Student T-Distribution

The t-distribution is a normal distribution used to determine population parameters when the sample size is small and population variance is unknown. A t-distribution curve has a lower height and wider spread than standard normal distribution. One of the important parameters in T-distribution is degree of freedom. It refers to the number of independent observations in a set of data. The shape of t-distribution is determined by the degree of freedom.

Degree of freedom is calculated by using the sample size and is given by n - 1                            

where, n = sample size

Properties

1. The total area under t distribution is equal to 1.

2. The mean of the distribution is equal to 0.

3. As the number of degrees of freedom increases , the curve looks more like standard normal distribution.

4. Variance = v / v -2                                where v is degree of freedom and v > 2