Table 3.

How to estimate the coefficient of error (CE) of the estimate in an individual animal

Section no.Q-A Embedded ImageB Embedded ImageC Embedded Image
114196224308
216256352288
322484396506
418324414216
523529276552
612144288312
724576624528
826676572884
922484726748
103310891122462
11341156476
1214196
Σ258611054704778
VARNOISEa258
VARSURSb1.89
CE(t)c0.007
CE(ΣQ-)d0.062
CE(N)e0.063
  • The precision, CE, of a fractionator estimate is a function of three independent factors: the noise variance (VARNOISE), the systematic uniform random sampling variance (VARSURS) and the variance attributable to variations in section thickness [CE(t)](see also West and Gundersen, 1990; West et al., 1991; West et al., 1996).

    From the calculations above (a—e), it is obvious that the CE(N) for all practical purposes may be considered a function of the NOISE variance. If one wants to reduce the CEs of the individual estimates further, this would, in this example, be achieved most effectively by sampling more on the sections already in the series.

  • a VARNOISE is the uncertainty' in the estimate that comes from disector counts within a section and is equal toΣ Q-.

  • b VARSURS is the `uncertainty' in the estimate that arises due to sampling between sections, i.e. because repeated estimates based on different sets of sections may vary. The VARSURS is calculated using a prediction model that takes into account the systematic nature of the sampling (Gundersen et al., 1999): VARSURS= [3(A—Noise)-4B+C]/240. For calculation of A, B and C, see columns above. When one uses more than 5-10 sections for a biological estimate, the SURS variance is usually negligible relative to the Noise variance. The denominator is a constant (Gundersen et al., 1999).

  • c CE(t)=[s.d.()/(√n)](1/), where is the mean section thickness in each section measured with the digital microcator, n is the number of sections and is the mean section thickness between all sections. The CE(t) usually contributes less than 1% to the overall estimator variance and can be ignored in most studies where section homogeneity is high.

  • d The total sampling variance, CE(ΣQ-), is calculated as: Embedded Image.

  • e The total CE for the final estimate, CE(N), is eventually calculated as: Embedded Image.