fractionator formulas

  •  : Particles counted
  • : Area sampling fraction (counting frame/grid size)

or

, ,

  • s2; Variance due to noise

  • : Particles counted
  • n: Number of sections used

  • VARSRS: Variance due to SRS
  • s2: Variance due to noise

  • TotalVar:Total variance
  • s2: Variance due to noise

  • f: Number of counting frames
  • : Total possible sampling sites
  • : Estimated variance
  • : Average particles counted

  • Qi: Particles counted
  • f: Number of counting frames

  • f: Number of counting frames
  • Qi: Particles counted
  • : Average particles counted

  • Cfp: Finite population correction
  • : Estimated variance
  • f: Number of counting frames
  • : Total possible sampling sites

  • Cfp: Finite population correction
  • : Estimated variance
  • f: Number of counting frames

  • Q1i: Counts in sub-sample 1
  • Q2i: Counts in sub-sample 2
  • n: Size of sub-sample

and

  • R: Number of counting spaces
  • S: Number of sections
  • : Counts in the “r”-th counting space
  • : Counts in the “s”-th section

 

References

Geiser, M., Cruz‐Orive, L.M., Hof, V.I., & Gehr, P. (1990) Assessment of particle retention and clearance in the intrapulmonary conducting airways of hamster lungs with the fractionator. Journal of Microscopy, 160 (1), 75–88.

Glaser, E. M., Wilson, P.D. (1998). The coefficient of error of optical fractionator population size estimates: a computer simulation comparing three estimators. Journal of Microscopy, 192 (2), 163–171.

Gundersen, H.J.G., Vedel Jensen, E.B., Kieu, K., & Nielsen, J. (1999). The efficiency of systematic sampling in stereology—reconsidered. Journal of Microscopy, 193 (3), 199–211.

Gundersen, H. J. G., Jensen, E.B. (1987). The efficiency of systematic sampling in stereology and its prediction. Journal of Microscopy, 147 (3), 229–263.

Howard, V., Reed, M. (2005). Unbiased stereology: three-dimensional measurement in microscopy (vol. 4, chapter 12). Garland Science/Bios Scientific Publishers.

Scheaffer, R.L., Ott, L., & Mendenhall, W. (1996). Elementary survey sampling (chapter 7). Boston: PWS-Kent.

Schmitz, C., Hof, P.R. (2000). Recommendations for straightforward and rigorous methods of counting neurons based on a computer simulation approach. Journal of Chemical Neuroanatomy, 20 (1), 93–114.

West, M. J., Slomianka, L., & Gundersen, H.J.G. (1991). Unbiased stereological estimation of the total number of neurons in the subdivisions of the rat hippocampus using the optical fractionator. The Anatomical Record, 231 (4), 482–497.

 

See Optical fractionator workflow Image Volume Fractionator workflow