Survey sample size

Survey plan and question

Add as many questions as you need, of any type, to a survey plan. Each calculation is saved under its question ID, and the plan can then be aggregated into an overall sample-size range.

Question type

Each calculation powers one question. Use several questions of the same type freely: give each its own question ID.

Sizing goal

The same question can be sized to detect a difference between groups, to estimate its numbers within a margin of error, or checked against a sample you already have or can afford.

Binary question

Probabilities can be typed as 0.05, 5% or 5. Values above 1 are read as percentages.

What to compare

Design

Effect to detect

Test and error rates

Allocation between groups

Single-choice question

Compare two or more groups. Each group's expected answers must add up to 100%.

What to compare

Groups and allocation

Effect to detect

Error rates

Likert item

What to compare

Design

Effect to detect

Test and error rates

Allocation between groups

Numerical rating scale

Compares average scores between two groups with a t-test, treating the scale as approximately continuous. The spread of scores (SD) matters as much as the means: a one-point difference is harder to detect when scores are widely scattered.

What to compare

Design

Scale

Effect to detect

Test and error rates

Allocation between groups

Continuous numerical response

Compares an amount, such as annual spending, between two groups with a t-test. Amounts like spending are often skewed by a few very large values, so check the expected skew with pilot or historical data.

What to compare

Planned analysis

Effect to detect

Test and error rates

Allocation between groups

Count response

Compares how many of something two groups report, such as vials purchased, using negative binomial regression. Counts often vary more between respondents than a Poisson model allows, so the dispersion matters as much as the means.

What to compare

Effect to detect

Model and dispersion

Test and error rates

Allocation between groups

Multiple choice: select all that apply

Each option becomes its own Yes/No outcome and gets its own two-proportion test. The family-wise alpha is split across the tested options, each test is sized separately, and the survey takes the largest requirement.

What to compare

Options and expected selection rates

The share of each group expected to select each option. These need not add up to 100%. Untick Test to describe an option without testing it.

Tests and error rates

Joint detection (simulation only)

Allocation between groups

Ranking question

One group of respondents ranks every attribute, with no ties, and the Friedman test checks whether the attributes differ in their rankings. A person's rankings are linked (only one attribute can be first), so the sample size is found by simulating complete rankings from a Plackett–Luce preference model.

What to compare

Preference pattern to detect

Test and error rates

Multi-item scale or composite score

Several agreement items are combined into one score, such as their mean, and the two groups' average scores are compared with a t-test. Use the SD of the composite score, not of a single item: averaging correlated items narrows the spread, by an amount that depends on how strongly the items correlate.

What to compare

Items

Test and error rates

How the simulation check generates scores

Allocation between groups

Open-ended text, after coding

Each free-text answer is coded Yes or No for one theme, and the two groups' shares are compared with a two-proportion test. Blank or unusable answers are treated as missing, not as "theme absent", and imperfect coding pulls the coded shares together; both are built into the sample size.

What to compare

Coding accuracy

Blank or unusable answers

Run settings

Response rates turn completed responses into invitations; the simulation re-checks power.

Usable-response rate

Small populations

Weighting

Checks