I have incorporated run by run polarization corrections. (see details and plots ) attached.

So far, analysis has used nominal 60% polarization for this set. Looking at measured polarization for these data the average is 60.7%.

The fill by fill correction is applied to a fill by fill measurement of pi0 AN. The correlation between AN and measured polarization is as expected.
 
Good news,

With linear fits to Cos(phi) distribution, three approaches for folding in polarization data
result in  less than 3% variation in corrected values for AN. The corresponding statistical error in the fit measurement of AN for the example data that I am showing is about 2%

However...

After careful fill polarization reweighting, I show that the form of the AN vs Cos(phi) distribution. It does not have a good chi2 for a straight line fit.  It is interesting that the apart from a single factor, the up/down luminosity ratio, the function we observe is an "odd" function of Cos(phi). In a power series fit

  f(Cos(phi))= Sum (C_n Cos(Phi)^n)

for n>0 the coefficients of even n's are consistent with zero but odd ones are not.

This result could be affected by acceptance but this can be physics! I am thinking about how to model this in the Monte Carlo. (more on that later).

The bottom line is that the best linear fit gives a value of AN that is about 10% smaller than that which would be obtained if small detectors, like the FPD, located at Cos(phi)=+/- 1 are used.

A more extreme example is that if we measure the slope of f(Cos(phi)) near Cos(phi)=0, the slope is nearly twice as large at the average slope (~2 standard deviations). We need to think about this!