onesample

One-sample refers to analytical methods that utilize a single sample drawn from a population to estimate a parameter or test a hypothesis about that parameter. It contrasts with two-sample or paired analyses that rely on two samples or paired observations.

In frequentist statistics, common one-sample procedures include the one-sample t-test for the mean when the population variance is unknown and the data are approximately normally distributed, and a one-sample z-test when the population variance is known or the sample size is large. For proportions, a one-sample proportion test assesses whether the observed proportion differs from a specified value. Nonparametric alternatives such as the Wilcoxon signed-rank test or the sign test can be used when distributional assumptions are questionable.

Estimation and confidence: a one-sample mean is estimated by the sample mean, and a confidence interval is computed with the t-distribution (or normal approximation for large samples). A one-sample proportion uses a binomial model, with exact, Wald, or score-based intervals.

Assumptions include independence and random sampling, with normality assumptions for small-sample mean tests and potential violations affecting validity. Nonparametric alternatives can mitigate these issues. In Bayesian contexts, a one-sample analysis can incorporate prior information to update beliefs about the parameter after observing the data.

One-sample methods are widely used in quality control, clinical research, and survey analysis to compare a metric against a standard or target. Software packages in statistics languages typically offer functions for one-sample tests under names like t.test, z.test, or prop.test.