The paper provides five tests of data normality at different sample sizes. The tests are the Shapiro-Wilk (SW) test, Anderson-Darling (AD) test, Kolmogorov-Smirnov (KS) test, Ryan-Joiner (RJ) test, and Jarque-Bera (JB) test. These tests were used to test for normality for two secondary data sets with sample size (155) for large and (40) for small; and then test the simulated scenario with standard normal “N(0,1)” data sets; where the large samples of sizes (150, 140, 130, 130, 110 and 100) and small samples of sizes (40. 35, 30, 25, 20, 15 and 10) are considered at two levels of significance (5% and 10%). However, the aim of this paper is to detect and compare the performance of the different normality tests considered. The normality test results shows Kolmogorov-Smirnov (KS) test is a most powerful test than other tests since it detect the simulated large sample data sets do not follow a normal distribution at 5%, while for small sample sizes at 5% level of significance; the results showed the Jarque-Bera (JB) test is a most powerful test than other tests since it detects that the simulated small sample data do not follow a normal distribution at 5%. This paper recommended JB test for normality test when the sample size is small and KS test when the sample size is large at 5% level of significance.

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The issues concerning global rainfall distribution and warming/climate change cannot be over emphasized since it affects virtually every part of live. The study used rainfall pattern in two states of Nigeria. Data on the monthly rainfall distribution in Imo and Rivers state, for a period of 37 years was examined. The result showed a continuous increase in the pattern of rainfall for a period of thirty seven years within the period under study. However the pattern was inconsistence for the remaining years with some kind of fluctuations. The monthly mean series plots showed a clear presence of trend with the peak period being September annually in both series with coefficient of determination- R square value of 83% and 86% for Imo and Rivers series respectively. The yearly mean series plots showed a clear irregular variation over the years in both series. The irregularity in the pattern of rainfall calls for serious commitment in joining the force for climate change abatement process. Pearson correlation coefficient between the two series is 0.80 (substantial correlation), which is the same result with cross correlation between the two rainfall series (0.79988 approx. 0.80). The series reveal the following characteristics: high correlations appear seasonality of order 12 in the monthly mean plots (every September), irregular variation and trend curve which is quadratic trend. ARIMAX model with independent variable was employed to identify the best bivariate time series model for prediction purpose. The result reveal an increase in Rivers series (Yt ) would tend to a linear combination of some increase of the preceding Imo series (It ) values which is vise visa. SARIMAX (1, 2) and SARIMAX (2, 1) models are identified as the best model with respect to Rivers on Imo series rainfall; via Imo on Rivers series rainfall.

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