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A. Puranik et al.
based on quartiles. Each category was color coded; darker shade represents higher
proportion, and lighter shade represents low proportion.
The global spatial autocorrelation in the percentage of households with access to
drinking water and sanitation obtained from the two surveys was estimated using
Moran’s I statistic, with Queen’s contiguity weight matrix. A Moran’s I value of zero
indicates the null hypothesis of no clustering, a positive Moran’s I indicates positive
spatial autocorrelation (i.e., clustering of areas with similar attribute values), and a
negative coefficient indicates negative spatial autocorrelation (i.e., neighboring areas
tend to have dissimilar attribute values).
The local spatial clusters were identified using the spatial analysis technique called
Getis-Ord Gi* statistic [19]. The null hypothesis for the cluster detection technique
is spatial randomness of proportion of event of interest in the geographic units under
consideration. The Getis-Ord Gi* statistic and the associated p value will determine
whether to reject or not reject the null hypothesis. If the null hypothesis is rejected,
it implies that the spatial clustering is statistically significant and has not occurred
due to chance.
The formula to compute Getis-Ord Gi* statistic is given as
Gi
∗
=
n
j=1 w i j x j − ¯
X
n
j=1 w i j
S
n
n
j=1 w
2
i j −(
n
j=1 w i j )
2
n−1
where n is the number of areas within the region of interest and x j is the observed
value for area j (i = j), and ¯
X the mean of the attribute under investigation. w i j is
a measure of the closeness of areas i and j represented using the weight matrix.
¯
X =
n
j=1 x j
n
S =
n
j=1 x
2
j
n
−
¯
X
2
E(Gi) = 0 and V ar(Gi) = 1 and the distribution of Gi* under the null hypothesis of no spatial association among the observed values is approximately normal.
Getis-Ord Gi* statistic is a z-score which is computed for every geographic unit
under consideration. The value of statistic for each geographic unit is compared with
the value of sum of statistic of all geographic units. If the value of statistic for each
geographic unit is different from the expected value of statistic, and if that difference
is too large to be the result of random chance, the resultant z-score of statistic is
considered to be statistically significant.
A positive value of the statistic indicates clustering of high values of attribute,
and a negative value of the statistic indicates clustering of low values of attribute.
Larger the value of statistic, the more intense is the clustering. The districts with
high proportion of access to drinking water form hot spots (high-high) if they are
A. Puranik et al.
based on quartiles. Each category was color coded; darker shade represents higher
proportion, and lighter shade represents low proportion.
The global spatial autocorrelation in the percentage of households with access to
drinking water and sanitation obtained from the two surveys was estimated using
Moran’s I statistic, with Queen’s contiguity weight matrix. A Moran’s I value of zero
indicates the null hypothesis of no clustering, a positive Moran’s I indicates positive
spatial autocorrelation (i.e., clustering of areas with similar attribute values), and a
negative coefficient indicates negative spatial autocorrelation (i.e., neighboring areas
tend to have dissimilar attribute values).
The local spatial clusters were identified using the spatial analysis technique called
Getis-Ord Gi* statistic [19]. The null hypothesis for the cluster detection technique
is spatial randomness of proportion of event of interest in the geographic units under
consideration. The Getis-Ord Gi* statistic and the associated p value will determine
whether to reject or not reject the null hypothesis. If the null hypothesis is rejected,
it implies that the spatial clustering is statistically significant and has not occurred
due to chance.
The formula to compute Getis-Ord Gi* statistic is given as
Gi
∗
=
n
j=1 w i j x j − ¯
X
n
j=1 w i j
S
n
n
j=1 w
2
i j −(
n
j=1 w i j )
2
n−1
where n is the number of areas within the region of interest and x j is the observed
value for area j (i = j), and ¯
X the mean of the attribute under investigation. w i j is
a measure of the closeness of areas i and j represented using the weight matrix.
¯
X =
n
j=1 x j
n
S =
n
j=1 x
2
j
n
−
¯
X
2
E(Gi) = 0 and V ar(Gi) = 1 and the distribution of Gi* under the null hypothesis of no spatial association among the observed values is approximately normal.
Getis-Ord Gi* statistic is a z-score which is computed for every geographic unit
under consideration. The value of statistic for each geographic unit is compared with
the value of sum of statistic of all geographic units. If the value of statistic for each
geographic unit is different from the expected value of statistic, and if that difference
is too large to be the result of random chance, the resultant z-score of statistic is
considered to be statistically significant.
A positive value of the statistic indicates clustering of high values of attribute,
and a negative value of the statistic indicates clustering of low values of attribute.
Larger the value of statistic, the more intense is the clustering. The districts with
high proportion of access to drinking water form hot spots (high-high) if they are