Student's t-distribution

A family of continuous probability distributions used to estimate population parameters when sample sizes are small and population variance is unknown. Its shape depends on degrees of freedom, with heavier tails than the normal distribution at low degrees of freedom.

Student's t-statistic: A statistic formed by dividing a sample-mean deviation by its estimated standard error. The distribution arises when a standardized mean uses sample variance instead of known population variance.
One-sample t-test: A hypothesis test comparing a sample mean with a specified population value when variance is unknown. Its test statistic follows a t-distribution under the null hypothesis when observations are normally distributed.
Sample mean: The arithmetic average of observations in a sample. Inference about a population mean is the distribution's classic use.
William Sealy Gosset: An English statistician who developed small-sample methods while working for the Guinness brewery. Gosset derived the distribution and published his work under the name Student.
Degrees of freedom: The number of independent values available to estimate a statistical quantity. They control the t-distribution's tail weight and often equal the sample size minus one.
Two-sample t-test: A test comparing the means of two groups using their observed data. Its pooled-variance form uses a t-distribution with degrees of freedom determined by both sample sizes.
Sample variance: An estimate of population variance calculated from deviations around the sample mean. Its uncertainty creates the extra tail variation in t-based statistics.
Student (statistician): The pen name William Sealy Gosset used for his statistical publications. The distribution bears this name because Gosset's 1908 paper appeared under the pseudonym.
Chi-squared distribution: A distribution of sums of squared independent standard normal variables. A chi-squared variable supplies the random variance estimate in the t-distribution's construction.
Welch's t-test: A test comparing two means without assuming equal population variances. It uses an approximate t-distribution with adjusted degrees of freedom.

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