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.

- Open the cumulative distribution function dialog box.
- Mac:
- PC:

- From Form of input, select A single value.
- From Value, enter
`2.44`. - From Distribution, select F.
- In Numerator degrees of freedom, enter
`3`. - In Denominator degrees of freedom, enter
`25`. - In Noncentrality parameter, enter
`0`. - Click OK.

The cumulative probability is 0.912050. Subtract this value from 1 to get the calculated p-value.

The calculated p-value is 0.08795. Using the 0.05 cutoff value, you would not conclude statistical significance because 0.08795 is not less than 0.05.
###### Note

This example is for an F-distribution; however, you can use a similar method for other distributions.