Test for Randomness: The Runs' Test A basic condition in almost all inferential statistics is that a set of data constitutes a random sample from a given homogeneous population. The condition of randomness is essential to make sure the sample is truly representative of the population. The widely used test for randomness is the Runs test. A “run" is a maximal subsequence of like elements. Consider the following sequence (D for Defective items, N for Non-defective items) from a production line: DDDNNDNDNDDD. Number of runs is R = 7, with n 1 = 8, and n 2 = 4 which are number of D's and N's. A sequence is a random sequence if it is neither “over-mixed" nor “under-mixed". An example of over-mixed sequence is DDDNDNDNDNDD, with R = 9 while under-mixed looks like DDDDDDDDNNNN with R = 2. There the above sequence seems to be a random sequence. The Runs Tests, which is also known as Wald-Wolfowitz Test, is designed to test the randomness of a given sample at 100(1- α )% confidence level. To conduct a runs test on a sample, perform
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