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From: Fred Hebard
Date: 2015 Jun 30, 16:03 -0400
Square( StdDev IC) = Square( .5 StdDevOn) + Square( .5 StdDevOff)
On Jun 30, 2015, at 3:16 AM, David Fleming <NoReply_Fleming@fer3.com> wrote:Fred,
My results show overlap as good or better than limb to limb.
In my spreadsheet I have an overlap IC = 3.56 moa (cell B18) +/- .115(cell B21) for the 11 measurements shown. Had I done 22 measurements, equivalent to the 11 ovelap measurements, the error would be +/- .081 (cell B25) not accounting for any additional reduction in the sample StdDev.
For the overlap measurement I had an IC = .61 +/- .088. It looks to me like the overlap measurements do at least as well as limb to limb for this data.
Now we agree on the IC values and the error bar for the overlap measurement. What we disagree on is the error bars for the limb to limb measurements.
How I calculate error bar for IC.
I carried out the same analysis, that we agreed on for the overlap, for the on limb and off limb separately. Took the average of from those analysis and got the agreed upon limb to limb IC value. To get the error bar I then used propagation of error theory:
Square(StdDev of a computed quantity) = Square(partial derivative of variable 1 x StdDev v1) +
Square(partial derivative of variable 2 x StdDev v2) + …
Given IC = (On +Off)/2 we have
Square( StdDev IC) = Square( .5 StdDevOn) + Square( .5 StdDevOff) This formula is implemented in cell I21. The StdDev IC is cell H21 = +/- .088.
Columns H and I were not used at all.
How you calculate error bar for IC.
As you indicated, you added a column J in your analysis. Column J took the differences of the on and off and divided by two. And applied statistical analysis to the 11 IC values. This is nonsense. The on values and the off values are totally independent of each other. The order of the on or off values can not influence the answer and the particular order shown is just random. Any other order must under proper analysis yield the the unique proper result.
Try duplicating your sheet and my sheet onto another worksheet in each workbook. Then sort the data in the on column in ascending or descending order the sort the off column also, In your calculation a new result will be produced. In my analysis nothing changes. This ordering produces a correlation which as you indicated affects the StdDevs etc in your calculation. It is ignored by mine.
In column K I'm not quite sure what you were calculating but I note that it doesn't agree with the column J results and so I don't know which results you are claiming are right.
Dave F
