PrintStudent's t-Distribution
Read It: Student's t-Distribution
Recall that the central limit theorem only applies for "sufficiently large" sample sizes. Often, you may encounter smaller datasets for which the central limit theorem doesn't apply. In those situations, we use an approximation known as the Student's t-Distribution. In this distribution, the shape is dependent on the degrees of freedom (i.e., the maximum amount of independent values), which is often calculated as the number of data points minus one, as shown below.
Ultimately, this results in a curve that is often shorter and wider than the standard normal, with smaller sample sizes resulting in larger differences. In other words, there are fewer data points close to the mean and more data points towards the outside. These changes are shown in the figure below.
Example of the Student's t-Distribution. Notice how the plot is becoming wider (e.g., more data on the outside) as the number of samples decreases.
Assess It: Check Your Knowledge