Agresti Coull Interval Calculator
Uses an adjusted count and adjusted sample size before applying a symmetric proportion interval. The form displays p̃ ± z*√(p̃(1−p̃)/ñ) beside agresti–coull interval, using a worked condition that can be recalculated with the labeled inputs.
Describe the observed sample
Agresti–Coull interval
The question behind agresti–coull interval
The agresti coull interval page uses an adjusted count and adjusted sample size before applying a symmetric proportion interval.
Agresti–Coull interval is limited to the statistical quantity named by the result panel. The agresti–coull interval calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
When the analysis changes, compare wilson score interval and one-sided proportion upper bound.
Inputs that define agresti–coull interval
- Successes: For agresti–coull interval, the worked value for successes is 18 successes. Treat the successes entry (18 successes) explicitly as a count, proportion, rate, estimate, or model parameter before comparing agresti–coull interval conditions. The form enforces minimum 0.
- Trials: For agresti–coull interval, the worked value for trials is 40 trials. Treat the trials entry (40 trials) explicitly as a count, proportion, rate, estimate, or model parameter before comparing agresti–coull interval conditions. The form enforces minimum 1.
- Critical z value: For agresti–coull interval, the worked value for critical z value is 1.96. Treat the critical z value entry (1.96) explicitly as a count, proportion, rate, estimate, or model parameter before comparing agresti–coull interval conditions. The form enforces minimum 0.
The entries used for agresti–coull interval must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid agresti–coull interval arithmetic for a nonexistent study.
How agresti–coull interval is calculated
For agresti–coull interval, match every symbol in the relationship to a labeled field before substituting numbers. Agresti–Coull interval is reported in %.
While checking agresti–coull interval, inspect every denominator in p̃ ± z*√(p̃(1−p̃)/ñ). For agresti–coull interval, a zero or near-zero denominator can make agresti–coull interval undefined or unstable.
A reproducible agresti coull interval case
The default agresti–coull interval condition is Successes = 18 successes, Trials = 40 trials, Critical z value = 1.96.
At z=1.96, the adjusted estimate is about 45.5% and the interval is roughly 30.8% to 60.2%.
The live calculator reports Adjusted proportion 45.438123 % · Lower bound 30.699133 % · Upper bound 60.177112 % · Adjusted n 43.8416. Repeating one intermediate step from p̃ ± z*√(p̃(1−p̃)/ñ) provides a fixed agresti–coull interval reference check for later code changes.
What the agresti coull interval arithmetic assumes
The adjustment depends on z squared; it is not always exactly the informal plus-four shortcut.
For agresti coull interval, the interval is produced by a repeated-sampling procedure; it is not the probability that a fixed parameter lies inside these particular endpoints.
When agresti–coull interval can mislead
When interpreting agresti coull interval, coverage depends on the stated standard-error model, critical value, independence conditions, and any approximation used by the method.
As a second check for agresti–coull interval, reversing the numerator and denominator answers a different question, so retain the direction printed in p̃ ± z*√(p̃(1−p̃)/ñ).
Testing how stable agresti–coull interval is
Change successes while holding the remaining entries fixed, then state why the direction and size of the agresti–coull interval change are plausible from p̃ ± z*√(p̃(1−p̃)/ñ).
Repeat the agresti–coull interval exercise with critical z value. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that agresti–coull interval scenario as exact.
Mistakes to avoid in the agresti coull interval setup
Before accepting agresti–coull interval, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For agresti–coull interval, do not move a number between fields merely because the units look compatible; each label gives the number a different statistical role.
Another agresti–coull interval failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on agresti–coull interval, then round only the reported value.
Rebuilding this agresti coull interval calculation later
Report agresti–coull interval using p̃ ± z*√(p̃(1−p̃)/ñ), followed by the entered values, units, exclusions, and analysis date. Name the agresti–coull interval population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Adjusted proportion 45.438123 % · Lower bound 30.699133 % · Upper bound 60.177112 % · Adjusted n 43.8416. A later agresti–coull interval review can then distinguish a changed input from a different convention or software implementation.
Questions about agresti–coull interval
How should agresti–coull interval be rounded?
Keep the unrounded agresti–coull interval for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in agresti–coull interval do not correct sampling or model error.
Which input deserves the closest boundary check?
For agresti–coull interval, start with critical z value and then successes. Confirm the agresti–coull interval units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.
Why could another program report a different agresti–coull interval?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change agresti–coull interval. Compare the printed agresti–coull interval formula and its input definitions before treating either output as wrong.
What does agresti–coull interval represent on this page?
It is the quantity produced by p̃ ± z*√(p̃(1−p̃)/ñ) from the displayed successes, trials, critical z value. This page uses an adjusted count and adjusted sample size before applying a symmetric proportion interval.