Calculator
Example Data Table
| Study need | Confidence | Main input | Adjustment | Use this target |
|---|---|---|---|---|
| Customer satisfaction rate | 95% | p = 50%, error = 5% | Population 10,000, nonresponse 10% | Single proportion |
| Average delivery time | 95% | SD = 12, error = 3 | Design effect 1.2 | Single mean |
| A/B conversion comparison | 95% | p1 = 50%, p2 = 45% | Power 80%, equal allocation | Two proportions |
| Two score averages | 95% | Difference = 5, SD = 10 | Power 80%, nonresponse 15% | Two means |
Formula Used
Single proportion: n0 = Z²p(1-p) / e².
Single mean: n0 = (Zσ / e)².
Finite population correction: n = n0 / (1 + ((n0 - 1) / N)).
Design effect: completed sample = n × DEFF.
Nonresponse: fielded sample = completed sample / (1 - nonresponse rate).
Two means: n1 = (Zα + Zβ)²(σ1² + σ2² / k) / Δ². Then n2 = k × n1.
Two proportions: n1 uses pooled proportion, power, allocation ratio, and the expected difference. Then n2 = k × n1.
How To Use This Calculator
Choose the target that matches your study. Use proportion for percentages. Use mean for numeric averages. Use comparison options for two independent groups. Enter confidence, margin, power, and adjustment values. Leave population as zero if it is unknown. Press calculate. Read completed sample first. Use fielded sample for invitations or outreach planning.
Planning A Statistically Valid Sample
A statistically valid sample is not a guess. It is a planned number. The plan connects confidence, precision, variability, and population size. Good planning protects a study from weak results. It also protects a budget from waste.
Why Sample Size Matters
Every survey or experiment uses limited observations. Those observations must represent a wider group. A small sample can miss real patterns. A very large sample may waste time. The right sample balances accuracy and effort. It also gives reviewers a clear reason to trust the results.
Key Inputs To Review
Confidence level describes how often the method should capture the true value. Margin of error sets the allowed uncertainty. Expected proportion controls the worst case for survey percentages. A value near fifty percent gives the largest sample. Standard deviation measures spread for numeric outcomes. Power is used for group comparisons. It is the chance of detecting a real difference. Design effect adjusts for clustering or complex sampling. Nonresponse adjustment increases invitations before data collection begins.
Finite Population Correction
Population size matters when the target group is not huge. The finite population correction reduces the needed completed sample. It is useful when the sample is a noticeable share of the population. It should not be used when the population is very large or unknown. In that case, the infinite population estimate is safer.
Using Results Responsibly
The calculator separates completed sample from fielded sample. Completed sample means usable records after adjustment. Fielded sample includes extra contacts for expected nonresponse. This distinction is important. It keeps planning realistic. If response quality is poor, a larger fielded number may still fail. Clean sampling frames and clear questions remain essential.
Practical Interpretation
Use conservative values when evidence is limited. Use p equals fifty percent for unknown proportions. Use a pilot standard deviation for means. Choose a practical effect size for group tests. Do not choose a tiny margin only because it looks impressive. Smaller margins can create very large sample needs. Report the assumptions with every final number. A valid sample is only valid under its stated assumptions.
Keep notes for assumptions. Record exclusions and replacements. These details help another analyst reproduce the sample plan without hidden judgement.
FAQs
What is a statistically valid sample size?
It is a sample planned from confidence, precision, variability, and population assumptions. It gives a defensible number for a stated research goal.
When should I use p equals fifty percent?
Use it when the expected proportion is unknown. It is conservative because it usually gives the largest required sample for one proportion.
What does margin of error mean?
Margin of error is the allowed sampling uncertainty. A smaller margin needs a larger sample, assuming other inputs stay the same.
What is finite population correction?
It reduces sample size when the target population is limited. It matters when the planned sample is a noticeable share of the population.
Why add a design effect?
Clustered, weighted, or complex designs may add sampling variance. Design effect increases the sample to protect precision under that design.
What is fielded sample size?
Fielded sample is the number to contact before response loss. It is higher than completed sample when nonresponse is expected.
Should I use power for surveys?
Power is mainly for detecting differences in experiments or comparisons. Simple estimation usually uses confidence level and margin of error.
Can this replace expert study design?
No. It supports planning. Complex surveys, stratification, repeated measures, and regulatory studies may need review from a qualified statistician.