Statistics Knowledge Base - p-Value for Student's t-Test

Tuesday, May 13, 2008

p-Value for Student's t-Test

The p-value for a one-tailed t-test is the probability that the absolute value of a point chosen at random from a particular Student t-distribution would be greater than or equal to the absolute value of an observed point (the t-value) from the same distribution.

PROPERTIES

Some of the important properties of Student's t-distribution include:

The t-distribution is a probability distribution, and as such the p-value for a one-tailed t-test also refers to the total area under a particular Student t-distribution from the absolute value of t to infinity.
The t-distribution is symmetric, and as such the p-value associated with t will always be the same as the p-value associated with -t, and vice versa.
Because every t-distribution is symmetric, the p-value for a two-tailed t-test will always be twice as large as the p-value for a one-tailed t-test.
The shape of a t-distribution depends upon its degrees of freedom. As the degrees of freedom increase, the shape of the t-distribution approaches the normal distribution.

ONLINE CALCULATOR

To calculate a p-Value for Student's t-Test, please click here.

FORMULAE

The formula involved in the computation of a p-Value for Student's t-Test is detailed below.

Integral of the Student t-distribution probability density function:
Where v is the degrees of freedom, and B is the Beta function.

REFERENCES

Student [William Sealy Gosset] (1908), "The probable error of a mean", Biometrika, vol. 6(1), pp. 1-25.

Fisher, R.A. (1925), "Applications of Student's distribution", Metron, vol. 5, pp. 90-104.

Abramowitz, M. and Stegun, I.A., eds. (1965), "Handbook of Mathematical Functions", Dover, New York, NY.