Testing Normality of Data for Uncertain Level of Significance

Among the normality test is the W/S, which has a standard table as the interval for the critical region with both lower and upper bound. The test is appropriate for sample sizes of 3 and up, as shown in the W/S Critical table. The test methodology is based on the single sampling plans and lacks in dealing with the double sampling schemes. In this paper, the design of the W/S test using the double sampling scheme is proposed. The operational procedure of the proposed test is given, and some necessary measures are derived using the double sampling scheme. The evaluation of the proposed test is discussed using the Weibull distribution, Chi-square distribution, and Normal distribution, t-distribution, and Cauchy distribution. The efficiency of the proposed test is compared with the existing W/S test, and found that the proposed test has a higher power of test than the existing test. The methodology of the proposed W/S test under a double sampling scheme is also illustrated by using generated data.