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Analytics | Learn SAS

Rick WicklinOctober 2, 2023 2

On computing Kendall's tau statistic in SAS

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.

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Analytics | Learn SAS | Programming Tips

Rick WicklinSeptember 6, 2023 7

Model data from published summary statistics

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

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Analytics | Data Visualization | Programming Tips

Rick WicklinAugust 28, 2023 6

Generate random uniform points in an ellipse

I have previously written about how to efficiently generate points uniformly at random inside a sphere (often called a ball by mathematicians). The method uses a mathematical fact from multivariate statistics: If X is drawn from the uncorrelated multivariate normal distribution in dimensiond, then S = r*X / ||X|| has

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Analytics | Learn SAS

Rick WicklinAugust 23, 2023 0

Bootstrap predicted means by using PROC GLMSELECT

A previous article shows how to use the MODELAVERAGE statement in PROC GLMSELECT in SAS to perform a basic bootstrap analysis of the regression coefficients and fit statistics. A colleague asked whether PROC GLMSELECT can construct bootstrap confidence intervals for the predicted mean in a regression model, as described in

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Analytics | Learn SAS

Rick WicklinAugust 21, 2023 1

A simple way to bootstrap linear regression models in SAS

I've written many articles about bootstrapping in SAS, including several about bootstrapping in regression models. Many of the articles use a very general bootstrap method that can bootstrap almost any statistic that SAS can compute. The method uses PROC SURVEYSELECT to generate B bootstrap samples from the data, uses the

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Analytics | Learn SAS | Programming Tips

Rick WicklinAugust 14, 2023 2

Bootstrap confidence intervals for the predicted mean in a regression model

In ordinary least squares regression, there is an explicit formula for the confidence limit of the predicted mean. That is, for any observed value of the explanatory variables, you can create a 95% confidence interval (CI) for the predicted response. This formula assumes that the model is correctly specified and

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Analytics | Programming Tips

Rick WicklinJuly 24, 2023 4

Modifications of the Wilcoxon signed rank test and exact p-values

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

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Analytics | Learn SAS | Programming Tips

Rick WicklinJuly 19, 2023 1

On the computation of the Wilcoxon signed rank statistic

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

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Analytics | Learn SAS

Rick WicklinJuly 17, 2023 0

Standardize regression coefficients for models that include categorical variables

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

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Analytics | Learn SAS | Programming Tips

Rick WicklinJune 28, 2023 2

Compute the geometric median in SAS

Given a set of N points in k-dimensional space, can you find the location that minimizes the sum of the distances to the points? The location that minimizes the distances is called the geometric median of the points. For univariate data, the "points" are merely a set of numbers \(\{p_1,

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