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Entry  Sun Feb 3 13:20:02 2013, Koji, Summary, General, Hypothesis mode_density_PRC.pdfmode_density_PRC.zip
    Reply  Mon Feb 4 10:45:51 2013, Jamie, Summary, General, rough analysis of aligned PRM-PR2 mode scan scan-labeled.pdf
       Reply  Mon Feb 4 11:10:59 2013, Koji, Summary, General, rough analysis of aligned PRM-PR2 mode scan 
          Reply  Mon Feb 4 19:33:19 2013, yuta, Summary, General, rough analysis of aligned PRM-PR2 mode scan 3peakdata.png
             Reply  Tue Feb 5 02:04:44 2013, yuta, Summary, General, rough analysis of aligned PRM-PR2 mode scan PRMPR2scan.png
                Reply  Tue Feb 5 03:16:51 2013, Koji, Summary, General, rough analysis of aligned PRM-PR2 mode scan 
                   Reply  Tue Feb 5 10:09:08 2013, yuta, Summary, General, rough analysis of aligned PRM-PR2 mode scan 
                      Reply  Tue Feb 5 11:30:19 2013, Koji, Summary, General, rough analysis of aligned PRM-PR2 mode scan 
                         Reply  Wed Feb 13 01:26:08 2013, yuta, Summary, General, rough analysis of aligned PRM-PR2 mode scan unbiased.png
       Reply  Wed Feb 6 15:20:55 2013, yuta, Summary, General, FWHM was wrong 
    Reply  Mon Feb 4 15:06:56 2013, Koji, Summary, General, Hypothesis 
    Reply  Mon Feb 4 19:48:32 2013, Jamie, Summary, General, arbcav recalc of PRC with correct ITM transmission mode_density_PRC_2.pdfmode_density_PRC_3.pdf
Message ID: 8074     Entry time: Wed Feb 13 01:26:08 2013     In reply to: 8002
Author: yuta 
Type: Summary 
Category: General 
Subject: rough analysis of aligned PRM-PR2 mode scan 

Koji was correct.

When you estimate the variance of the population, you have to use unbiased variance (not sample variance). So, the estimate to dx in the equations Koji wrote is

dx = sqrt(sum(xi-xavg)/(n-1))
   = stdev*sqrt(n/(n-1))


It is interesting because when n=2, statistical error of the averaged value will be the same as the standard deviation.

dXavg = dx/sqrt(n) = stdev/sqrt(n-1)

In most cases, I think you don't need 10 % precision for statistical error estimation (you should better do correlation analysis if you want to go further). You can simply use dx = stdev if n is sufficiently large (n > 6 from plot below).
unbiased.png



Quote:

Makes sense. I mixed up n and n-1

Probability function: X = (x1 + x2 + ... + xn)/n, where xi = xavg +/- dx

Xavg = xavg*n/n = xavg

dXavg^2 = n*dx^2/n^2
=> dXavg = dx/sqrt(n)

Xavg +/- dXavg = xavg +/- dx/sqrt(n)

 

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