How this calculator works
A realised sampling error is an estimate minus the actual population parameter; it can be calculated only when that parameter is known. Standard error instead describes the variability of an estimator over repeated samples. Select a standard error, a confidence margin, or an inverse calculation for sample size or confidence. A sample-SD mean margin uses a t cutoff and finite factor sqrt(1 - n/N). The other modes use the usual independent-sample formulas and a finite-population correction for simple random sampling without replacement. The population SD input uses divisor N, which determines the stated correction factor.
Formula
Observed discrepancy = estimate - parameter. SE(mean) = σ/√n; SE(proportion) = √(p(1 - p)/n). For a finite population multiply by √((N - n)/(N - 1)).
Worked example
A sample estimate 52 against a known parameter 50 has signed sampling discrepancy 2. With population SD 10 and n = 100, the uncorrected standard error of the sample mean is 1.
Advertisement
Frequently asked questions
Can I know the realised error from one ordinary sample?
Usually the population parameter is unknown, so you estimate uncertainty rather than calculate the actual discrepancy.
Is a standard error a confidence margin?
No. A confidence margin multiplies it by a critical value appropriate to a confidence level and model.
Does a bigger sample remove bias?
No. It usually reduces sampling variability, while systematic selection or measurement bias can remain.