Coefficients of Error

There are several coefficients of error commonly used in stereology, all of them estimate the precision of an estimate obtained using a stereological procedure. The coefficient of error usually gauges the distribution of counted objects in the tissue. While the Gundersen CE is the most commonly used, we recommend following the CE protocol established within your field, and reading references on coefficients of errors to determine which CE best fits your needs.

CE Gundersen

Estimated precision of the population size estimated using Optical Fractionator. At least three sections must be sampled for this value to be computed and displayed.

There are two values for many of the Gundersen categories:

m=0 was used in the original CE calculations (Gundersen, 1987)
m=1 is used in the newer CE estimate formula (Gundersen, 1999).

Variance due to noise

Formerly called the nugget variance, also known as the nugget effect, this is a measure of the intra-sectional variance. It is a primary contributor to the total variance. Ideally, this value will be both small and of roughly the same magnitude as the variance of systematic random sampling.

If this value is too high, more sampling needs to be performed on each section.

Variance of systematic random sampling

A measure of the inter-sectional variance, the variance of systematic random sampling is another primary contributor to the total variance. Ideally, this value will be both small and of roughly the same magnitude as the variance due to noise.

If this value is too high, more sections need to be sampled. At least three sections must be sampled for this value to be statistically meaningful. If less than three sections have been sampled, these values are not shown in the results. Although this value depends to some degree upon the variance due to noise, this dependency will normally be very small if the variance due to noise is reasonably small.

Total variance

Total variance is the sum of the variance due to noise and the variance of systematic random sampling over all the sections sampled. It is the primary contributor to the final coefficient of error for a given estimate over a series of sections.

At least three sections must be sampled for this value to be statistically meaningful.

CE Scheaffer

Estimated mean cell count: Mean number of cells per counting frame across one or more sections.
Estimated variance of cell counts: Estimated variance of the number of cells per counting frame over one or more sections.

This is an indicator of how evenly the cell count was distributed over the counting frames.
Estimated variance of mean cell counts: Estimated variance of the estimated mean number of cells per counting frame from the true mean.

A sufficient number of counting frames should be used to ensure that this number is small.
Contour area / counting frame area: Inverse of the fraction of the total area sampled.
Estimated cell population count: [Contour area or Counting frame area] * [Estimated mean cell count]

This is a simple linear, biased, approximation.
Estimated variance of estimated cell population: Variance of the population size estimated using the linear approximation formula for estimated cell population count.