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Variance Reduction

Posted By: rambiz
Date: Friday, 18 July 2014, at 7:51 a.m.

In Response To: DQ: Consider the bar point? *** Rollout *** (Timothy Chow)

I think, there exists some consensus on how to calculate a confidence interval for a long Bernoulli experiment (by using the normal distribution).
However, I don't know how to factor in the effect of Variance Reduction. I know that Variance Reduction virtually increases the number of trials but I don't know by how much! I doubt there is a rigorous theory out there, which actually quantifies this effect. As long as no theory has been developed (or exposed to the public for proof-reading purposes), I am not going to put much confidence in all the confidence intervals reported by the bots.

Messages In This Thread

• DQ: Consider the bar point?
  leobueno -- Wednesday, 16 July 2014, at 11:33 a.m.
  • DQ: Consider the bar point?
    Wolfgang -- Wednesday, 16 July 2014, at 12:31 p.m.
  • DQ: Consider the bar point?
    ah_clem -- Wednesday, 16 July 2014, at 2:06 p.m.
    • Calculating gammon values
      Tom Keith -- Wednesday, 16 July 2014, at 4:07 p.m.
      • Calculating gammon values
        Bob Koca -- Wednesday, 16 July 2014, at 6:42 p.m.
      • Calculating gammon values
        Bob Koca -- Wednesday, 16 July 2014, at 6:45 p.m.
      • Calculating gammon values
        phil simborg -- Thursday, 17 July 2014, at 12:55 a.m.
  • 62S-53P-63
    Nack Ballard -- Wednesday, 16 July 2014, at 3:09 p.m.
    • 62S-53P-63
      leobueno -- Wednesday, 16 July 2014, at 3:30 p.m.
  • Interesting Variants: 62S-31P-61 – 62S-42P-61 – 62S-53P-61
    Taper_Mike -- Wednesday, 16 July 2014, at 9:57 p.m.
    • Interesting Variants: 62S-31P-61 – 62S-42P-61 – 62S-53P-61
      Nack Ballard -- Thursday, 17 July 2014, at 12:15 a.m.
      • Interesting Variants: 62S-31P-61 – 62S-42P-61 – 62S-53P-61
        Igor -- Thursday, 17 July 2014, at 1:46 a.m.
    • 62S-31P-61 – 62S-42P-61 – 62S-53P-61 – 3-ply XG2 Rollouts
      Taper_Mike -- Friday, 18 July 2014, at 8:38 a.m.
  • DQ: Consider the bar point?
    ben -- Wednesday, 16 July 2014, at 10:41 p.m.
  • DQ: Consider the bar point? *** Rollout ***
    leobueno -- Thursday, 17 July 2014, at 11:13 a.m.
    • 62S-53P-63, Rollout for money
      Nack Ballard -- Thursday, 17 July 2014, at 2:15 p.m.
      • 62S-53P-63, 1296 trial Rollout AtS
        ah_clem -- Thursday, 17 July 2014, at 7:07 p.m.
        • 62S-53P-63, 1296 trial Rollout At reversed score
          ah_clem -- Thursday, 17 July 2014, at 8:38 p.m.
          • 62S-53P-63, 1296 trial Rollout At reversed score
            Bob Koca -- Thursday, 17 July 2014, at 11:16 p.m.
    • DQ: Consider the bar point? *** Rollout ***
      Timothy Chow -- Thursday, 17 July 2014, at 11:38 p.m.
      • DQ: Consider the bar point? *** Rollout ***
        Bob Koca -- Friday, 18 July 2014, at 12:59 a.m.
      • DQ: Consider the bar point? *** Rollout ***
        Tom Keith -- Friday, 18 July 2014, at 2:12 a.m.
        • DQ: Consider the bar point? *** Rollout ***
          leobueno -- Friday, 18 July 2014, at 11:23 a.m.
          • DQ: Consider the bar point? *** Rollout ***
            Bob Koca -- Friday, 18 July 2014, at 12:45 p.m.
          • DQ: Consider the bar point? *** Rollout ***
            Timothy Chow -- Friday, 18 July 2014, at 10:14 p.m.
        • DQ: Consider the bar point? *** Rollout ***
          Timothy Chow -- Friday, 18 July 2014, at 10:00 p.m.
          • DQ: Consider the bar point? *** Rollout ***
            Tom Keith -- Saturday, 19 July 2014, at 12:02 p.m.
            • DQ: Consider the bar point? *** Rollout ***
              Bob Koca -- Saturday, 19 July 2014, at 4:38 p.m.
              • DQ: Consider the bar point? *** Rollout ***
                Tom Keith -- Saturday, 19 July 2014, at 6:24 p.m.
                • DQ: Consider the bar point? *** Rollout ***
                  Timothy Chow -- Wednesday, 23 July 2014, at 10:12 p.m.
                  • DQ: Consider the bar point? *** Rollout ***
                    Tom Keith -- Thursday, 24 July 2014, at 12:44 a.m.
      • Variance Reduction
        rambiz -- Friday, 18 July 2014, at 7:51 a.m.
        • Variance Reduction
          Bob Koca -- Friday, 18 July 2014, at 12:51 p.m.
        • Variance Reduction
          Timothy Chow -- Friday, 18 July 2014, at 10:27 p.m.
          • Variance Reduction
            rambiz -- Saturday, 19 July 2014, at 12:33 p.m.
            • Variance Reduction
              Tom Keith -- Saturday, 19 July 2014, at 1:23 p.m.
            • Variance Reduction
              Bob Koca -- Saturday, 19 July 2014, at 4:34 p.m.
              • Variance Reduction
                rambiz -- Saturday, 19 July 2014, at 9:12 p.m.
                • Variance Reduction
                  Bob Koca -- Monday, 21 July 2014, at 12:37 a.m.
                  • Variance Reduction
                    rambiz -- Monday, 21 July 2014, at 3:01 p.m.
                    • Variance Reduction
                      Tom Keith -- Monday, 21 July 2014, at 5:53 p.m.
                      • Variance Reduction
                        rambiz -- Monday, 21 July 2014, at 6:19 p.m.
                        • Variance Reduction
                          Bob Koca -- Monday, 21 July 2014, at 6:37 p.m.
                          • Variance Reduction
                            rambiz -- Monday, 21 July 2014, at 9:42 p.m.
                            • Variance Reduction
                              Bob Koca -- Tuesday, 22 July 2014, at 3:53 a.m.
                              • Variance Reduction
                                rambiz -- Tuesday, 22 July 2014, at 6:27 p.m.
                                • Variance Reduction
                                  Maik Stiebler -- Wednesday, 23 July 2014, at 1:33 p.m.
                                  • Variance Reduction
                                    rambiz -- Friday, 25 July 2014, at 4:58 p.m.
        • Variance Reduction
          Neil Robins -- Wednesday, 23 July 2014, at 10:47 p.m.
        • Variance Reduction
          Timothy Chow -- Saturday, 26 July 2014, at 8:14 p.m.
          • Slight correction
            Timothy Chow -- Sunday, 27 July 2014, at 2:53 p.m.
            • Slight correction
              Bob Koca -- Monday, 28 July 2014, at 12:33 a.m.
              • Slight correction
                Timothy Chow -- Monday, 28 July 2014, at 4:54 p.m.
          • Variance Reduction
            Bob Koca -- Monday, 28 July 2014, at 12:36 a.m.