5. Ranking Analysis The above developed Basic Needs indicators are used to rank the SA3 regions through various methods: Decile Ranking of Basic Needs Index: The SA3 regions of the Greater Sydney are ranked by using the Basic Needs Index in scale of 1-10; the lowest 10% areas are given value 1 and highest 10% areas are given value 10. The choropleth map clearly shows a higher Basic Needs Index in the inner suburbs around Sydney CBD and Northern Beaches, while the Basic Needs Index decreases towards the outer regions, which indicates the lack of overall facilities for the target group in the outer regions of Greater Sydney.
Figure 5: Basic Needs Index Ranking.
In order to observe the global autocorrelations, we have used Moran’s I statistic (Levine, N. 1999) It is a cross-product statistic between a variable and its spatial lag. The variable is expressed in deviations from its mean. For an observation at location i, this is expressed as zi = xi - x ̅ where x ̅ = mean of the variable. Moran’s I statistic = I is described as:
where, S0=∑_i▒∑_j▒〖wij 〗 = sum of all weights n = number of observations The null hypothesis in Moran’s I test infers spatial randomness. The test can be based on normality assumption; however, such an assumption may produce erroneous results as discussed by Griffith (2005) and hence rather than employing normality, we have used a randomization technique. Under this technique, a reference distribution is created by randomly assigning the variable values over different locations. Then, reference distribution is used to calculate pseudo-p-value given as: p = (R+1)/(M+1) Where, R = Number of time the computed Moran’s I is equal to or more than the observed values, and M = the number of permutations. We have calculated Moran’s I with 999 permutations and got the pseudo-p-value as 0.001, inferring that we can reject the null hypothesis and that Sydney is highly structured.
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