Reporting stereological methods and results means showing how sampled observations became an estimate of a three dimensional quantity. Readers need to identify what you measured, where you sampled, which estimator you used, and how much uncertainty remains. “Cells were counted using unbiased stereology” does not provide that information.
A useful report separates the sampling design from the findings. Methods describe the rules and calculations; results show the achieved sampling effort, individual estimates, variability, and comparisons. Keep those records during planning and running a stereology study, rather than trying to reconstruct them when the manuscript is due.
Define the Quantity and Reference Region
Start with a precise statement of the outcome. Total cell number, numerical density, volume fraction, total surface area, and mean particle volume answer different questions. Name the quantity and its units consistently in the methods, results, tables, and figure captions.
Define the region of interest and the objects being measured. For an anatomical region, describe its boundaries, landmarks, subdivisions, and treatment of ambiguous borders. For cells, specify the staining and morphological criteria used for identification. For a material, define the phase, pore, grain, or particle classification rule. These definitions belong alongside the sampling description in a complete stereological methods report.
Prefer wording such as “estimated total number of marker positive nuclei in the left dentate granule cell layer” over “hippocampal cell count.” The longer version identifies the measured population, anatomical scope, and laterality. It also avoids implying that a marker positive population represents every cell of that type.
Use an annotated image when prose cannot resolve a boundary. Explain how the region was followed across sections, not just how it looked in one convenient field.
State What Counts as an Independent Sample
Report the number of independent units in each group and explain how that number was chosen. Distinguish experimental units from the sections, fields, and probe placements sampled within them. In an animal experiment, the unit may be an animal, litter, or cage, depending on treatment allocation. The ARRIVE 2.0 reporting guidelines address experimental units, sample size justification, exclusions, randomisation, and who knew the group allocation at each study stage.
Consider a hypothetical experiment with eight independently treated animals per group, ten sections per animal, and twenty fields per section. The group sample size is eight animals, not eighty sections or 1,600 fields. Keep the lower sampling levels in the methods and sampling records. Do not promote them into independent biological replicates.
State who selected specimens, outlined regions, classified objects, and analysed the estimates. Replace “the study was blinded” with a description of which tasks were performed without access to group identities. If masking was not possible, explain why.
Report exclusions at the level where they occurred. A damaged section, an unreadable field, and an excluded specimen are different events. Record the reason, whether the rule was established beforehand, and what changed in the analysis.
Describe the Sampling Chain from Specimen to Probe
Write the sampling account in the order the material passed through the study: specimen selection, tissue blocks, sections, fields, and probes. At each stage, identify the selection rule and any sampling fraction. A compact sampling diagram can help when several stages or anatomical strata are involved.
For systematic uniform random sampling, report both the random starting procedure and the fixed interval. “Every tenth section” describes the interval but leaves the start unexplained. State how you selected the initial section and how you positioned the sampling grid within sections.
For example, a reporting sentence might read: “The first section was selected uniformly from positions 1–10, after which every tenth section was sampled through the complete reference region.” This is an illustrative format, not a substitute for the procedure actually used.
Also document section orientation and, where relevant, how orientation was randomised. Record separate sampling settings for regions or groups if they differed. Explain how those settings entered the estimator rather than presenting one nominal grid size for the entire study.
Describe missing material explicitly. If a sampled section was lost, identify whether you used a predefined replacement procedure, revised the estimator, or excluded the affected specimen. A replacement is part of the method, not an administrative detail.
Report the Parameters Needed to Reconstruct the Estimate
Name the estimator and cite its methodological basis in the manuscript. Then describe its implementation. A software name or a reference to an earlier paper cannot tell readers which settings were used for the present specimens.
Optical Disector and Optical Fractionator Studies
For optical counting, provide the counting frame dimensions, grid spacing, disector height, guard zones, and measured section thickness. Describe the object feature used for counting, the inclusion and exclusion boundaries, and how objects were followed through focus. Report the objective magnification, numerical aperture, immersion medium, and the equipment used to measure axial movement. Published optical fractionator and immunofluorescence protocols demonstrate the value of reporting these parameters alongside sampling output and identification checks.
The following table is a practical layout for an optical fractionator methods supplement. Populate it with actual settings and measurements, not recommended defaults.
| Component | Information to record |
|---|---|
| Section sampling | Random start, interval, section sampling fraction, and sections analysed per specimen |
| Area sampling | Counting frame width and height, grid spacing in both directions, and area sampling fraction |
| Depth sampling | Disector height, upper and lower guard zones, thickness measurement procedure, and thickness sampling fraction |
| Counting rule | Identification criteria, counting feature, forbidden boundaries, and handling of uncertain objects |
| Calculation | Estimator equation, definitions of symbols, software version, and treatment of variable thickness |
Do not describe an optical disector density estimate as an optical fractionator estimate of total number. State whether total number came from inverse sampling fractions or from numerical density multiplied by reference volume.
Volume, Fraction, Surface, and Length Studies
Use the same reporting logic for other estimators: identify the probe, its dimensions, its placement, the observed interactions, and the calculation. A short equation with defined symbols often communicates more than several paragraphs of software terminology.
For Cavalieri volume estimation, record the distance between sampled section planes and the area measurement method, including area per point if point counting was used. For volume fractions, identify both the target compartment and the reference compartment. For surface and length estimates, describe the probe geometry and orientation design.
Keep densities separate from total quantities. A higher density can reflect a smaller reference volume rather than more structure. The ATS/ERS standards for quantitative lung structure describe this reference trap and the need to account for the containing volume.
As a hypothetical example, 100,000 cells in 10 mm3 gives 10,000 cells/mm3. The same number in 8 mm3 gives 12,500 cells/mm3. Density has increased by 25%; cell number has not changed. Report the quantity your design estimates, rather than the biological interpretation you hoped it would support.
Document Preparation, Thickness, and Identification Quality
Describe fixation, embedding, sectioning, staining, and mounting sufficiently to identify the material examined. State when dimensional measurements were made: before processing, after embedding, or in the mounted sections. Keep the nominal cutting thickness separate from the thickness measured during microscopy.
For optical methods, report where and how frequently thickness was measured, its observed distribution, and how it entered the calculation. Dimensional changes along the section depth can affect optical estimates; the methodological work on tissue deformation and stereological number estimation addresses why the chosen estimator must match those conditions.
A useful supplement should also state how you assessed staining through the counting depth, surface damage, tissue folds, and object visibility. Explain the evidence used to choose guard zones rather than reporting their dimensions alone. Where measurements varied between groups or processing batches, show that variation.
Keep this section focused on what was done and observed. The separate guide to section thickness, guard zones, and tissue shrinkage covers the methodological decisions behind those records.
Separate Sampling Precision from Between-Specimen Variation
Report the coefficient of error, or CE, with the method used to estimate it. Identify the estimator variant and any required settings, including the smoothness parameter where applicable. Variance estimation for systematic samples depends on the sampling design and assumptions, as developed in the research on systematic sampling efficiency and error estimation.
Keep CE separate from the standard deviation and coefficient of variation across specimens. CE describes the estimated sampling uncertainty of an individual stereological estimate. Between-specimen variation describes the spread of the resulting estimates across the group. Neither should be relabelled as the other.
Provide specimen level CE values in a supplement where practical, with a clearly identified summary in the main report. Include achieved counts and sampling effort beside them. A group mean CE alone can conceal a specimen with sparse observations or uneven sampling.
A small CE does not establish freedom from bias. It cannot validate a misdrawn region, an incorrect classification rule, or selective field placement. Discuss those issues separately from sampling precision, using the distinctions covered in bias, precision, and coefficients of error.
Present Results at the Specimen Level
Organise the results around the stated outcome, not the microscope workload. Give the estimate for each independent specimen, the group summary, and clearly labelled measures of spread or uncertainty. Keep raw object counts separate from estimated totals.
For animal experiments, reporting group summaries with variability and, where applicable, effect sizes with confidence intervals is part of ARRIVE’s results guidance. In your manuscript, also identify the statistical model, the unit analysed, any transformations, and how repeated or clustered observations were handled.
Prefer plots that show individual specimen estimates. Identify what each point represents and define every error bar. If observations are paired, make the pairing visible. Report numerical results in a table or accessible data file so readers do not have to extract values from an image.
A practical results package has two layers. The main article presents the biological estimates and comparisons. The supplement contains the sampling audit: specimen identifier, sections analysed, sites visited, counted events or probe interactions, relevant thickness measurements, sampling fractions, estimate, and CE. Include separate records for each outcome when their sampling differs.
Make the Report Auditable
Archive enough information to trace a published value back to its observations. Where permissions allow, retain section identifiers, region outlines, sampling coordinates, annotations, raw counts, thickness measurements, and calculation files. Record software versions and describe manual corrections to automated classifications.
Before submission, choose one specimen and attempt to reconstruct its reported estimate from the methods and supplementary records. Check that dimensions have units, fractions match the recorded sampling, and counts reconcile with the calculated total. Then compare the methods against what actually happened, including departures from the original plan.
The final test is straightforward: can another researcher identify the measured population, reproduce the sampling rules, reconstruct the calculation, and judge the uncertainty? A report that answers those questions lets the results stand on their evidence rather than on the word “unbiased.”