Analysis of Trend and Periodicity in Long-Term Annual Rainfall Time Series of Nigeria - Hydrologic Time Series Analysis: Theory and Practice - page 256

Savannah zone and the Nigeria average are very similar. Generally, it has been
wet before the 1970s, whereas in the post 1970s, there has been dramatic
reduction in annual rainfall over Nigeria.
12.4.1.3 Temporal trends

1. Normality analysis: Prior to applying parametric trend tests, normality of
the annual rainfall was tested by using both graphical and statistical tests.
Using data averaged over Nigeria, histogram of the annual rainfall was plotted
along with the theoretical normal distribution curve as shown in Fig. 12.3.
The results showed that apart from the one outlier, 870 mm (with a distance
of slightly more than three times the standard deviation from mean), the series
can be approximated by a normal distribution. A similar result was obtained
by plotting a box plot, presented in Fig. 12.4, where the outlier was clearly
flagged better than the histogram. The results of statistical tests such as the
Kolmogorov-Smirnov test and a more robust Shapiro-Wilk test are presented
in Table 12.2. For these tests , p - value for normality determines the probability
of being incorrect in concluding that the data is not normally distributed ( p -
value is the risk of falsely rejecting the null hypothesis that the data is normally
distributed). If the p -value computed by the test is greater than the p -value set
a priori, the test passes. To require a stricter adherence to normality then the
p -value must be increased. The suggested value in SigmaPlot and SPSS
software is 0.05. Larger p -values (for example, 0.10) require less evidence to
conclude that the residuals are not normally distributed. One often rejects the
null hypothesis when the p -value is less than 0.05 or 0.01, corresponding
respectively to a 5% or 1% chance of rejecting the null hypothesis when it is
true (Type I error). It was observed from Table 12.2 that the Kolmogorov-
Smirnov test accepted the null hypothesis that our sample is normally distributed
for data with 'the outlier' and a more robust Shapiro-Wilk test also barely
accepted the null hypothesis. However, both the statistical tests confirmed
presence of normality in annual rainfall time series after the removal of single
outlier (Table 12.2). In a sample of 1000 observations, the presence of up to
five observations deviating from the mean by more than three times the standard

Table 12.2. Results of two normality tests for annual rainfall time series of Nigeria

Kolmogorov-Smirnov a test Shapiro-Wilk test

Test-statistic df Significance Test-statistic df Significance

(a) Annual rainfall time series with outlier

0.058 100 0.200* 0.989 100 0.612

(b) Annual rainfall time series after removing single outlier
0.053 99 0.200* 0.992 99 0.853
Note: a Lilliefors Significance Correction; df = degree of freedom; *Lower bound of
true significance.