NavList:

Attached is a summary of your data.  The results are the same except that you did not multiply the variances by the square of one half.  I did so in the last column of the attachment.  The standard deviation of the raw index-error values once again is similar to the standard deviation computed from the individual on and (60-off) the arc measurements (last column).  Both are smaller than the standard deviation of the overlap data, in disagreement with your hypothesis.

If you compare these data with those I reported, your standard deviations are about 4x larger than mine, which merely means you need more practice.

Regarding combining variances, also attached is a piece from Wikipedia about that.  Note that if there is a significant covariance between measurements, it should be subtracted from a difference between them and added to their sum.  Adding variances is only appropriate when they are uncorrelated.  I’ll leave it to you to compute the covariance between your on and off the arc measurements because I’m approaching the edge of my comfort zone in statistics.

Best Regards,