Small Denominator Instability Warning Checker
Expose rate sensitivity to a single numerator event and explicit caller denominator evidence floor; not just per-capita rate, inferential uncertainty interval, suppressed-data permission or a universal small-sample cutoff.
Description
A single numerator event changes a rate more when its denominator is small.
A single numerator event changes a rate more when its denominator is small. This sensitivity is different from a confidence interval.1
Enter integer denominator 1–1,000,000,000, numerator 0–denominator, minimum evidence1–1,000,000,000 and positive display scale. Return rate, event step and strict-below flag.
When to use Small Denominator Instability Warning Checker
Use Small Denominator Instability Warning Checker when you need to evaluate the supplied records under the calculation and evidence rules below. No universal sample cutoff, inferential uncertainty or data-suppression permission is determined.
Prepare the actual editorial, source, layout, timing or audience records requested. Supply explicit house-policy limits and preserve missing evidence.
How to use Small Denominator Instability Warning Checker and understand its results
- Prepare the actual editorial, source, layout, timing or audience records requested. Supply explicit house-policy limits and preserve missing evidence.
- Enter numeratorCount, denominatorCount, callerSmallDenominatorThreshold, callerDisplayScale using the field table and calculation rules, then run the tool.
- Read displayedObservedRate, oneAdditionalNumeratorRateStep, belowCallerDenominatorEvidenceThreshold. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| numeratorCount | Numerator count | number | Required |
| denominatorCount | Denominator count | number | Required |
| callerSmallDenominatorThreshold | Caller small denominator threshold | number | Required |
| callerDisplayScale | Caller display scale | number | Required |
Enter integer denominator 1–1,000,000,000, numerator 0–denominator, minimum evidence1–1,000,000,000 and positive display scale. Return rate, event step and strict-below flag.
rate=scale×numerator/denominator; oneEventStep=scale/denominator Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| displayedObservedRate | Displayed observed rate | number |
| oneAdditionalNumeratorRateStep | One additional numerator rate step | number |
| belowCallerDenominatorEvidenceThreshold | Below caller denominator evidence threshold | boolean |
{
"input": {
"numeratorCount": 2,
"denominatorCount": 10,
"callerSmallDenominatorThreshold": 30,
"callerDisplayScale": 100
},
"output": {
"displayedObservedRate": 20,
"oneAdditionalNumeratorRateStep": 10,
"belowCallerDenominatorEvidenceThreshold": true
}
}Limitations and assumptions
No universal sample cutoff, inferential uncertainty or data-suppression permission is determined.
Numeric inputs, where present, must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Poll Horse Race Rounding Sum 100 Checker: Rounded exhaustive disjoint poll categories may sum above or below 100. Caller-supplied rounding intervals can test arithmetic feasibility. For a complementary task, use Newsletter Send Time Open Rate Optimum Lookup: Observed newsletter open rates depend on delivered cohorts and filtered human opens. A minimum evidence floor can exclude small cohorts.
References
Similar or alternative tools
- Poll Horse Race Rounding Sum 100 Checker
Rounded exhaustive disjoint poll categories may sum above or below 100. Caller-supplied rounding intervals can test arithmetic feasibility.
- Newsletter Send Time Open Rate Optimum Lookup
Observed newsletter open rates depend on delivered cohorts and filtered human opens. A minimum evidence floor can exclude small cohorts.