A statistical estimator is a specially designed function applied to an observed dataset to produce empirical estimates of underlying theoretical model parameters, such as probabilities. For example, a natural estimator for the true probability of an event is the ratio of its observed occurrences to the total number of sampling trials.

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A sample statistic is a descriptive numerical summary—such as a mean or a correlation coefficient—that is calculated from the data of a specific sample. Researchers compute these statistics to summarize their observed data and to make inferences about the corresponding, unknown values in the broader population.

Sample Statistic

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A population parameter is a numerical value representing a specific characteristic of an entire population, such as the true mean or correlation. Because researchers typically cannot measure every individual within a population, they must rely on sample statistics to estimate these corresponding population-level values.

Population Parameter

A statistical range calculated around a sample statistic designed to contain the true population parameter a specified percentage of the time, most commonly $$95\%$$. Some researchers advocate using confidence intervals as an alternative to traditional null hypothesis testing because they are often more intuitive to interpret. Furthermore, a confidence interval inherently provides the data needed to perform a null hypothesis test; if a hypothetical population mean falls completely outside the calculated interval, the sample mean is considered statistically significantly different from that hypothetical value.

Confidence Interval

There is a fundamental distinction between probabilities and statistics. Probabilities are theoretical quantities that describe the underlying data generating process, such as the inherent fairness of a coin. In contrast, statistics are empirical quantities computed directly from observed data, such as the observed frequency of a specific outcome in a sample.

Probability vs. Statistics

Statistical Estimator

A descriptive numerical summary, such as a mean or a correlation coefficient, that is calculated from the data of a specific subset of observed individuals is called a ____.

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