The cumulative distribution function (CDF) calculates the cumulative probability for a given x-value. Use the CDF to determine the probability that a random observation that is taken from the population will be less than or equal to a certain value. You can also use this information to determine the probability that an observation will be greater than a certain value, or between two values.
For example, soda can fill weights follow a normal distribution with a mean of 12 ounces and a standard deviation of 0.25 ounces. The probability density function (PDF) describes the likelihood of possible values of fill weight. The CDF provides the cumulative probability for each x-value.
Use the CDF to determine the probability that a randomly chosen can of soda has a fill weight that is less than 11.5 ounces, greater than 12.5 ounces, or between 11.5 and 12.5 ounces.
In order to calculate a p-value for an F-test, you must first calculate the cumulative distribution function (CDF). The p-value is 1 – CDF
Suppose you perform a multiple linear regression analysis with the following degrees of freedom: DF (Regression) = 3; DF (Error) = 25; and the F-statistic = 2.44.
The cumulative probability is 0.912050. Subtract this value from 1 to get the calculated p-value.
This example is for an F-distribution; however, you can use a similar method for other distributions.