An Empirical Likelihood Ratio-Based Omnibus Test for Normality with an Adjustment for Symmetric Alternatives

Table 3

Type I error rates along with the standard error for the proposed test statistics using .

Alpha	Simulated probabilities of the type I error along with standard error
	Sample size	CUSUM-type test statistic	Shiryaev–Roberts test statistic
0.01	20	0.009214  1.3509e − 04	0.009346  1.3606e − 04
	30	0.010163  1.4181e − 04	0.010291  1.4269e − 04
	50	0.010589  1.4469e − 04	0.009849  1.3963e − 04
	80	0.010893  1.4675e − 04	0.009613  1.3796e − 04
	100	0.009706  1.3862e − 04	0.009916  1.4003e − 04
0.05	20	0.050133  3.0859e − 04	0.049785  3.0758e − 04
	30	0.049841  3.0774e − 04	0.050578  3.0989e − 04
	50	0.052238  3.1464e − 04	0.049027  3.0534e − 04
	80	0.051434  3.1235e − 04	0.050018  3.0826e − 04
	100	0.048295  3.0317e − 04	0.051756  3.1327e − 04
0.10	20	0.102066  4.2812e − 04	0.100521  4.2523e − 04
	30	0.100938  4.2601e − 04	0.098578  4.2156e − 04
	50	0.101902  4.2781e − 04	0.099039  4.2242e − 04
	80	0.101586  4.2722e − 04	0.099829  4.2392e − 04
	100	0.095552  4.1573e − 04	0.101395  4.2686e − 04