Efficacy of Time Series Tests: A Critical Assessment - Hydrologic Time Series Analysis: Theory and Practice - page 143

Table 7.1. Observed test-statistics and the results of three normality tests

Test-Statistic Annual Rainfall One-day max. 2-day max. 3-day max. 4-day max. 5-day max. 6-day max.

(a) Geary's Test

Geary's test-statistic 0.981 0.951 1.036 1.017 0.994 1.007 1.003

Normality Yes Yes Yes Yes Yes Yes Yes

(b) Kolmogorov-Smirnov (KS) Test

KS test-statistic 0.1053 0.1877 0.1504 0.1499 0.1446 0.1283 0.1185

P -value >0.1 0.0003 0.0094 0.0099 0.0152 0.0509 0.0964

Normality Ye s No No No No Ye s Ye s

(c) D'Agostino-Pearson Omnibus Test

K 2 test-statistic 9.788 19.11 6.367 6.661 5.475 4.907 4.624

P -value 0.0075 <0.0001 0.0414 0.0358 0.0647 0.0860 0.0991

Normality No No No No Ye s Ye s Ye s

(d) D'Agostino-Pearson Omnibus Test after removing mild outliers

Number of removed outliers - 3 1 3 - - -

K 2 test-statistic - 5.475 4.603 5.480 - - -

P -value - 0.0647 0.1001 0.0646 - - -

Normality - Ye s Ye s Ye s - - -

Note: max.: maximum.