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standard error reported by gnu

Posted By: Tom Keith
Date: Friday, 4 February 2011, at 3:30 a.m.

In Response To: standard error reported by gnu (rambiz)

Suppose you roll out two plays and want to know whether they are correctly ranked by their rollout results. (The plays could be wrongly ranked if the poorer play had luckier dice in the rollout.).

If the standard deviations of the two plays are SD1 and SD2, compute a "joint standard deviation", JSD = sqrt( SD1² + SD2² ). Then take D, the difference between the rollout results, and divide by the JSD. Consult the following table to find the probability the plays are correctly ranked.

D / JSD	Probability the plays are correctly ranked
0.0	50%
0.5	69%
1.0	84%
1.5	93.3%
2.0	97.7%
2.5	99.4%

Your example:  If R1 = 0.70 and SD1 = 0.005, and R2 = 0.68 and SD2 = 0.008, then

JSD = sqrt( 0.005² + 0.008² ) = 0.0094
D = 0.70 - 0.68 = 0.02
D / JSD = 0.02 / 0.0094 = 2.13

From the table, there is roughly a 98% chance that an infinite rollout won't reverse the order of these plays.

Messages In This Thread

• standard error reported by gnu
  rambiz -- Thursday, 3 February 2011, at 10:11 p.m.
  • standard error reported by gnu
    Tom Keith -- Friday, 4 February 2011, at 3:30 a.m.
    • standard error reported by gnu
      rambiz -- Friday, 4 February 2011, at 9:32 p.m.