Run Test

For a sequence of measured values x_i, i = 1, 2, 3, ..., N, with a mean value x, where each observation is

x_i > x     (+)

or

x_i < x     (-)

In any case, the sequence of plus and minus observations might be as follows.

In this example:

The number of sequence, N = 20

The number of runs, r = 12

Hypothesis:

There is no trend in the sequence of N independent observations of the same random variable.

Acceptance region:

at a level of significance α (or with a probability of 1-α), where n = N/2.