As a general rule, when SAS programmers want to manipulate data row by row, they reach for the SAS DATA step. When the computation requires column statistics, the SQL procedure is also useful. When both row and column operations are required, the SAS/IML language is a powerful addition to a

## Tag: **vectorization**

One way to assess the precision of a statistic (a point estimate) is to compute the standard error, which is the standard deviation of the statistic's sampling distribution. A relatively large standard error indicates that the point estimate should be viewed with skepticism, either because the sample size is small

Many intervals in statistics have the form p ± δ, where p is a point estimate and δ is the radius (or half-width) of the interval. (For example, many two-sided confidence intervals have this form, where δ is proportional to the standard error.) Many years ago I wrote an article

I recently needed to solve a fun programming problem. I challenge other SAS programmers to solve it, too! The problem is easy to state: Given a long sequence of digits, can you write a program to count how many times a particular subsequence occurs? For example, if I give you

Two of my favorite string-manipulation functions in the SAS DATA step are the COUNTW function and the SCAN function. The COUNTW function counts the number of words in a long string of text. Here "word" means a substring that is delimited by special characters, such as a space character, a

I was a freshman in college the first time I saw the Cantor middle-thirds set and the related Cantor "Devil's staircase" function. (Shown at left.) These constructions expanded my mind and led me to study fractals, real analysis, topology, and other mathematical areas. The Cantor function and the Cantor middle-thirds

Last week I showed how to use PROC EXPAND to compute moving averages and other rolling statistics in SAS. Unfortunately, PROC EXPAND is part of SAS/ETS software and not every SAS site has a license for SAS/ETS. For simple moving averages, you can write a DATA step program, as discussed

Recently I blogged about how to compute a weighted mean and showed that you can use a weighted mean to compute the center of mass for a system of N point masses in the plane. That led me to think about a related problem: computing the center of mass (called

Every year near Halloween I write a trick-and-treat article in which I demonstrate a simple programming trick that is a real treat to use. This year's trick features two of my favorite functions, the CUSUM function and the LAG function. By using these function, you can compute the rows of

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