Titering Calculator

∞ generated and posted on 2022.05.19 ∞
∞ updated on 2022.06.05 ∞

Alternative approaches to determining numbers of phages per unit volume as based on three or more determinations per data point.

Please cite as:

Stephen T. Abedon
Titering Calculator.

Click here for calculator or see immediately below for further explanation and discussion.

The number of phages present per ml, commonly referred to as a phage's titer, can be determined by a number of approaches including via plaque assays. Here what is considered is what to do with the raw titer determinations once you've generated them, particularly in terms of how to "average" these numbers together.

If you have generated only a single data point, then this app is not really for you. Single data points are problematic since there is no way of knowing, at least within that data "set", whether the number is in error. The assumption, looking from the outside in, is that determining titers based on only single data points represents a cutting of corners…

If you have generated two data points, then this app still was not written with you in mind since all that can be done is to average the two numbers together. Here, within the data "set", it is possible to recognize that one or more data points are in error, but there is no way of knowing which or both are in error, at least from that data alone.

"Everything" changes if you have obtained three or more data points for a given titer determination, since now you have some reasonable means of 'guessing' which if any data points are in error based solely on the plaque counts just collected. Lacking outliers, you also can have more confidence in the accuracy of your results (or, at least, their precision).


Also with three or more data points, even if you do have outlier data, or have Too Few To Count (TFTC) or even Too Numerous to Count (TNTC), you can still not only calculate a single titer value, but you can do so without completely throwing out any of the data points.

To do this, one employs what is known as a trimmed mean, the ultimate trimmed mean being a median.

If all data points are TFTC (however you define that) or all are TNTC, then you should revisit your titering/diluting efforts. But if only some of the data points are TFTC or TNTC, then using a trimmed mean may have you covered, even without throwing out the TFTC or TNTC data (hint: you really really should not be throwing that data out…).


What this app does is to calculate a trimmed mean for you – actually, various trimmed means – even given values for some of the data as TNTC, the latter which I'll have you enter as a value of -1.

Of course, whichever approach you choose, you should be consistent in using it, no "the data looks better this way, this time approach…" You also can't just throw data out just because it doesn't "look" right (or is TFTC or TNTC—you just can't throw data out). And don't forget that it's important that data points are as independent as possible, which basically means no taking of/using multiple data points from individual dilution series! Each to-be-averaged plaque count should instead be based on a separate dilution.


For further reading, see:

Abedon, S. T. and Katsaounis, T. I. (2021). Detection of bacteriophages: statistical aspects of plaque assay. In Harper, D., Abedon, S. T., Burrowes, B. H., and McConville, M. (eds), Bacteriophages: Biology, Technology, Therapy, New York City, Springer, pp. 539-560.

Abedon, S. T. and Katsaounis, T. I. (2018). Basic Bacteriophage Mathematics. Advances in Applied Microbiology (this is for the Clokie, Kropinski, and Lavigne protocols book, third volume).

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above is set to 1 if left blank or not number or ≤ 0
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above is set to 0 if left blank or not number or < 0