Impacts of Node Connectivity on Reliability of Water Distribution Networks - Pattern Recognition for Reliability Assessment of Water Distribution Networks - page 166

Table 6.22 Pearson correlation - results per cluster (undirected, fixed D, variable Q)

Measures NGI NCF3 NCF avg NCI3 NSI3 AGD GD Deg avg BC avg Cc avg
cluster 1 - 50 nodes, 66-76 links
ADFavg 0.13 -0.07 -0.04 0.02 0.02 0.03

NBI 0.07 -0.11 -0.08 0.18 0.18 -0.12

In 0.09 0.08 0.08 0.77 0.77 -0.68

cluster 2 - 151 nodes, 217-246 links
ADFavg 0.45 0.40 0.40 -0.29 -0.29 0.34

NBI 0.32 0.30 0.30 0.05 0.05 0.02

In -0.12 -0.14 -0.14 0.42 0.42 -0.38

cluster 3 - 200 nodes, 285-313 links
ADFavg 0.28 0.26 0.26 -0.19 -0.19 0.23

NBI 0.31 0.30 0.30 -0.17 -0.17 0.19

In 0.40 0.41 0.41 0.13 0.13 -0.07

6.9 STATISTICAL ANALYSIS

To verify the above conclusions, more complete statistical analysis has been conducted of all
the results. The Spearman test has been used for this purpose being an alternative for the
Pearson test that is known to be more suitable for linear correlations of normalised data.
Despite large number of calculations, the number of analysed networks in each set/cluster has
been relatively small from the perspective of statistical significance, to be sure about the data
normalisation. Also, the assumption of linear correlation between the connectivity and
reliability measures is highly questionable, having in mind quadratic head/flow relation in
pipes. Hence, the idea of using also the Spearman test was to compare the results with the
Pearson test and also having in mind its resistance towards isolated high or low values. The
Spearman's Rank Correlation Coefficient, R , is calculated as:

∑

2

6 d

R = 1 −

n

6.18

2

n ( n − 1

In Equation 6.18, d stands for difference in the ranking between n pairs of data. This ranking
is done for each of the two data sets that are to be correlated, as it is shown in Table 6.12.
The bandwidth of correlation is given in Table 6.23. The closer is the value of R to +1 or -1,
the stronger is the likely correlation. The R -value of zero assumes no correlation, whatsoever.

Table 6.23 R -value bandwidth

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Strong positive
correlation

Weak positive
correlation

Little
correlation

No
correlation

Little
correlation

Weak positive
correlation

Strong positive
correlation

The correlation level, P , of probability distribution to determine whether two data sets have
different degrees of diversity, is calculated as in Equation 6.19; parameter d f , in the equation
stands for the degree of freedom (equals n-2 ). The bandwidth of the significance level is
shown in Table 6.24. The final conclusion about the correlation will depend on the
comparison of the R and P against the value of d f .