Geoscience Reference
In-Depth Information
3
Methods for Testing Normality of
Hydrologic Time Series
Statistical methods are applied in all the phases of time series analysis from
collecting data to evaluating results in hydrologic studies. Advances in computer
technology has enabled most of the scientists/researchers to apply statistical
analyses effectively; however, some of the researchers do not check parametric
test assumptions, especially the normality assumption (Adeloye and Montaseri,
2002). Many methods of time series analysis depend on the basic assumption
that data were sampled from a normal distribution (Madansky, 1988; USEPA,
1996; Thode, 2002). This assumption is very crucial for the reliability of
results especially for parametric tests. These days many statistical software
packages are available, which include several tests for checking the normality
of time series data. However, the important point is to judge which test should
be used under what condition (USEPA, 1996).
In general, the normality assumption can be evaluated by graphical and
statistical methods (USEPA, 1996; Thode, 2002). The graphical methods
provide us with some information about the shape of the distribution, but do
not guarantee that the distribution is normal and do not test whether the
difference between the normal distribution and the sample distribution is
significant. On the other hand, numerical methods provide only quantitative
information. Major statistical methods to assess the assumption of normality
are (USEPA, 1996; Thode, 2002): Chi-square goodness-of-fit test, Kolmogorov-
Smirnov (KS) test, Lilliefors corrected Kolmogorov-Smirnov test, Anderson-
Darling test, Cramer-von Mises test, Shapiro-Wilk test, Jarque-Bera test, and
D'Agostino-Pearson omnibus test. It is worth mentioning that there is an
inherent problem with normality tests. Because of a small sample size, normality
tests have little power to reject the null hypothesis that the data come from a
normal distribution. Hence, small samples always pass normality tests.
However, with large samples, minor deviations from normality may be treated
as statistically significant, even though small deviations from a normal
distribution may not affect the results of a parametric test (GraphPad, 2007).
 
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