Sample Size & Power Analysis: How Many Observations Do You Need?

What you'll build

What you will be able to do

Each lab ends with a concrete result that you build yourself and the checker confirms, cell by cell.

• For a checkout wait-time study you find the z value, the margin of error of a planned sample, the t-based margin of error of a small pilot, and the sample size for five target margins.
• For a member survey of a 2,400-member gym you size the sample for a share, shrink it with the finite population correction, check the margin achieved by the responses received and see how little the population size matters.
• From a 12 + 12 pilot you compute the pooled standard deviation, Cohen's d and its size label, and turn the smallest difference worth detecting into an effect size for the power calculation.
• Size the full onboarding study: z values for α and power, n per group for a 1.5-minute difference, the small-sample correction, and a table of n for standard effect sizes.
• For a checkout redesign you derive the target conversion rate, compare the unpooled and the pooled sample-size formula and build a table that shows how the needed traffic explodes for small lifts.
• Compute the power of the two-group comparison for ten sample sizes and two effect sizes, find the first n that reaches 80% and draw the power curves.
• The budget fixes the sample. You calculate the standard error, the power for the difference the client hopes for, the MDE the study can detect with 80% power, and the relative MDE of a conversion test.
• A study compares three new membership offers with a control. You adjust α for three comparisons, size the arms with a larger control group and inflate the sample for dropout and invitation non-response.