Determine Randomness of the Data based on the Size and Number of Runs for Large Sample

Wald-Wolfowitz Run test of randomness is a statistical test that is used to know the randomness in data. Run test of randomness assumes that the mean and variance are constant and the probability is independent. The Run Test is actually one of the most interesting statistical tests ever and it is so easy to understand, or even the easiest. There is a risk of selection bias when collecting a sample using consecutive sampling for an ordered population. No assurance that the sequence of data generated will be random because there is no mechanism to ensure random selection. In the proposed work we have taken more 1000 populations which have been vaccinated with corona vaccine for Covid-19 from 10 different vaccination center data from 10 different. We used run test to check the randomness between male and female. We applied properties of run test to check the randomness of data .First we taken 500 person’s data in with 330 Male and 170 female and the numbers of runs are 237. Similarly for second population we have taken 1000 persons data in which 453 Male and 547 Female and number of runs are 512. We calculate z statistics we found in both the cases the calculated z statistics value with run test we found in both the cases the calculated value is less than the critical z value of tabulated value.so can say that both the sample have taken have randomness.