the census table datasets instead of the calculated percentages. The resulting calculations provided us with a percentage value, which was used as the weight to determine the influence of each sub-variable within the deprivation factor.

Xa / ( SXa + Xb + Xc ) = % of influence of Xa

Standardizing the Z scores

            Urban neighborhoods can suffer from not only one but several types of urban deprivation at the same time (Langlois, 2001). Due to the large number of variables it is necessary to normalize the deprivation scores before comparing their values within the index. In order to compare this index table with the other index tables it was necessary to establish a standard range to describe the relationship between the values in the dataset. Using each factor score, we re-scaled each weighted variable in relation to the minimum and maximum values within its field within a range of 0 to 1, with 0 representing the least deprived and 1 representing the most deprived.

(Xi  - min) / DXi 

Where:

Xi  = the observed value

min = the minimum value of Xi 

Dx = the change in Xi , as the product of (Xi  max - Xi  min)

 

            In cases where the resulting table was reversed, such that the value below the mean would be more deprived and the value above the mean less deprived, a value of -1 was multiplied to the table in order that their relationship match those records where a low value (0) represented less deprived.