Student’s t distribution

The Student's t-distribution is a probability density function used in statistics, particularly for hypothesis testing when the population standard deviation is unknown. Developed by William Sealy Gosset under the pseudonym "Student" around 1908, it's crucial for analyzing small samples drawn from a normally distributed population.12

The t-distribution is a family of curves, with each curve defined by its "degrees of freedom," which relates to the sample size. As the sample size increases, the t-distribution approximates the standard normal distribution.2

A common use is the Student's t-test, which assesses if there's a significant difference between a sample mean and a hypothesized population mean, or between the means of two samples. The test involves calculating a t-statistic and comparing it to critical values from the t-distribution to determine if the null hypothesis (no significant difference) can be rejected.2