BGonline.org Forums

my solution

Posted By: Chuck Bower
Date: Monday, 25 July 2011, at 3:40 p.m.

In Response To: NOW I understand why you guys are struggling (Chuck Bower)

I suspect either I didn't define the problem well (even after the posted adenda) or I'm just wrong. But here is what I came up with:

For each xi, calculate the mean success rate, p_bar(xi), and the sample standard deviation, s(xi) for which I used the binomial formula for calculating reduced s.d.: sqrt(p*(1-p)/N). Then minimize the function

[p_bar(xi)]/s(xi)]^2 - [A*Q(xi)]^2

where A is the variable of minimization. (I.e. find the value of A where this relationship is a minimum.) Note the smaller the standard deviation, the more weight that datapoint gets.

I got this idea from Data Reduction and Error Analysis for the Physical Sciences by Philip R. Bevington.

BTW, the idea of taking more data to beat down the s.d. isn't always an option.

Messages In This Thread

• math/stat question (OT)
  Chuck Bower -- Saturday, 23 July 2011, at 5:42 p.m.
  • Clarification
    Chuck Bower -- Saturday, 23 July 2011, at 7:15 p.m.
  • math/stat question (OT)
    rambiz -- Saturday, 23 July 2011, at 8:00 p.m.
    • math/stat question (OT)
      Bob Koca -- Saturday, 23 July 2011, at 8:57 p.m.
      • math/stat question (OT)
        rambiz -- Saturday, 23 July 2011, at 9:47 p.m.
        • NOW I understand why you guys are struggling
          Chuck Bower -- Saturday, 23 July 2011, at 10:14 p.m.
          • Siamese or Persian!?
            rambiz -- Sunday, 24 July 2011, at 12:59 a.m.
          • NOW I understand why you guys are struggling
            Casper van der Tak -- Sunday, 24 July 2011, at 8:30 a.m.
          • my solution
            Chuck Bower -- Monday, 25 July 2011, at 3:40 p.m.
        • But for each value of i you have a different number of measurements
          rambiz -- Sunday, 24 July 2011, at 12:45 a.m.