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Rick WicklinMay 2, 2022 0

Simulate the null distribution for a hypothesis test

Recently, I wrote about Bartlett's test for sphericity. The purpose of this hypothesis test is to determine whether the variables in the data are uncorrelated. It works by testing whether the sample correlation matrix is close to the identity matrix. Often statistics textbooks or articles include a statement such as

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Analytics | Learn SAS

Rick WicklinApril 27, 2022 2

On Bartlett's sphericity test for correlation

When you have many correlated variables, principal component analysis (PCA) is a classical technique to reduce the dimensionality of the problem. The PCA finds a smaller dimensional linear subspace that explains most of the variability in the data. There are many statistical tools that help you decide how many principal

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Analytics | Learn SAS

Rick WicklinApril 18, 2022 1

The McNemar test in SAS

What is McNemar's test? How do you run the McNemar test in SAS? Why might other statistical software report a value for McNemar's test that is different from the SAS value? SAS supports an exact version of the McNemar test, but when should you use it? This article answers these

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Rick WicklinApril 13, 2022 0

Pascal matrices and inverses

Some matrices are so special that they have names. The identity matrix is the most famous, but many are named after a researcher who studied them such as the Hadamard, Hilbert, Sylvester, Toeplitz, and Vandermonde matrices. This article is about the Pascal matrix, which is formed by using elements from

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Analytics | Learn SAS

Rick WicklinApril 11, 2022 4

New methods for solving differential equations in SAS

Many discussions and articles about SAS Viya emphasize its ability to handle Big Data, perform parallel processing, and integrate open-source languages. These are important issues for some SAS customers. But for customers who program in SAS and do not have Big Data, SAS Viya is attractive because it is the

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Analytics | Programming Tips

Rick WicklinApril 6, 2022 2

A differential equation for quantiles of a distribution

The graph to the right is the quantile function for the standard normal distribution, which is sometimes called the probit function. Given any probability, p, the quantile function gives the value, x, such that the area under the normal density curve to the left of x is exactly p. This

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Analytics | Learn SAS | Programming Tips

Rick WicklinMarch 16, 2022 0

Least-squares optimization and the Gauss-Newton method

A previous article showed how to use SAS to compute finite-difference derivatives of smooth vector-valued multivariate functions. The article uses the NLPFDD subroutine in SAS/IML to compute the finite-difference derivatives. The article states that the third output argument of the NLPFDD subroutine "contains the matrix product J`*J, where J is

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Analytics | Programming Tips

Rick WicklinMarch 7, 2022 0

Finite-difference derivatives of vector-valued functions

I previously showed how to use SAS to compute finite-difference derivatives for smooth scalar-valued functions of several variables. You can use the NLPFDD subroutine in SAS/IML software to approximate the gradient vector (first derivatives) and the Hessian matrix (second derivatives). The computation uses finite-difference derivatives to approximate the derivatives. The

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Analytics | Programming Tips

Rick WicklinMarch 2, 2022 3

Finite-difference derivatives in SAS

Many applications in mathematics and statistics require the numerical computation of the derivatives of smooth multivariate functions. For simple algebraic and trigonometric functions, you often can write down expressions for the first and second partial derivatives. However, for complicated functions, the formulas can get unwieldy (and some applications do not

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Analytics | Programming Tips

Rick WicklinFebruary 14, 2022 16

Passing-Bablok regression in SAS

This article implements Passing-Bablok regression in SAS. Passing-Bablok regression is a one-variable regression technique that is used to compare measurements from different instruments or medical devices. The measurements of the two variables (X and Y) are both measured with errors. Consequently, you cannot use ordinary linear regression, which assumes that

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