Summary Statistics

Runs Z Test Exploration

Z for different run lengths

Ratio	Mean	Stdev	#up	#down	#trials	#runs	z
0.5	52.2	28.6	463	537	1000	537	2.46
0.5	50.6	30	483	517	1000	513	0.8
0.5	51.2	28.5	468	532	1000	510	0.7
0.5	50.1	29.2	499	501	1000	485	-1.01
0.5	51.9	29.6	466	534	1000	498	-0.04
0.5	52.4	28.4	469	531	1000	463	-2.29
0.5	51.5	29	472	528	1000	486	-0.85
0.5	52.3	28.8	467	533	1000	499	0.01
0.5	51.6	28.6	463	537	1000	501	0.17
0.5	49.9	28.4	504	496	1000	504	0.19
0.5	50.6	28.7	4920	5080	10000	5053	1.07
0.5	50.4	28.9	4952	5048	10000	5020	0.39
0.5	50.4	28.7	4908	5092	10000	4950	-0.99
0.5	50.2	29.2	4917	5083	10000	5023	0.47
0.5	50.5	28.9	4921	5079	10000	5060	1.21
0.5	50.5	28.8	4876	5124	10000	4906	-1.84
0.5	50.5	28.8	4915	5085	10000	4932	-1.35
0.5	50.3	28.9	4935	5065	10000	4876	-2.48
0.5	50.6	28.9	4892	5108	10000	4967	-0.63
0.5	50.5	28.8	4902	5098	10000	4972	-0.54
0.5	50.3	28.8	49222	50778	100000	49614	-2.37
0.5	50.6	28.8	48762	51238	100000	49930	-0.26
0.5	50.5	28.8	49058	50942	100000	50084	0.64
0.5	50.4	28.9	49069	50931	100000	49748	-1.49
0.5	50.4	28.8	49178	50822	100000	49922	-0.41
0.5	50.6	28.9	48774	51226	100000	49900	-0.45
0.5	50.5	28.8	48841	51159	100000	50113	0.88
0.5	50.5	28.9	49028	50972	100000	49943	-0.25
0.5	50.4	28.9	48996	51004	100000	49846	-0.85
0.5	50.6	28.9	48912	51088	100000	50317	2.15

Notes: 5 out of the 30 experiments have "unusual" z values,
and z value is relatively independent of number of trials if n>1000

Z for different up-down ratios

Ratio	Mean	Stdev	#up	#down	#trials	#runs	z
0.25	50.5	28.9	23944	76056	100000	36459	0.32
0.3	50.5	28.9	29139	70861	100000	41362	0.49
0.35	50.4	28.9	34181	65819	100000	44981	-0.11
0.4	50.5	28.8	38937	61063	100000	47311	-1.61
0.45	50.5	28.9	43112	56888	100000	48985	-0.43
0.5	50.4	28.8	48123	51877	100000	49981	0.32
0.55	50.4	28.9	53096	46904	100000	50044	1.49
0.6	50.4	28.9	59031	40969	100000	48357	-0.08
0.65	50.6	28.9	63954	36046	100000	46231	0.85
0.7	50.6	28.9	68834	31166	100000	43170	1.94

Note: The z value is independent of probability of an up data value