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        "description": "Skid Marks: Check for runs in sequences\n---------------------------------------\n\n  Q: how do you check for runs?\n\n  A: look for skidmarks.\n\nThis module implements some functions to check a sequence for randomness.\nin some cases, it is assumed to be a binary sequence (not only 1's and 0's\nbut containing only 2 distinct values).\nAny feedback, improvements, additions are welcomed.\n\n    >>> from skidmarks import gap_test, wald_wolfowitz, auto_correlation, serial_test\n\n\nWald-Wolfowitz\n--------------\n\nhttp://en.wikipedia.org/wiki/Wald-Wolfowitz\\_runs\\_test\n\nhttp://support.sas.com/kb/33/092.html\n\n    >>> r = wald_wolfowitz('1000001')\n    >>> r['n_runs'] # should be 3, because 1, 0, 1\n    3\n\n    >>> r['p'] < 0.05 # not < 0.05 evidence to reject Ho of random sequence\n    False\n\nthis should show significance for non-randomness\n\n    >>> li = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]\n    >>> wald_wolfowitz(li)['p'] < 0.05\n    True\n\n\n\nAutocorrelation\n---------------\n\n    >>> result = auto_correlation('00000001111111111100000000')\n    >>> result['p'] < 0.05\n    True\n\n    >>> result['auto_correlation']\n    0.83766233766233755\n\n\nSerial Test\n-----------\n\nhttp://books.google.com/books?id=EIbxfCGfzgcC&lpg=PA141&ots=o-8ymmqbs9&pg=PA142#v=onepage&q=&f=false\n\n    >>> serial_test('101010101111000')\n    {'chi': 1.4285714285714286, 'p': 0.69885130769248427}\n\n    >>> serial_test('110000000000000111111111111')\n    {'chi': 18.615384615384617, 'p': 0.00032831021826061683}\n\n\nGap Test\n--------\n\nhttp://books.google.com/books?id=EIbxfCGfzgcC&lpg=PA141&ots=o-8ymmqbs9&pg=PA142#v=onepage&q=&f=false\n\n    >>> gap_test('100020001200000')\n    {'chi': 756406.99909855379, 'item': '1', 'p': 0.0}\n\n    >>> gap_test('101010111101000')\n    {'chi': 11.684911193438811, 'item': '1', 'p': 0.23166089118674466}\n\ngap\\_test() will default to looking for gaps between the first value in\nthe sequence (in this case '1') and each later occurrence. use the `item`\nkwarg to specify another value.\n\n    >>> gap_test('101010111101000', item='0')\n    {'chi': 11.028667632612191, 'item': '0', 'p': 0.27374903509732523}",
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