Sampling error refers to the natural, random variability that occurs in a statistic from one sample to another, even when all samples are randomly drawn from the same population. This random variability means that a sample statistic is rarely a perfect estimate of its corresponding population parameter, and it does not imply that a mistake was made during the research process.

Sampling Error

In psychological research, investigators calculate statistics from a specific group to estimate corresponding values in a larger group. For instance, if a researcher studies $$50$$ adults with clinical depression and calculates their average number of depressive symptoms, this calculated average is a sample statistic. The researcher then uses this statistic to draw conclusions about the corresponding population parameter, which is the true average number of depressive symptoms for all adults living with clinical depression.

Example of Sample Statistics and Population Parameters

Which of the following best defines a population parameter in psychology research?

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.

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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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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

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.

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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