Rick Wicklin, PhD, is a distinguished researcher in computational statistics at SAS and is a principal developer of SAS/IML software. His areas of expertise include computational statistics, simulation, statistical graphics, and modern methods in statistical data analysis. Rick is author of the books Statistical Programming with SAS/IML Software and Simulating Data with SAS.
There are many techniques for generating random variates from a specified probability distribution such as the normal, exponential, or gamma distribution. However, one technique stands out because of its generality and simplicity: the inverse CDF sampling technique. If you know the cumulative distribution function (CDF) of a probability distribution, then
In a previous article I discussed how to bin univariate observations by using the BIN function, which was added to the SAS/IML language in SAS/IML 9.3. You can generalize that example and bin bivariate or multivariate data. Over two years ago I wrote a blog post on 2D binning in
It is often useful to partition observations for a continuous variable into a small number of intervals, called bins. This familiar process occurs every time that you create a histogram, such as the one on the left. In SAS you can create this histogram by calling the UNIVARIATE procedure. Optionally,
Are you still using the old RANUNI, RANNOR, RANBIN, and other "RANXXX" functions to generate random numbers in SAS? If so, here are six reasons why you should switch from these older (1970s) algorithms to the newer (late 1990s) Mersenne-Twister algorithm, which is implemented in the RAND function. The newer
Every programming language has an IF-THEN statement that branches according to whether a Boolean expression is true or false. In SAS, the IF-THEN (or IF-THEN/ELSE) statement evaluates an expression and braches according to whether the expression is nonzero (true) or zero (false). The basic syntax is if numeric-expression then do-computation;
On the Web site for the book Statistical Programming with SAS/IML Software, I provide instructions on how to download the sample data sets and install them so that they can be used from within SAS/IML Studio. When I wrote the book I did not anticipate that SAS users might want
As I wrote in my previous post, a SAS customer noticed that he was getting some duplicate values when he used the RAND function to generate a large number of random uniform values on the interval [0,1]. He wanted to know if this result indicates a bug in the RAND
Tossing dice is a simple and familiar process, yet it can illustrate deep and counterintuitive aspects of random numbers. For example, if you toss four identical six-sided dice, what is the probability that the faces are all distinct, as shown to the left? Many people would guess that the probability
The CLUSTER procedure in SAS/STAT software creates a dendrogram automatically. The black-and-white dendrogram is nice, but plain. A SAS customer wanted to know whether it is possible to add color to the dendrogram to emphasize certain clusters. For example, the plot at the left emphasizes a four-cluster scenario for clustering
How do you count the number of unique rows in a matrix? The simplest algorithm is to sort the data and then iterate down the rows, comparing each row with the previous row. However, this algorithm has two shortcomings: it physically sorts the data (which means that the original locations
I am not a big fan of the macro language, and I try to avoid it when I write SAS/IML programs. I find that the programs with many macros are hard to read and debug. Furthermore, the SAS/IML language supports loops and indexing, so many macro constructs can be replaced
A regular reader noticed my post on initializing vectors by using repetition factors and asked whether that technique would be useful to expand data that are given in value-frequency pairs. The short answer is "no." Repetition factors are useful for defining (static) matrix literals. However, if you want to expand
In a previous blog post, I described how to use a spread plot to compare the distributions of several variables. Each spread plot is a graph of centered data values plotted against the estimated cumulative probability. Thus, spread plots are similar to a (rotated) plot of the empirical cumulative distribution
Suppose that you have several data distributions that you want to compare. Questions you might ask include "Which variable has the largest spread?" and "Which variables exhibit skewness?" More generally, you might be interested in visualizing how the distribution of one variable differs from the distribution of other variables. The
Last week I showed how to use simulation to estimate the power of a statistical test. I used the two-sample t test to illustrate the technique. In my example, the difference between the means of two groups was 1.2, and the simulation estimated a probability of 0.72 that the t
A SAS user told me that he computed a vector of values in the SAS/IML language and wanted to use those values on a statement in a SAS procedure. The particular application involved wanting to use the values on the ESTIMATE and CONTRAST statements in a SAS regression procedure, but
The power of a statistical test measures the test's ability to detect a specific alternate hypothesis. For example, educational researchers might want to compare the mean scores of boys and girls on a standardized test. They plan to use the well-known two-sample t test. The null hypothesis is that the
Has anyone noticed that the REG procedure in SAS/STAT 12.1 produces heat maps instead of scatter plots for fit plots and residual plots when the regression involves more than 5,000 observations? I wasn't aware of the change until a colleague informed me, although the change is discussed in the "Details"
In my article "Simulation in SAS: The slow way or the BY way," I showed how to use BY-group processing rather than a macro loop in order to efficiently analyze simulated data with SAS. In the example, I analyzed the simulated data by using PROC MEANS, and I use the
Last week I discussed a program that had three nested loops that used scalar operations in the innermost loop. I mentioned that this program was not vectorized, and would therefore be slow in a matrix language such as SAS/IML, MATLAB, or R. I then went through a series of steps
For programmers who are learning the SAS/IML language, it is sometimes confusing that there are two kinds of multiplication operators, whereas in the SAS DATA step there is only scalar multiplication. This article describes the multiplication operators in the SAS/IML language and how to use them to perform common tasks
Last week someone posted an interesting question to the SAS/IML Support Community. The problem involved four nested DO loops and took hours to run. By transforming several nested DO loops into an equivalent matrix operation, I was able to reduce the run time to about one second. The process of
I've conducted a lot of univariate analyses in SAS, yet I'm always surprised when the best way to carry out the analysis uses a SAS regression procedure. I always think, "This is a univariate analysis! Why am I using a regression procedure? Doesn't a regression require at least two variables?"
At a recent conference, I talked with a SAS customer who told me that he was using an R package to create a three-panel visualization of a distribution. Unfortunately, he couldn't remember the name of the package, and he has not returned my e-mails, so the purpose of today's article
PROC UNIVARIATE has provided confidence intervals for standard percentiles (quartiles) for eons. However, in SAS 9.3M2 (featuring the 12.1 analytical procedures) you can use a new feature in PROC UNIVARIATE to compute confidence intervals for a specified list of percentiles. To be clear, percentiles and quantiles are essentially the same
The TV show Cheers was set in a bar "where everybody knows your name." Global knowledge of a name is appealing for a neighborhood pub, but not for a programming language. Most programming languages enable you to define functions that have local variables: variables whose names are known only inside
In my constant effort to keep pace with Chris Hemedinger, I am pleased to announce the availability of my new book, Simulating Data with SAS. Chris started a tradition for SAS Press authors to post a photo of themselves with their new book. Thanks to everyone who helped with the
I've previously described how to overlay two or more density curves on a single plot. I've also written about how to use PROC SGPLOT to overlay custom curves on a graph. This article describes how to overlay a density curve on a histogram. For common distributions, you can overlay a
I recently showed someone a trick to create a graph, and he was extremely pleased to learn it. The trick is well known to many SAS users, but I hope that this article will introduce it to even more SAS users. At issue is how to use the SGPLOT procedure
I often see variations of the following question posted on statistical discussion forums: I want to bin the X variable into a small number of values. For each bin, I want to draw the quartiles of the Y variable for that bin. Then I want to connect the corresponding quartile
