Determine Sample Size Calculator

Study design

What to calculate

BasisApplies to the one-proportion and one-mean designs. Comparative designs are always power-based.

Confidence level (%)

Statistical power (%)

Test sidedness

Expected proportion (group 1) (%)50% is the most conservative choice for a survey because p(1-p) is largest there.

Expected proportion (group 2) (%)

Margin of error (%)Half-width of the confidence interval, in percentage points.

Standard deviation

Margin of error (mean scale)

Difference to detectThe smallest difference in means that the study should be able to detect.

Noninferiority / equivalence margin

Correlation to detect

Hazard ratio to detect

Overall event rate (%)Used to turn a required number of events into a number of participants, and as the outcome rate for the events-per-variable rule.

Expected sensitivity or specificity (%)

Disease prevalence (%)

Number of predictor variables

Events per variable

Allocation ratio (group 2 : group 1)

Population sizeLeave at 0 for a very large or unknown population (no finite-population correction).

Average cluster size

Intraclass correlation (ICC)

Cluster trial outcome type

Work-sampling accuracy

Relative accuracy (%)

Expected attrition / non-response (%)

Sample size you already haveUsed by the margin-of-error, power, design-effect and finite-population-correction modes.

Recommended sample size

385

Sample Size Calculator

Unrounded requirement

384.145882

Total across all groups

385

Recruit this many to allow for attrition

385

Margin of error

5 %

z for the confidence level

1.959964

z for the power

0.841621

Significance level (alpha)

0.05

Formula used

n = z^2 p(1-p) / e^2

Worked out from Cochran, W.G. (1977), Sampling Techniques, 3rd edition, Wiley, chapters 4 and 5 and 8 other sources.

Sample-size calculations for clinical, regulatory or published research should be confirmed by a qualified statistician against the actual analysis plan before a study is registered or a protocol is finalised.

How this is worked out

3 steps

alpha = 1 - 95/100 = 0.05, two-sided, so z(alpha) = 1.959963985.
z(beta) for 80% power = 0.841621234.
n = z^2 p(1-p) / e^2 = 3.841458821 x 0.25 / 0.0025 = 384.145882

Results are general information, not financial, tax, legal, medical or engineering advice.