Understand the relationship
The reasoning behind the result
The probability must match the counted event
E[observed] = Np; N̂ = observed/p
The simple count correction assumes each population unit has the stated probability p of being included in the observed count. Dividing by p reverses that expected thinning. It produces an estimate under the assumption, not a newly observed count.
If the count includes individuals detected at least once across several visits, p must describe inclusion at least once across those visits. A per-visit probability cannot simply be substituted without a model for repeated observations.
Small probabilities imply large corrections
The multiplier is 1/p. At p = 0.5, twenty observations correspond to an estimate of forty; at p = 0.8, the same count corresponds to twenty-five. The comparison shows how strongly the assumption affects the answer.
Uncertainty in p is not propagated here because only a point probability is entered. Heterogeneous probabilities, repeated counting and dependence can require individual weights or a different model.
A zero point estimate does not settle absence
Zero observations divided by any positive probability remains zero. That arithmetic does not rule out an unobserved population. Estimating an upper bound requires a specified stochastic model and study design.
This tool accepts probabilities; it does not estimate them from survey histories or validate a detection process. A zero probability is rejected because the count cannot identify population size under no possible inclusion.
Follow the numbers
One count under two assumptions
- Twenty observations and inclusion probability 0.5 give 20/0.5 = 40.
- The same count and probability 0.8 give 20/0.8 = 25.
- These are alternative estimates for the same record, not two populations to sum.
The supplied probability is part of the scientific model and must be justified independently.
Quick guide
How to use this calculator
- Enter the observed counting unit and an externally established probability of inclusion in that count.
- Use separate rows for alternative probability assumptions or records.
- Read each correction factor and adjusted estimate separately; alternative scenarios are not added.
- Retain the source, population and period of the supplied probability in your study documentation.
Calculation method
Calculation and interpretation
Explore what a supplied detection or inclusion probability implies for a count estimate.
Adjusted count estimate = observed count / supplied inclusion probability
Worked example
One count under two assumptions
The supplied probability is part of the scientific model and must be justified independently.
Adjusted count estimate = observed count / supplied inclusion probability
Supported inputs
Precision and limits
Observed records only
Entered records do not establish unbiased observation, independent sampling or a biological cause. Missing observations must remain distinguishable from measured zeros. No diagnosis or intervention is inferred.
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