A specific t distribution depends on the parameter known as:

The t distribution is a family of distributions that vary according to a specific parameter known as degrees of freedom. This parameter is crucial because it influences the shape of the t distribution, which is wider and has heavier tails compared to the normal distribution, especially with smaller sample sizes. As the degrees of freedom increase (which typically happens when the sample size increases), the t distribution approaches the normal distribution.

Degrees of freedom typically correspond to the sample size minus one (n-1) when estimating the population mean. This adjustment accounts for the fact that one parameter (the sample mean) is being estimated from the data, which affects the distribution's variability. Understanding how degrees of freedom impacts the t distribution is vital when conducting hypothesis tests or constructing confidence intervals, particularly when sample sizes are small. Thus, this parameter is key in determining the characteristics of the t distribution in statistical analyses.