The FREQ procedure in SAS supports computing exact p-values for many statistical tests. For small and mid-sized problems, the procedure runs very quickly. However, even though PROC FREQ uses efficient methods to avoid unnecessary computations, the computational time required by exact tests might be prohibitively expensive for certain tables. If
Did you know that the FREQ procedure in SAS can compute exact p-values for more than 20 statistical tests and statistics that are associated with contingency table? Mamma mia! That's a veritable smorgasbord of options! Some of the tests are specifically for one-way tables or 2 x 2 tables, but many apply
How do you simulate a contingency table that has a specified row and column sum? Last week I showed how to simulate a random 2 x 2 contingency table when the marginal frequencies are specified. This article generalizes to random r x c frequency tables (also called cross-tabulations) that have the same marginal row
A recent question posted on a discussion forum discussed storing the strictly upper-triangular portion of a correlation matrix. Suppose that you have a correlation matrix like the following: proc iml; corr = {1.0 0.6 0.5 0.4, 0.6 1.0 0.3 0.2, 0.5 0.3 1.0 0.1, 0.4 0.2 0.1 1.0}; Every correlation
When modeling and simulating data, it is important to be able to articulate the real-life statistical process that generates the data. Suppose a friend says to you, "I want to simulate two random correlated variables, X and Y." Usually this means that he wants data generated from a multivariate distribution,
This article shows how to visualize a surface in SAS. You can use the SURFACEPLOTPARM statement in the Graph Template Language (GTL) to create a surface plot. But don't worry, you don't need to know anything about GTL: just copy the code in this article and replace the names of
Suppose that you are tabulating the eye colors of students in a small class (following Friendly, 1992). Depending upon the ethnic groups of these students, you might not observe any green-eyed students. How do you put a 0 into the table that summarizes the number of students who have each
You can use SAS to generate random integers between 1–10 or in the range 1–100. This article shows how to generate random integers as easily as Excel does. I was recently talking with some SAS customers and I was asked "Why can't SAS create an easy way to generate random
In a previous post I described how to simulate random samples from an urn that contains colored balls. The previous article described the case where the balls can be either of two colors. In that csae, all the distributions are univariate. In this article I examine the case where the
If not for probability theory, urns would appear only in funeral homes and anthologies of British poetry. But in probability and statistics, urns are ever present and contain colored balls. The removal and inspection of colored balls from an urn is a classic way to demonstrate probability, sampling, variation, and
