Sampling distributions
The bridge between one sample and the population, and the reason inference works at all.
15 terms
10% conditionThe 10% condition says a sample drawn without replacement should be no more than 10% of the population, so the observations stay nearly independent.Bias of an estimatorThe bias of an estimator is the gap between the mean of its sampling distribution and the parameter it estimates, so it measures being off target on average.Central limit theoremThe central limit theorem says the sample mean's sampling distribution becomes approximately normal as the sample size grows, whatever the population's shape.Independence conditionThe independence condition requires that one observation gives no information about another, argued from random selection plus the 10% condition.Large Counts conditionThe Large Counts condition checks that np is at least 10 and n(1-p) is at least 10, so the sampling distribution of p-hat is close to normal.Point estimateA point estimate is a single number computed from sample data and used as the best guess for an unknown population parameter.Randomness conditionThe randomness condition requires data from a random sample or a randomized experiment, which is what makes inference beyond the data valid.Sampling distributionA sampling distribution is the distribution of a statistic across all possible samples of the same size drawn from a population.Sampling distribution of the sample meanThe distribution of the sample mean over every possible random sample of a fixed size drawn from one population, describing how much that mean varies.Sampling distribution of the sample proportionThe sampling distribution of the sample proportion collects p-hat from every sample of size n. It centers at p and its spread is the square root of p(1-p)/n.Sampling errorSampling error is the ordinary sample-to-sample variation between a statistic and the parameter it estimates. It is not a mistake anyone made.Standard deviation of the sampling distributionThe true standard deviation of a statistic across all samples of a given size, computed from population parameters rather than estimated from one sample.Standard errorThe standard error estimates the standard deviation of a statistic's sampling distribution, using sample data rather than population parameters.Unbiased estimatorAn unbiased estimator is a statistic whose average value across all samples equals the true parameter, so it has no systematic tendency to be too high or low.Variability of an estimatorThe variability of an estimator is the spread of its sampling distribution: how much the estimate moves from one random sample to the next.