Efficacy of Time Series Tests: A Critical Assessment - Hydrologic Time Series Analysis: Theory and Practice - page 144

test-statistic value approaches one (Walpole and Myers, 1989). Given this
criterion, all the seven rainfall time series can be considered normal based on
the Geary's test (Table 7.1). The results of the Kolmogorov-Smirnov test and
the D'Agostino-Pearson Omnibus test can be interpreted by comparing
observed P -values with 0.05. If the P -value is more than 0.05, the null
hypothesis of normality cannot be rejected. It can be seen from Table 7.1 that
observed P -values for the annual rainfall and 5- and 6-day maximum rainfalls
are greater than 0.05 for the Kolmogorov-Smirnov test. Similarly, observed P-
values are greater than 0.05 for the 4-, 5- and 6-day maximum rainfall time
series for the D'Agostino-Pearson Omnibus test. Thus, based on the box
plots, normal probability plots and three normality tests, the rainfall series
under study can be considered to be normal, though one-day and consecutive
2-day maximum rainfall time series have few mild outliers that causes deviation
from normality. After removing these mild outliers and then applying the
D'Agostino-Pearson Omnibus test, which is reported as powerful normality
test (e.g., DeCarlo, 1997; Öztuna et al., 2006), it was found that observed P -
value is not significant (Table 7.1). Thus, all the seven rainfall series under
study could be considered to be normal.
7.5 Checking Homogeneity
In this study, three homogeneity tests (i.e., von Neumann test, Cumulative
Deviations test and Bayesian test) were employed to examine the homogeneity
in the annual and maximum rainfall series. The results of the three homogeneity
tests are presented in Table 7.2. The von Neumann ratio is a statistic that has
an expected value of 2 for a homogeneous series, but it tends to be less than
2 for a non-homogeneous series. It is apparent from Table 7.2 that the von
Neumann ratio (N) becomes smaller than 2 for the one-day and consecutive
2-day maximum rainfall series, which suggests non-homogeneity in these
rainfall series of Kharagpur. However, N reaches close to 2 for the total
annual, consecutive three-, four-, five- and six-day maximum rainfall series.
In case of Cumulative Deviations and Bayesian tests, all the applied test-
statistics (i.e., Q, R, U and A) have the smaller values compared to their
critical values (Buishand, 1982) at 5% significance level for the total annual
and the maximum rainfall series, which indicate that all the rainfall time series
are homogenous and belong to the same population. Furthermore, as mentioned
in Chapter 4, non-homogeneity arises due to changes in the method of data
collection and/or the environment in which it is done. Environmental or physical
factors are type, height and exposure of the raingauge, which may affect
homogeneity (Buishand, 1982). For the present study, location of the raingauge
station and the method of recording rainfall did not change since its
establishment. Also, the surrounding environment of the raingauge station
and/or physical factors has not altered over the years. Therefore, the physical
factors affecting homogeneity did not change for the raingauge station under