Microsoft Excel supplies two useful statistical functions for making beta probability calculations, BETADIST and BETAINV. Perhaps surprisingly, neither function is difficult to use as long as understand the inputs that supply data to the function.

Understanding the beta probability density function, BETADIST

The BETADIST function returns the cumulative beta probability density function.

Statisticians often use the cumulative beta probability density function to study variation across samples, such as when comparing two groups of people performing the same task to see whether they have the same success rate.

The BETADIST function uses the following syntax:

=BETADIST (x, alpha, beta, A, B)

where x is a value between two optional bounds A and B, and alpha and beta are the two positive parameters.

An Example of the BETADIST Function

For example, if x equals 2, alpha equals 85, beta equals 90, A equals 1, and B equals 3, you would enter the function as follows:

=BETADIST (2, 85, 90, 1, 3)

The formula returns the value 0.647616.

Note that the uniform probability distribution is a special case of the beta probability distribution where alpha=beta=1.

Using the inverse beta probability density function, BETAINV

The BETAINV function returns the inverse of the cumulative beta probability density function. That is, you use the BETADIST function if you know x and want to find the probability, and you use the BETAINV function if you know the probability and want to find x.

The BETAINV function uses the following syntax:

=BETAINV (probability, alpha, beta, A, B) where probability is a value between two optional bounds A and B, and alpha and beta are the two positive parameters.

An Example of the BETAINV Function

For example, if the probability equals 0.647616., alpha equals 85, beta equals 90, A equals 1, and B equals 3, you would enter the function as follows:

The formula returns the value 2.

About the author: Seattle accountant and author Stephen L. Nelson wrote the MBA's Guide to Microsoft Excel, from which this short article is adapted. Nelson also writes and edits downloadable do-it-yourself small business incorporation kits that entrepreneurs can use for setting up a Mississippi limited liability company or a Missouri limited liability company.

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