Confidence and margin jointly shape the sample-size surfaceUpdates with every input
Math & Statistics
Sample Size Value Table Calculator
Build a reusable planning matrix of proportion sample sizes across confidence levels and margins of error, with finite-population correction, design effect, conservative prevalence comparison, and live heatmap shading.
Smallest matrix n-
Largest matrix n-
Largest / smallest-
95% at midpoint margin-
95% conservative p=50%-
n saved versus p=50%-
Largest sampling fraction-
Matrix cells-
PRECISION PLANNING MATRIX
Confidence and margin jointly shape the sample-size surface
A heatmap uses actual completed-response counts, so the steep cost of tight margins is visible across four confidence policies.
VALUE MATRIX
Exact completed-response targets for every heatmap cell
Rows are confidence levels; columns are evenly spaced margins. Every cell includes finite-population correction and design effect.
| Confidence / margin | Dynamic margin columns |
|---|
MATRIX SETUP
Use the table before the precision policy is finalized
- Enter one credible prevalence and population.
- Choose a practical margin range.
- Keep the column count small enough to compare cells.
- Read across a row to price tighter precision.
- Read down a column to price higher confidence.
POLICY SURFACE
The matrix exposes tradeoffs hidden by a single answer
A table prevents stakeholders from treating 95% confidence and a particular margin as automatic defaults.
Expected prevalence below or above 50% reduces binomial variance, but a fragile prior estimate may make that apparent saving unsafe.
MATRIX ENGINE
Recalculate the same design over a two-dimensional policy grid
For each confidence and margin pair, the calculator evaluates Cochran's proportion formula, finite correction, and design inflation. Expected prevalence stays fixed so comparisons isolate policy choices.
Detailed calculation process and general formulas
n0(C,e) = z_C^2 p(1-p)/e^2nF(C,e) = n0 / [1+(n0-1)/N]n(C,e) = ceil(DEFF x nF)matrix spread = max(n)/min(n)saving = n_(p=.5) - n_(entered p)Symbols, meanings, and units
- C
- confidence level assigned to a matrix rowpercent
- e
- absolute margin assigned to a columnpercentage points
- n(C,e)
- completed-response target for one cellobservations
- p
- expected prevalence shared by all cellsdecimal
- N
- finite populationunits
TABLE INTERPRETATION
Use cell comparisons to negotiate evidence requirements
Different comparisons answer different planning questions.
Horizontal move
-Shows the square-law cost of a tighter margin.
Vertical move
-Shows the critical-value cost of more confidence.
Prevalence assumption
-Compares entered prevalence with the conservative 50% design.
Decision takeaway: Choose one matrix cell by decision consequences, then freeze it before fieldwork.
Applied decisions
Planning matrix use cases
Budget negotiation
A research team shows how 2-, 3-, and 4-point margins change completed-response costs.
What the result clarifies: The table makes the evidence-budget tradeoff explicit.
Rare attribute estimate
Prior evidence suggests prevalence near 18%.
What the result clarifies: The conservative comparison quantifies dependence on that prior assumption.
Worked current scenario
Substitution, intermediate values, and reconciliation
Method references
Sources for this calculator's specific method
Scope and limitations
The matrix compares formula-based precision targets; it does not select the appropriate cell. Complex allocation, subgroup reporting, rare-event exact intervals, weighting, nonresponse bias, and design-based variance estimation require additional planning.
Sample Size Value Table Calculator | Confidence-by-Margin Planning Matrix FAQ
Why are the heatmap cells not linear across margins?
Sample size is approximately proportional to one divided by margin squared.
Can I pick the cheapest cell?
Only if its confidence and precision are adequate for the intended decision.
Why show p=50%?
It is the maximum-variance benchmark when prevalence is uncertain.