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There are several tests for randomness, one is runs up and down, another is run against mean or some other values, of cause, Bartel's rank test can also be used.

There are studies shows where Bartel's rank test is more powerful than run up&down, and a pure guess could be that the runs up & down is more powerful than runs against mean/some values since it uses more information of the data.

However, in practices it is not the case, in my application, I found the runs against mean/median is more powerful for most samples I tested, which is quite surprising.

Are there any studies/simulations that compare the two runs tests' statistical power?

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    $\begingroup$ It doesn't generally make sense to talk about the relative power of tests against very broad alternatives without specifying which kinds of alternative you want power against. $\endgroup$ – Glen_b -Reinstate Monica Feb 6 '13 at 10:29

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