How the Calculation Works

What you provide

A Selection sheet

Exactly 20 rows, each the measured volume of a single cell. Their mean becomes the yardstick every other measurement is expressed in.

A Detailed sheet

One row per segmented object in the field of view, with its volume. Some are single cells, some are clusters, some are debris.

A starting cluster size

The smallest number of cells you want to count as a cluster. Usually 2. This is a decision, not a measurement, and the result moves with it.

The six stages

Stage	What happens
1	The reference measurements are reduced to a single figure for the volume of one cell. Every threshold and every count below is expressed against it.
2	Objects too small to be a cell are set aside as debris. They count towards nothing after this point.
3	The volume retained is converted into a cell count for the field — derived from volume, without resolving individual cells.
4	The starting cluster size fixes the volume an object must reach to be counted as a cluster at all.
5	Each retained object is assigned the number of cells its volume corresponds to. Objects that come out below the starting size are kept in the cell count but are not clusters.
6	The clusters are counted, the cells within them are totalled, and the count is expressed against the cells in the field.

Cluster sizes are assigned from volume rather than counted directly. Every result page reports how closely your own data sits to the size model behind them, because that is what decides whether the sizes should be read as exact or approximate.

A representative result

One of the reference datasets this project tests against, at a starting cluster size of 2.

Mean of the 20 reference volumes	323.03	So one cell is about 323 units of volume.
Rows read from the Detailed sheet	3,248
Discarded as debris	345	10.6% of the rows.
Retained but not clustered	2,121	Counted in the field total, not clusters.
Counted as clusters (α)	782	24% of the rows read.
Cells in the field (Y)	4,054	Derived from the volume retained.
Cells inside clusters (β)	1,992	49% of the field is clustered.
Clusters per 100 cells (γ)	19.29	The headline density figure.

Read the third and fourth rows together. Two thirds of the objects examined are retained but never become clusters. They are not errors and they are not missing: they are the single cells the field is mostly made of. A result that reported only α would be describing a quarter of the data.

What this assumes, and what it cannot tell you

Assumptions

That cells are close enough to a common volume for their mean to stand in for any one of them. The spread of your 20 references is reported on every result, because that assumption is exactly as good as they are.
That an object of roughly k times the single-cell volume contains roughly k cells. Volume is a proxy for a count.
That objects below the minimum retained volume are debris rather than real signal. That threshold is a convention of this method.
That the segmentation upstream separated touching cells correctly. NCQ sees volumes, not images.

Limits

Cluster sizes are estimates, not counts. Every result reports how well your objects fit the size model, against the figure volumes with no relationship to cell size would give.
Two touching clusters and one large cluster are the same object to this method. The largest-object check exists to point you back at the image.
α, β and γ all depend on the starting cluster size you chose. Every result shows what they would have been at neighbouring values.
The uncertainty reported on Y and Z comes from the precision of the 20 reference measurements only. It does not cover segmentation error, and it is not a confidence interval on the biology.

The checks run on every analysis

None of these stops a run. They are the things an experienced operator would notice about a result, said out loud.

Check	What it means
Reference cells vary in size	Every threshold in the method is a multiple of that mean, so the spread carries into Y, α and γ. Re-picking references of more consistent size tightens every figure below.
A reference measurement stands apart	One mis-picked reference moves the single-cell volume and every threshold with it. Worth checking those rows are single cells.
A large share of objects was discarded as debris	Normal for a noisy segmentation, but it shrinks Y and therefore raises γ. If these are real cells, the segmentation needs revisiting rather than the analysis.
Cluster sizes are estimates	This is expected in dense tissue, where objects do not divide into whole cells by volume. Read the cluster sizes as estimates and the distribution as a shape, not as exact counts.
The two cell counts disagree	The two routes to a cell count only agree when object volumes sit close to whole multiples of the single-cell volume. A wide gap points at the same thing the size-assignment check does.
Very few clusters were found	A handful of clusters makes γ jump around between fields. Treat it as indicative and pool more fields before comparing conditions.
One object is very large	A single object that big can be a real cluster or two touching regions the segmentation did not separate. It contributes its whole size to β either way, so it is worth looking at.

Every figure NCQ reports

Headline figures

Single-cell volume X	The mean volume of the 20 reference measurements on the Selection sheet.	Every threshold in the method is a multiple of this number, so its accuracy sets the accuracy of everything below.
Cells in the field of view Y	The number of cells the field of view is estimated to contain.	A volume-derived count, not a headcount: it does not require any object to be resolved into individual cells.
Smallest counted cluster volume Z	The volume an object must reach before it is counted as a cluster at the starting size you chose.	Objects smaller than this are not counted as clusters.
Starting cluster size N	The smallest number of cells that counts as a cluster. You choose it before the run.	It is an operator decision, not a measurement, which is why the sensitivity table below exists.
Clusters found α	How many retained objects were large enough to be assigned a cluster size of N or more.
Cells inside clusters β	The assigned cluster sizes added together.	Counts cells, where α counts clusters: ten pairs and one group of twenty are both α=10 but β=20 and β=200.
Clusters per 100 cells γ	The number of clusters as a percentage of the cells in the field.	The headline density figure. Its denominator is Y, so it inherits Y's uncertainty.
Mean cluster size	Cells inside clusters divided by the number of clusters (β/α).	Distinguishes many small clusters from a few large ones, which α on its own cannot.
Median cluster size	The middle assigned cluster size.	Below the mean whenever a handful of large clusters pull the average up.
Largest cluster	The largest cluster size assigned to any single object.
Largest object	The volume of the largest retained object, as a multiple of the single-cell volume.	A very large multiple can be a genuine cluster or two merged regions that segmentation failed to separate. It is worth looking at the image.

Where the objects went

Rows read	Every data row found under the header of the Detailed sheet.
Blank rows	Rows with neither an ID nor a volume, dropped before analysis.	Trailing empty rows are normal in an Excel export and are not a problem.
Below the debris threshold	Objects below the debris threshold, removed before anything is counted.	These are treated as debris and partial cells. They are excluded from Y as well as from the clusters, so they affect every figure.
Retained objects	Objects at or above the debris threshold — the population the analysis actually runs on.
Retained but not clustered	Objects large enough to keep but smaller than the smallest counted cluster.	They count towards Y but appear nowhere in α or β. Before ADR-0002 they were absent from the output entirely — on this project's own sample data that was most of the objects examined.
Counted as clusters	Retained objects assigned a cluster size of N or more. The same number as α.
Cells outside clusters	Cells in the field that are not inside a counted cluster (Y − β).	The complement of β. Together they account for the whole field.
Cells outside clusters	Cells outside clusters as a percentage of Y.
Cells inside clusters	Cells inside clusters as a percentage of Y (β/Y).	How much of the field is clustered, as opposed to how many clusters there are.

How well the size model fits

Cell count from volume	Y — the field's cell count derived from total volume.
Cell count from rounding	The same objects counted a second way, independently of their combined volume.
Gap between the two counts	How far the rounded count sits from the volume count, as a percentage.	Near zero means the two independent routes to a cell count agree. A large gap means object volumes sit systematically off the whole cell counts the method assigns them.
Mean distance from a whole number	How closely the retained objects sit to whole numbers of cells, averaged.	The lower it is, the better whole cell counts explain the volumes measured. Every result reports it against the figure volumes unrelated to cell size would give, so it can be read as structured or not.
Median distance from a whole number	The middle value of the same measurement.
Objects close to a whole number	The share of retained objects sitting close to a whole number of cells.	Reported against the share volumes unrelated to cell size would give.

Single-cell reference (Selection sheet)

Reference measurements	How many single-cell volumes the Selection sheet supplied. The method requires exactly 20.
Smallest reference volume	The smallest of the 20.
Median reference volume	The middle of the 20.
Largest reference volume	The largest of the 20.
Reference spread	The standard deviation of the 20 reference volumes.
Reference variability	The spread of the reference volumes as a percentage of their mean.	A high value says the cells chosen as single-cell references were not consistent in size, which loosens every threshold derived from them.
Standard error of X	The standard deviation of the 20 references divided by the square root of 20.	How precisely the mean of 20 measurements pins down the true single-cell volume.
Uncertainty in X	The standard error of X as a percentage of X.	Y and Z are both proportional to X, so this percentage carries straight through to them.
Uncertainty in Y	The uncertainty in X, propagated to the cell count.	Reported as Y ± this. It is a precision estimate for the reference measurement only; it does not cover segmentation error.
Uncertainty in Z	The uncertainty in X, propagated to the cluster threshold.

Retained objects (Detailed sheet)

Retained objects	The number of objects the analysis ran on.
Total retained volume	The combined volume of every retained object.
Smallest retained object	By volume.
Median object volume	The middle retained volume.
Largest retained object	By volume.
Mean object volume	The average retained volume.
Object volume spread	The standard deviation of the retained volumes.

Columns the workbook leaves for you

The results sheet ends with five empty columns. NCQ never reads or writes them.

Strep + — For manual entry. Not produced or read by NNCQ.
Leakage Association — For manual entry. Not produced or read by NNCQ.
Total strep + Cells — For manual entry. Not produced or read by NNCQ.
Image Volume — For manual entry. Not produced or read by NNCQ.
CD31 Volume — For manual entry. Not produced or read by NNCQ.