Determining Bacteriophage Concentrations by Plaque Assays
by Stephen T. Abedon Ph.D. (abedon.1@osu.edu)
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Version 2026.04.07
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The number of bacteriophages present per ml — commonly referred to as a phage titer — can be determined by a number of approaches including via plaque assays. What this calculator addresses is what to do with the raw titer determinations once you have generated them — particularly how to "average" these numbers together when you have three or more data points. The calculator also supports comparison of two data sets, including efficiency of plating (EOP) determinations and comparison of results across independent experiments.
Single data points are problematic: there is no way of knowing whether the number is in error within that data "set". Single determinations represent a cutting of corners.
Two data points allow you to average two numbers together, and it is possible to recognize that one or both may be in error — but there is no way to tell which from the data alone.
Three or more data points change everything. Now you have a reasonable basis for identifying which data points might be outliers. Lacking outliers, you can have greater confidence in the accuracy and precision of your results.
For EOP determinations, however, it is best to plate from a single dilution/tube across multiple conditions simultaneously. This removes dilution variability from the within-experiment comparison, so that any observed differences reflect plating efficiency rather than dilution noise.
Note also that this calculator can be used to compare individual results that come from different experiments — for example, Experiment 1 gave a count of 50, Experiment 2 gave 75, Experiment 3 gave 40, and so on. In that case each entry represents an independent experimental result, and the statistical outputs describe variability across those experiments rather than across replicate plates from a single session.
With three or more data points — even if some are TFTC (Too Few To Count) or TNTC (Too Numerous To Count) — you can still calculate a single titer value without discarding any data, using a trimmed mean. You really really should not be throwing data out.
For statistical comparisons using two data sets, TNTC values are excluded from parametric statistics. Results should be interpreted with caution when TNTC values are present.
The trimmed mean works by sorting your data and removing a specified fraction of the lowest and highest values before averaging. The extreme trimmed mean is the median. These approaches let you include TFTC and TNTC data without letting outliers dominate the result. Whichever trimming level you choose, apply it consistently — do not select post hoc based on which result looks best.
For a trimmed-mean plaque count C̄ and total dilution D = m × 10n:
When you calculate, this tool automatically reports descriptive and inferential statistics on each entered data set. Statistics are computed from the raw plate counts (not converted titers), since statistical properties are most straightforwardly evaluated on the raw count scale.
For each data set the following are reported:
Plaque counts are expected to follow a Poisson distribution when plaques arise independently and randomly on a plate. For a Poisson distribution, the variance equals the mean (σ² = μ, where σ² is the population variance and μ is the population mean). The variance-to-mean ratio (VMR), also called the index of dispersion, is therefore expected to equal 1.0 for ideal Poisson data.
A formal goodness-of-fit test for Poisson uses the chi-squared statistic χ² = (N−1) × VMR with N−1 degrees of freedom. Large values (and small p-values) indicate significant departure from Poisson. Note that TNTC values are excluded from all statistics, since their true counts are unknown.
Because plaque counts are non-negative integers, Poisson statistics are generally more appropriate than normal-distribution statistics for small counts. For large counts (typically >20–30 per plate), the two approaches converge.
Quite apart from replicate-to-replicate variability (captured by the VMR and χ² test above), there is a second, independent source of uncertainty: the intrinsic Poisson imprecision of each individual plate count. For a Poisson-distributed count with true mean λ, the expected coefficient of variation of a single observation is:
This means that at λ = 100 plaques/plate, each individual count has ~10% CV before any replicate variability is considered. At λ = 10, each count has ~32% CV; at λ = 4, ~50%. The uncertainty in the mean across N independent plates is correspondingly:
The calculator reports a counting-statistics reliability assessment for each data set based on the observed mean count, using the following thresholds:
Importantly, these TFTC counts should still be included in the calculation rather than discarded — they carry real information, and discarding them biases the mean upward. The appropriate response to TFTC data is to flag the titer as imprecise and to re-plate at a more favorable dilution when possible.
For comparison, the calculator also reports statistics under a normal distribution assumption. Normal-distribution assumptions are less appropriate for small raw plaque counts but become more reasonable when counts are large, or when entries represent results from separate experiments rather than replicate plates from a single session. The 95% confidence interval is computed as:
where t(0.025, N−1) is the two-tailed critical value from Student's t-distribution.
When two data sets are entered, a two-sample Welch's t-test (which does not assume equal variances) is performed to compare the means. The result is reported with degrees of freedom, t-statistic, and two-tailed p-value. As with the confidence interval, this test assumes approximate normality and is most reliable for larger counts or cross-experiment comparisons.
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