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.
The collinearity problem is to determine whether three points in the plane lie along a straight line. You can solve this problem by using middle-school algebra. An algebraic solution requires three steps. First, name the points: p, q, and r. Second, find the parametric equation for the line that passes
Plot rates, not counts. This maxim is often stated by data visualization experts, but often ignored by practitioners. You might also hear the related phrases "plot proportions" or "plot percentages," which mean the same thing but expresses the idea alliteratively. An example in a previous article about avoiding alphabetical ordering
Converting a program from one language to another can be a challenge. Even if the languages share many features, there is often syntax that is valid in one language that is not valid in another. Recently, a SAS programmer was converting a program from R to SAS IML. He reached
Howard Wainer, who used to write the "Visual Revelations" column in Chance magazine, often reminded his readers that "we are almost never interested in seeing Alabama first" (2005, Graphic Discovery, p. 72). His comment is a reminder that when we plot data for a large number of categories (states, countries,
Sometimes it is helpful to display a table of statistics directly on a graph. A simple example is displaying the number of observations and the mean or median on a histogram. In SAS, the term inset is used to describe a table that is displayed on a graph. This article
In several previous articles, I've shown how to use SAS to fit models to data by using maximum likelihood estimation (MLE). However, I have not previously shown how to obtain standard errors for the estimates. This article combines two previous articles to show how to obtain MLE estimates and the
A previous article shows how to use Monte Carlo simulation to approximate the sampling distribution of the sample mean and sample median. When x ~ N(0,1) are normal data, the sample mean is also normal, and there are simple formulas for the expected value and the standard error of the
An elementary course in statistics often includes a discussion of the sampling distribution of a statistic. The canonical example is the sampling distribution of the sample mean. For samples of size n that are drawn from a normally distribution (X ~ N(μ, σ)), the sample mean is normally distributed as
A previous article discusses the birthday problem and its generalizations. The classic birthday problem asks, "In a room that contains N people, what is the probability that two or more people share a birthday?" The probability is much higher than you might think. For example, in a room that contains
The birthday-matching problem (also called the birthday paradox or simply the birthday problem), is a classic problem in probability. Simply stated, the birthday-matching problem asks, "If there are N people in a room, what is the chance that two of them have the same birthday?" The problem is sometimes called
