One thing I have learned about rank-based statistics over the years is "Be careful of tied values!" On multiple occasions, I have been asked, "Why doesn't the SAS result for [NAME] statistic agree with my hand calculation?" The answer is sometimes because of the way that tied values are handled.
Many SAS procedures support a BY statement that enables you to perform an analysis for each unique value of a BY-group variable. The SAS IML language does not support a BY statement, but you can program a loop that iterates over all BY groups. You can emulate BY-group processing by
There are many ways to model a set of raw data by using a continuous probability distribution. It can be challenging, however, to choose the distribution that best models the data. Are the data normal? Lognormal? Is there a theoretical reason to prefer one distribution over another? The SAS has
Does anyone write paper checks anymore? According to researchers at the Federal Reserve Bank of Atlanta (Greene, et al., 2020), the use of paper checks has declined 63% among US consumers since the year 2000. The researchers surveyed more than 3,000 consumers in 2017-2018 and discovered that only 7% of
In a previous article, I discussed the Wilcoxon signed rank test, which is a nonparametric test for the location of the median. The Wikipedia article about the signed rank test mentions a variation of the test due to Pratt (1959). Whereas the standard Wilcoxon test excludes values that equal μ0
Wilcoxon's signed rank test is a popular nonparametric alternative to a paired t test. In a paired t test, you analyze measurements for subjects before and after some treatment or intervention. You analyze the difference in the measurements for each subject, and test whether the mean difference is significantly different
A previous article discusses standardized coefficients in linear regression models and shows how to compute standardized regression coefficients in SAS by using the STB option on the MODEL statement in PROC REG. It also discusses how to interpret a standardized regression coefficient. Recently, a SAS user wanted to know how
A previous article explains the Spearman rank correlation, which is a robust cousin to the more familiar Pearson correlation. I've also discussed why you might want to use rank correlation, and how to interpret the strength of a rank correlation. This article gives a short example that helps you to
SAS supports many ways to compute the rank of a numeric variable and to handle tied values. However, sometimes I need to rank the values in a character categorical variable. For example, the values {"Male", "Female", "Male"} have ranks {2, 1, 2} because, in alphabetical order, "Female" is the first-ranked
A previous article defines the silhouette statistic (Rousseeuw, 1987) and shows how to use it to identify observations in a cluster analysis that are potentially misclassified. The article provides many graphs, including the silhouette plot, which is a bar chart or histogram that displays the distribution of the silhouette statistic
Assigning observations into clusters can be challenging. One challenge is deciding how many clusters are in the data. Another is identifying which observations are potentially misclassified because they are on the boundary between two different clusters. Ralph Abbey's 2019 paper ("How to Evaluate Different Clustering Results") is a good way
The "Teacher’s Corner" of The American Statistician enables statisticians to discuss topics that are relevant to teaching and learning statistics. Sometimes, the articles have practical relevance, too. Andersson (2023) "The Wald Confidence Interval for a Binomial p as an Illuminating 'Bad' Example," is intended for professors and masters-level students in
A journal article listed the mean, median, and size for subgroups of the data, but did not report the overall mean or median. A SAS programmer wondered what, if any, inferences could be made about the overall mean and median for the data. The answer is that you can calculate
A SAS user asked how to interpret a rank-based correlation such as a Spearman correlation or a Kendall correlation. These are alternative measures to the usual Pearson product-moment correlation, which is widely used. The programmer knew that words like "weak," "moderate," and "strong" are sometimes used to describe the Pearson
A previous article discusses rank correlation and lists some advantages of using rank correlation. However, the article does not show examples where an analyst might prefer to report the rank correlation instead of the traditional Pearson product-moment correlation. This article provides three examples where the rank correlation is a better
A previous article discusses the issue of a confounding variable and uses correlation to give an example. The example shows that the correlation between two variables might be affected by a third variable, which is called a confounding variable. The article mentions that you can use the PARTIAL statement in
A data analyst wanted to estimate the correlation between two variables, but he was concerned about the influence of a confounding variable that is correlated with them. The correlation might affect the apparent relationship between main two variables in the study. A common confounding variable is age because young people
In a previous article about Markov transition matrices, I mentioned that you can estimate a Markov transition matrix by using historical data that are collected over a certain length of time. A SAS programmer asked how you can estimate a transition matrix in SAS. The answer is that you can
As in most other sectors, health care is changing at lightning speed. Access to data makes it possible to speed up clinical trials, develop more personalized medication, make quicker and better diagnoses, improve the quality of patient care and save lives. The pandemic has sped up digital transformation in every
Most homeowners know that large home improvement projects can take longer than you expect. Whether it's remodeling a kitchen, adding a deck, or landscaping a yard, big projects are expensive and subject to a lot of uncertainty. Factors such as weather, the availability of labor, and the supply of materials,
A previous article describes the metalog distribution (Keelin, 2016). The metalog distribution is a flexible family of distributions that can model a wide range of shapes for data distributions. The metalog system can model bounded, semibounded, and unbounded continuous distributions. This article shows how to use the metalog distribution in
Undergraduate textbooks on probability and statistics typically prove theorems that show how the variance of a sum of random variables is related to the variance of the original variables and the covariance between them. For example, the Wikipedia article on Variance contains an equation for the sum of two random
The metalog family of distributions (Keelin, Decision Analysis, 2016) is a flexible family that can model a wide range of continuous univariate data distributions when the data-generating mechanism is unknown. This article provides an overview of the metalog distributions. A subsequent article shows how to download and use a library
A SAS programmer was trying to simulate poker hands. He was having difficulty because the sampling scheme for simulating card games requires that you sample without replacement for each hand. In statistics, this is called "simple random sampling." If done properly, it is straightforward to simulate poker hands in SAS.
A profile plot is a way to display multivariate values for many subjects. The optimal linear profile plot was introduced by John Hartigan in his book Clustering Algorithms (1975). In Michael Friendly's book (SAS System for Statistical Graphics, 1991), Friendly shows how to construct an optimal linear profile by using
A profile plot is a compact way to visualize many variables for a set of subjects. It enables you to investigate which subjects are similar to or different from other subjects. Visually, a profile plot can take many forms. This article shows several profile plots: a line plot of the
The area of a convex hull enables you to estimate the area of a compact region from a set of discrete observations. For example, a biologist might have multiple sightings of a wolf pack and want to use the convex hull to estimate the area of the wolves' territory. A
A common question on SAS discussion forums is how to use SAS to generate random ID values. The use case is to generate a set of random strings to assign to patients in a clinical study. If you assign each patient a unique ID and delete the patients' names, you
Monotonic transformations occur frequently in math and statistics. Analysts use monotonic transformations to transform variable values, with Tukey's ladder of transformations and the Box-Cox transformations being familiar examples. Monotonic distributions figure prominently in probability theory because the cumulative distribution is a monotonic increasing function. For a continuous distribution that is
A SAS customer asked how to use the Box-Cox transformation to normalize a single variable. Recall that a normalizing transformation is a function that attempts to convert a set of data to be as nearly normal as possible. For positive-valued data, introductory statistics courses often mention the log transformation or
