Determining sampling precision

Background

In order to determine how many counted objects is enough to generate a valid population estimate, it is important to look at the coefficient of error (CE). CEs gauge the distribution of counted objects and approximate the precision of a population estimate obtained from a stereological procedure. Since the heterogeneity and distribution frequency of the features affect sampling precision, sampling parameters may need to be adjusted based on the target CE.

We recommend a CE no greater than 0.1. If a CE is too high, it may be necessary to recount the specimen using stricter sampling parameters. If a CE is well below 0.1, you may be able to decrease the amount of sampling for subsequent specimens.

How many events do I need to count?

• 1 to 5 events per disector probe on average.
• Starting point: 100 events in 100 probes containing 10 sections when using the optical disector (Optical Fractionator or Fractionator) or 10 section pairs when using the physical disector (Physical Fractionator).
• Over-count a pilot and draw sub-samples.
• Use a sampling strategy that results in an acceptable variance and CE.

How do I account for heterogeneity?

For distributions of non-homogeneous features (such as those found in biological tissues), the precision also depends on the fraction of the volume sampled. If one distribution is more heterogeneous than the other, you must sample a larger volume to achieve the same precision as for the more homogeneous distribution.

While you can't control the heterogeneity of the distribution, you can control the sampling. If you use Optical Fractionator, you can change two sampling parameters to affect the volume fraction (and therefore the precision): serial section interval and disector spacing (grid size).

• Inter-section: Is there a clump of features in the direction you are sectioning that it is imperative to sample? Make the section interval small enough to include these features no matter what the random starting section is.

• Intra-section: Is the distribution of features quite heterogeneous, thus warranting a larger area fraction (closer spacing of the disectors that results in more sampling)? Use a larger area fraction (smaller grid size) if there are peaks in your data that you don’t want to miss.

How can I adjust the parameters to increase or decrease sampling precision?

Adjust the systematic random sampling parameters for grid size and serial section interval to refine the population estimate based on target cell count and target CE:

To increase the number of cells sampled:

• Decrease the grid size to visit more sampling sites on each section.
• Decrease the section interval to sample more sections (for example, counting every third section instead of every sixth section).

To decrease the number of cells sampled:

• Increase the grid size to visit fewer sampling sites on each section.
• Increase the section interval (for example, counting every sixth section instead of every third section).

See Systematic random sampling to learn more.

How do I choose the parameters?

Use the existing literature

Search the published literature for previous work done in the anatomical region you want to analyze.

The probe you'd like to use may have been used in the same region under similar conditions with regards to the heterogeneity of the distribution of the features. For instance, many researchers examine cell birth in the hippocampus by using Optical Fractionator to estimate the number of newly-born neurons (e.g., Horsenpiller & Peterson, 2007).

Talk to experts

If there is no guidance in the literature, seek the help of experts in the anatomical region you are sampling and/or become familiar with the salient features of the region.