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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 Nondefective 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 “overmixed" nor “undermixed". An example of
overmixed sequence is DDDNDNDNDNDD, with R = 9 while undermixed looks like
DDDDDDDDNNNN with R = 2. There the above sequence seems to be a random sequence.
The Runs Tests, which is also known as WaldWolfowitz 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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 Spring '08
 Staff

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