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Sampling uncertainty calculators
Explore standard errors, normal-model margins and planning sample sizes.
Choose the right calculation
Use a critical value and model appropriate to the study. Simple random-sampling approximations do not correct for selection bias or clustered observations. Normal approximations can be poor for small samples or extreme proportions.
Find a tool for your question
Standard Error Calculator
Estimate the standard error of a sample mean.
Proportion Standard Error Calculator
Estimate the standard error of a sample proportion under a simple independent-sampling model.
Normal Confidence Interval Margin Calculator
Calculate the margin around a mean from a supplied z critical value.
Sample Size for a Proportion Calculator
Estimate a normal-approximation sample size for a target proportion margin.
Z Test P Value Calculator
Find an approximate normal-model p-value from a supplied z statistic and a chosen tail.
Normal Mean Confidence Interval Calculator
Find a symmetric normal-model interval from a mean, known population deviation and chosen critical value.
Does a larger sample remove selection bias?
No. More observations can reduce sampling variability without repairing a systematically biased selection process.
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