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.
In a matrix-vector language such as SAS/IML, it is useful to always remember that the fundamental objects are matrices and that all operations are designed to work on matrices. (And vectors, which are matrices that have only one row or one column.) By using matrix operations, you can often eliminate
A reader asked whether it is possible to find a bootstrap sample that has some desirable properties. I am using the term "bootstrap sample" to refer to the result of randomly resampling with replacement from a data set. Specifically, he wanted to find a bootstrap sample that has a specific
Graphing data is almost always more informative than displaying a table of summary statistics. In a recent article about "dynamite plots," I briefly mentioned that graphs such as box plots and strip plots are better at showing data than graphs that merely show the mean and standard deviation. This article
The field of probability and statistics is full of asymptotic results. The Law of Large Numbers and the Central Limit Theorem are two famous examples. An asymptotic result can be both a blessing and a curse. For example, consider a result that says that the distribution of some statistic converges
The SAS/IML language supports lists, which are containers that store other objects, such as matrices and other lists. A primary use of lists is to pack objects of various types into a single symbol that can be passed to and from modules. A useful feature of using lists is that
I previously wrote about one way to solve the partition problem in SAS. In the partition problem, you divide (or partition) a set of N items into two groups of size k and N-k such that the sum of the items' weights is the same in each group. For example,
The partition problem has many variations, but recently I encountered it as an interactive puzzle on a computer. (Try a similar game yourself!) The player is presented with an old-fashioned pan-balance scale and a set of objects of different weights. The challenge is to divide (or partition) the objects into
A statistical programmer asked how to simulate event-trials data for groups. The subjects in each group have a different probability of experiencing the event. This article describes one way to simulate this scenario. The simulation is similar to simulating from a mixture distribution. This article also shows three different ways
A colleague spent a lot of time creating a panel of graphs to summarize some data. She did not use SAS software to create the graph, but I used SAS to create a simplified version of her graph, which is shown to the right. (The colors are from her graph.)
The number of possible bootstrap samples for a sample of size N is big. Really big. Recall that the bootstrap method is a powerful way to analyze the variation in a statistic. To implement the standard bootstrap method, you generate B random bootstrap samples. A bootstrap sample is a sample
