Two-Stratum Neyman Allocation Calculator
Splits a fixed sample between two strata in proportion to population size times within-stratum standard deviation. The form displays nh = n Nh Sh / sum(Nj Sj) beside neyman allocation, using a worked condition that can be recalculated with the labeled inputs.
Set the design inputs for neyman allocation
Neyman allocation
What neyman allocation answers
The two-stratum neyman allocation page splits a fixed sample between two strata in proportion to population size times within-stratum standard deviation.
Neyman allocation is limited to the statistical quantity named by the result panel. The neyman allocation calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
A nearby method may answer the next question: proportional stratum allocation and sampling fraction.
How the inputs shape neyman allocation
- Total sample size: For neyman allocation, the worked value for total sample size is 500 observations. Treat the total sample size entry (500 observations) explicitly as a count, proportion, rate, estimate, or model parameter before comparing neyman allocation conditions. The form enforces minimum 2.
- Stratum 1 population: For neyman allocation, the worked value for stratum 1 population is 6000 members. Treat the stratum 1 population entry (6000 members) explicitly as a count, proportion, rate, estimate, or model parameter before comparing neyman allocation conditions. The form enforces minimum 1.
- Stratum 1 standard deviation: For neyman allocation, the worked value for stratum 1 standard deviation is 12 units. Treat the stratum 1 standard deviation entry (12 units) explicitly as a count, proportion, rate, estimate, or model parameter before comparing neyman allocation conditions. The form enforces minimum 0.
- Stratum 2 population: For neyman allocation, the worked value for stratum 2 population is 4000 members. Treat the stratum 2 population entry (4000 members) explicitly as a count, proportion, rate, estimate, or model parameter before comparing neyman allocation conditions. The form enforces minimum 1.
- Stratum 2 standard deviation: For neyman allocation, the worked value for stratum 2 standard deviation is 20 units. Treat the stratum 2 standard deviation entry (20 units) explicitly as a count, proportion, rate, estimate, or model parameter before comparing neyman allocation conditions. The form enforces minimum 0.
The entries used for neyman allocation must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid neyman allocation arithmetic for a nonexistent study.
From inputs to neyman allocation
For neyman allocation, match every symbol in the relationship to a labeled field before substituting numbers. Neyman allocation is reported in observations.
While checking neyman allocation, inspect every denominator in nh = n Nh Sh / sum(Nj Sj). For neyman allocation, a zero or near-zero denominator can make neyman allocation undefined or unstable.
Verifying the default two-stratum neyman allocation result
The default neyman allocation condition is Total sample size = 500 observations, Stratum 1 population = 6000 members, Stratum 1 standard deviation = 12 units, Stratum 2 population = 4000 members, Stratum 2 standard deviation = 20 units.
The inputs allocate approximately 237 observations to stratum 1 and 263 to stratum 2.
The live calculator reports Stratum 1 allocation 237 observations · Stratum 2 allocation 263 observations · Stratum 1 unrounded 236.842105. Repeating one intermediate step from nh = n Nh Sh / sum(Nj Sj) provides a fixed neyman allocation reference check for later code changes.
What the two-stratum neyman allocation arithmetic assumes
This Neyman allocation assumes equal per-unit sampling cost; unequal costs call for cost-adjusted optimum allocation.
For two-stratum neyman allocation, a planning or survey quantity is only as defensible as its frame, response assumptions, clustering, and population definition.
A second check on neyman allocation
When interpreting two-stratum neyman allocation, changing a design effect, allocation rule, response rate, or finite-population boundary can matter more than another displayed decimal.
As a second check for neyman allocation, reversing the numerator and denominator answers a different question, so retain the direction printed in nh = n Nh Sh / sum(Nj Sj).
Mistakes to avoid in the two-stratum neyman allocation setup
Before accepting neyman allocation, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For neyman allocation, do not move a number between fields merely because the units look compatible; each label gives the number a different statistical role.
Another neyman allocation failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on neyman allocation, then round only the reported value.
Documenting the two-stratum neyman allocation result
Report neyman allocation using nh = n Nh Sh / sum(Nj Sj), followed by the entered values, units, exclusions, and analysis date. Name the neyman allocation population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Stratum 1 allocation 237 observations · Stratum 2 allocation 263 observations · Stratum 1 unrounded 236.842105. A later neyman allocation review can then distinguish a changed input from a different convention or software implementation.
Questions about neyman allocation
What should be saved with neyman allocation?
Save the entered values and units for total sample size, stratum 1 population, stratum 1 standard deviation, stratum 2 population, stratum 2 standard deviation, along with the analysis date, exclusions, software or formula version, and the relationship nh = n Nh Sh / sum(Nj Sj). That record is sufficient to rebuild this specific neyman allocation calculation.
Does neyman allocation establish a causal or population conclusion?
No. The displayed two-stratum neyman allocation value is conditional on the entered data and named method. The neyman allocation design, measurement process, and assumptions determine what can be concluded beyond those values.
How should neyman allocation be rounded?
Keep the unrounded neyman allocation for subsequent arithmetic, then report only the precision supported by the source measurements and the decision context. Extra digits in neyman allocation do not correct sampling or model error.