# Cell Counting Error

An error is encountered when trying to approximate a population (original sample) to a sample from
that population that is too small. This is also true when you do a cell counting (see Yeast Cell Counting with a Neubauer Chamber).
Cell counting error depends on the number of cells counted under the microscope and is approximated by the square root of the total count [1][2]:

$\text{Error Max} = \pm 2 \times \left(\frac{100}{\sqrt{n}}\right) \%$

n = number of cells count

The formula assumes random distribution of cells and gives a 95% confidence interval as the percentage of cells counted.

For example, if you count 100 cells, the error is 20,0%, but if you count 200 the error is about 14,1%.

This statistic error can be increased if the counting procedure is not performed properly. The most common errors in cell counting are:

Error in obtaining the sample
Usually, a small quantity is extracted from the original sample in order to carry out the counting.
This sample may have a different concentration than the original one.
In order to reduce this error it is convenient to shake the sample, and extract the necessary quantity to carry out the cell counting as soon as possible.
Likewise, a pipette can be used to shake the sample, pipetting repeatedly into the recipient where the
sample is taken from.

It is common to load the Neubauer chamber with a quantity slightly greater or smaller than 10 μl. When the quantity is greater than 10 μl, the cover slip will slightly rise in order to allocate the overload. When the quantity is smaller than 10 μl, the chamber will not hold enough quantity, leading to an error.
In order to reduce this error being careful when introducing the sample in the chamber not to overload it and keeping the 10 μl micro-pipettes perfectly calibrated.

Error in the allocation of the cells around the Neubauer chamber
Occasionally, the sample does not distribute equally around the counting chamber, due to its inclination or manipulation.
In order to reduce this error shake the sample before introducing it into the counting chamber and Make sure that the counting chamber lies completely flat.

Error in dilution
Any error made when using the liquids to carry out the dilution will translate into an error made in the diluted sample.
In order to reduce this error calibrate periodically the pipettes and micro-pipettes.

References
[1] Javornicky, P. 1958. Die revision einiger methoden zum feststellen der qantat des phytoplankton. Inst. Chem. Technol., Prague, Faculty Technol. Fuel Water. Scient. – Papers 2, pt 1:283-367.
[2] Lund, J.W.G., C. Kipling and E. D. LeCren. 1958. The inverted microscope method of estimating algal numbers and the statistical basis of estimations by counting. Hydrobiologia 11:143-170.