# How to analyze  Pooling Replicate Wells

Pooling a set of wells in which the same sample has been loaded allows an increase in both detection sensitivity and quantification precision. Indeed, by considering each set of pooled wells as one larger well, this pooling strategy aids to increase the analyzed volume.

The pooling formula for estimation of the target concentration $$C$$ is based on the sum of the positive partitions and on the sum of the negative partitions among the $$k$$ pooled wells:

$$C = – \frac{1}{v} \ln\left(1-\frac{\sum_{i=1}^{k}p_i}{\sum_{i=1}^{k}N_i}\right)$$

where:

• $$k$$ refers to the number of pooled wells, assuming that these wells are pure replicates that received the same input sample
• $$v$$ refers to the partition volume
• $$N_i$$ refers to the total number of partitions analyzed in well $$i$$
• $$p_i$$ refers to the number of positive partitions observed in well $$i$$ for the target of interest

The higher the number of pooled wells, the higher the total number of analyzed partitions, so the lower the sampling error and the partitioning error, which means that the quantification uncertainty gets lower.

Assuming a Limit of Blank equal to zero, the formula of the Limit of Detection (LOD) shows that the LOD is inversely proportional to the number of pooled wells (e.g. pooling 2 wells will divide the LOD by 2). Indeed, if $$N$$ is the average number of partitions analyzed per well and for a confidence level of 95%:

$$LOD(95\%) = \frac{3}{k N v}$$

To learn more about the LOB and the LOD, see the LOB & LOD Definition and Calculation item.

Check out the memos which explain how you can calculate the LOB and the LOD, and