Point count error calculation

The variable ERRORmj n represents the error in the position of the mandrel over an increment in TIME, in seconds. ERRORman is calculated by subtracting the actual pulses accumulated, PULSEman, from the desired number of pulses that would be generated under perfect control. The desired number of pulses for perfect control is determined by the set point speed, RPSman, revolutions per second and the mechanical gear reduction. The constant 15630 is the product of encoder counts per revolution and the thirty to one gear reduction of the mandrel. 

Figure 5.24(B) shows a line profile extracted from the map of Figure 5.24(A) by averaging over 30 pixels parallel to the boundary direction corresponding to an actual distance of about 20 nm. The analytical resolution was 4 nm, and the error bars (95% confidence) were calculated from the total Cu X-ray peak intensities (after background subtraction) associated with each data point in the profile (the error associated with A1 counting statistics was assumed to be negligible). It is clear that these mapping parameters are not suitable for measurement of large numbers of boundaries, since typically only one boundary can be included in the field of view.

Figure 3. The front-to-back activity ratio as measured by method 1 as function of the total wire surface area times the thickness of the screen. The numbers by the points are mesh size per inch. The error bars are calculated from counting statistics. The reason for 500 mesh having higher F/B than 635 mesh is not understood.

In order to achieve reasonable statistical significance, most authorities recommend counting about 3(X) to 5(X) points or grains on a slide. The probable error of the resulting percent of individual components (at 95% confidence) can be calculated by ... 

The dialyzers are shaken in a constant temperature shaking machine at 3TC. At the desired intervals two dialyzers are removed and 0.5 ml counting samples are taken from front and back compartments thus, each point on the dialysis curve is established by means of individual dialyzers in duplicate. No dialyzer is returned to the shaker and sampled again after a further interval since errors are introduced if several samples are taken from the same dialyzer because of the change in the ratio of solution volume to membrane area. The samples are counted with a gamma scintillation spectrometer. Although we base our calculations on the counts of the samples taken from the front compartments (in which the concentration of labeled chromium(III) is increasing), counts of the samples from the backs are obtained as a check. 

The calculation of the excess Rn activity of the sample must include (1) a decay correction from the time the sample was collected until the mid-point of the counting time, (2) the fraction of equilibrium attained with the Rn daughters ( Po, Pb, Bi) before counting, (3) the efficiency of the detector, (4) the background of the detector and (5) the blank associated with the sample container and extraction system. These calculations and the errors associated with the measurements have been discussed by Lucas and Woodward (1964), Sar-miento et al. (1976) and Key et al. (1979). The best precision (2o) obtained for the scintillation counting procedures is approximately 13 %. Schlosser et al. (1984) claimed a precision of 11 % for the proportional counting technique. 

It is sometimes advised that the correction for decay during counting can be neglected if the mid-point of the count, instead of the start time, is used when making the normal decay correction. If the count period is short compared to the half-life, the error introduced by doing this is indeed small. However, the error after a one half-life count period is 2%. It would not seem worthwhile accepting an unnecessary error of this magnitude for the sake of a small amount of calculation. I would not advocate it. 

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