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On Jun 27, 2015, at 10:14 AM, Fred Hebard <mbiew@comcast.net> wrote:

David,

If you could resend the spreadsheet in another format that would be helpful.

Fred

Fred Hebard

mbiew@comcast.net

On Jun 27, 2015, at 8:56 AM, David Fleming <NoReply_Fleming@fer3.com> wrote:

Fred:

I have looked over my spreadsheet and as you suggested the variance was calculated wrong.  I inadvertantly calculated .5 square(StdDev) instead of square(.5 StdDev) for the terms in the overlap error propagation.  This was not apparent in the spreadsheet print out so now I'll attach the spreadsheet and you can see if I calculated what I think I calculated.  I hope that attachment will be visible to you.

Let me discuss the analysis of the overlap data first.  11 measurements were made of IC.  Their average was 3.56 and the measurements had a .38 StdDev.  Dividing the .38 sample StdDev by squareroot(11)  = .115 ; we have an IC measurement of 3.56 +/- .115 moa.  Had I worked as hard at the overlap measurements, ie 22 measurements, and assuming same sample statistics and average I would report IC= 3.56 +/- .081 moa.

Now consider the Limb to Limb measurements.  First see the graph of on residuals, (on Mean - on datapoint) versus off rsiduals.  A lack of correlation of the off and on measurements is clear, a trendline would have basically zero slope and the fit parameter would show the trendline to be meaningless.  Not that the graph is really meanigless as the pairing of on and off is meaningless.  The order in wich the data was enterd on the paper can not be significant.

Analyzing the on and off data seperately as was done for the overlap data we get

1) on Mean = 32.16 +/- .099 moa     and   2)  off Mean = -30.95 +/-.145

Average of on & off Means = .61 moa for IC     and Range of on and off = 63.11  for 4 SD      and How do error bars affect the precision of these values?

 If we compute value c from values a and b ie c=f(a,b)

Square(StdDeva) = Square( df/da StdDeva) + Square( df/db StdDevb)   actually partial derivatives.

 Given IC = 1/2 ( off + on)  then the partials are each 1/2.  While SD= 1/4 (off-on) then partials are each 1/4

StdDevIC=1/2*square root( .099^2+.145^2)= .088  so IC = .61 +/- .088

StdDevSD=1/2 StdDevIC   so SD = 15.777 +/- .044

Recall overlap IC = 3.56 +/- .081

Bottom line overlap is as good as limb to limb.  Whatever role visual accuity might play it is not determinative of these measurement statistics ie their precision. 

 

Dave F

Attached File:
raw-data-IC-measurements-comparison.ods (no preview available)