C. Cahillane, J. Kissel

I have taken a look at our measurements of the actuation coefficients on ETMY L3 as reported by  LHO aLOG 18767.
We have three measurements of actuation:  Free Swinging Mich, ALS DIFF VCO, and PCAL, which each have different measurement values and uncertainty bars.

The measurements were significantly different, so I looked for mathematical motivation for seeing if the weighted mean and uncertainty calculated in aLOG 18767 was meaningful.

I found a document that walks you through the basics:  Understanding Data Better with Bayesian and Global Statistical Methods by William H. Press.  The document claims that if the chi^2 value is outside the range of (N-1) +- sqrt( 2*(N-1) ) where N = number of measurements, then our measurements are incompatible and our weighted mean has no justification.

For our actuation coefficients:
chi^2 = 72.4250
acceptable range (N=3) = [0, 4]
(Calculation of the above found here: /ligo/svncommon/CalSVN/aligocalibration/trunk/Runs/PreER7/H1/Scripts/ETMY_L3_Actuation_Coefficient_Compatibility_Test.m )

Our chi^2 is clearly outside the acceptable range, meaning that at least one of our measurements has high systematic uncertainty that renders our weighted mean are poor estimate of the actuation coefficient.

Bayesian methods are advocated to identify the problematic measurement and appropriately quantify our actuation coefficient given our current measurements and uncertainty, or else we may search our measurement methods of sources of systematic uncertainty.