tdist

This function is Student’s T-distribution function. It returns the probability that a T-distributed random variable is less than a specified independent variable value.

A T-distributed random variable is defined as a scaled ratio of a standard normal variable and a chi-square variable. The degrees of freedom of a T-distributed variable is defined to be the degrees of freedom of the chi-square variable in the denominator.

This distribution is used in computing confidence intervals and for testing the homogeneity of populations for two groups of normally distributed observations.

Syntax

tdist(x,n)

The x argument represents the independent variable and can either be a scalar or a range of numbers. If x is a range, then it must be defined by either using braces { } or by specifying a worksheet column. The n argument can be any positive integer and equals the degrees of freedom.

Example

Suppose T is a T-distributed random variable with 14 degrees of freedom. To compute the probability that the absolute values of T exceed 2, we calculate:

P( |T| > 2 ) = P( T > 2) + P( T < -2) = 2*P( T > 2) = 2*( 1 – P( T < 2) ) = 2*(1-tdist(2,14)) = .06529

This is a typical calculation that is used to test whether two normally distributed groups of observations have the same mean. In this context, the value 2 in our example is called the critical value and is equal to the absolute difference in the sample means of the two groups divided by the pooled standard deviation of the groups. The resulting probability, .06529, is called the probability of significance.

関連情報

• tinv
• tden