Standard Deviation of REG devices

Mike Meyer has constructed Java modules to process huge amounts of data. His application to 6 months of data showed that the mean of all the REG devices was within specification, but that the standard deviation for many of the eggs is slightly different from the theoretical value. The average change is an increase of 0.0127%. Using this value as an estimate for the change that would result in the usual calculations if the empirical value were substituted for the theoretical value gives some idea of the implications. An application to the formal database indicates that the net effect is to reduce the cumulative effect by a factor of 0.00025. Because this is not consequential, we will continue to use the theoretical value for computations. Mike has constructed a table showing the result of using empirical estimates for SD per egg, based on 6-month samples. The tabled values are (I believe) the Z-scores representing the difference between theoretical and empirical results, which would be zero in a perfect world.

Here are the details of a summary of the SD change by egg type, and a worst-case assessment of the implication for the formal results accumulated thus far in the EGG project.

            Theoretical SD          7.0711 
            PEAR device SD, N=4     7.0687 
            Mindsong SD, N=16       7.0732 
            Orion SD, N=7           7.0709 
            
            Prop smaller PEAR      -0.00033941 
            Prop larger Mindsong   +0.00029698 
            Prop smaller Orion     -2.8284e-05 
            Prop larger All 3      +0.00012728
            
            Proportional overestimate of Z-scores using All 3 is       0.00012728
            Corresponding overestimate of Z2 is on the order of        0.00025456
            The degrees of freedom across the 76 events are            26120 
            The original Chi-square based on theoretical SD is         27195
            The reduced Chi-square based on the All 3 SD is            27188
            The worst case reduction, based on the Mindsong SD is      27179 
            The theoretically based calculation gives probability      1.715e-6
            The estimated SD from the All 3 calculation yields p=      1.9805e-06
    

My conclusion is that using the theoretical standard deviation does not produce misleading bottom-line conclusions. The difference of actual device parameters from theory is on the order of a hundredth of one percent, and this means that in general, the calculations are accurate to three or four decimal places. Since we are dealing with statistical estimates always, I can accept this level of inaccuracy as being well within the noise, even if it is a systematic error. At some point in the future, when someone wishes to do a more precise calculation, based on locally computed empirical standard deviations for all eggs, we will use it, but at this point, there are other interesting analyses and projects that must be given higher priority.