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Rick WicklinOctober 12, 2022 0

Reduced regression models and tests for linear hypotheses

On a SAS discussion forum, a statistical programmer asked about how to understand the statistics that are displayed when you use the TEST statement in PROC REG (or other SAS regression procedures) to test for linear relationships between regression coefficients. The documentation for the TEST statement in PROC REG explains

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Analytics | Learn SAS | Programming Tips

Rick WicklinOctober 3, 2022 1

Compute moments of probability distributions in SAS

A previous article discusses the definitions of three kinds of moments for a continuous probability distribution: raw moments, central moments, and standardized moments. These are defined in terms of integrals over the support of the distribution. Moments are connected to the familiar shape features of a distribution: the mean, variance,

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Rick WicklinSeptember 28, 2022 2

Definitions of moments in probability and statistics

The moments of a continuous probability distribution are often used to describe the shape of the probability density function (PDF). The first four moments (if they exist) are well known because they correspond to familiar descriptive statistics: The first raw moment is the mean of a distribution. For a random

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Analytics | Learn SAS

Rick WicklinSeptember 21, 2022 1

The noncentral t distribution in SAS

The noncentral t distribution is a probability distribution that is used in power analysis and hypothesis testing. The distribution generalizes the Student t distribution by adding a noncentrality parameter, δ. When δ=0, the noncentral t distribution is the usual (central) t distribution, which is a symmetric distribution. When δ >

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Analytics | Learn SAS | Programming Tips

Rick WicklinSeptember 7, 2022 0

A test for monotonic sequences and functions

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

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Analytics | Learn SAS

Rick WicklinAugust 22, 2022 2

The univariate Box-Cox transformation

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

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Rick WicklinAugust 17, 2022 1

The Box-Cox transformation for a dependent variable in a regression

In the 1960s and '70s, before nonparametric regression methods became widely available, it was common to apply a nonlinear transformation to the dependent variable before fitting a linear regression model. This is still done today, with the most common transformation being a logarithmic transformation of the dependent variable, which fits

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Analytics | Data Visualization | Learn SAS

Rick WicklinAugust 15, 2022 0

Tukey's ladder of variable transformations

John Tukey was an influential statistician who proposed many statistical concepts. In the 1960s and 70s, he was fundamental in the discovery and exposition of robust statistical methods, and he was an ardent proponent of exploratory data analysis (EDA). In his 1977 book, Exploratory Data Analysis, he discussed a small

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Analytics | Learn SAS

Rick WicklinAugust 8, 2022 1

Means and medians as minimizers of a loss function

On Twitter, I saw a tweet from @DataSciFact that read, "The sum of (x_i - x)^2 over a set of data points x_i is minimized when x is the sample mean." I (@RickWicklin) immediately tweeted out a reply: "And the sum of |x_i - x| is minimized by the sample

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Analytics | Learn SAS

Rick WicklinAugust 1, 2022 0

Introductory examples of Monte Carlo simulation in SAS

When I was writing Simulating Data with SAS (Wicklin, 2013), I read a lot of introductory textbooks about Monte Carlo simulation. One of my favorites is Sheldon Ross's book Simulation. (I read the 4th Edition (2006); the 5th Edition was published in 2013.) I love that the book brings together

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