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Analytics | Learn SAS | Programming Tips

Rick WicklinApril 17, 2023 3

Should you use the Wald confidence interval for a binomial proportion?

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

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Learn SAS | Programming Tips

Rick WicklinMarch 29, 2023 2

Using SAS to solve an introductory programming assignment

I recently discussed introductory programming with a colleague who teaches Python at a university. He told me about the following introductory programming assignment: Let N be an integer parameter in the range [1, 9]. For each value of N, find all pairs of one-digit positive integers d1 and d2 that

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Analytics | Learn SAS | Programming Tips

Rick WicklinMarch 22, 2023 4

Partial correlation: controlling for confounding variables

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

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Learn SAS | Programming Tips

Rick WicklinMarch 20, 2023 7

Estimate a Markov transition matrix from historical data

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

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Analytics | Learn SAS | Programming Tips

Rick WicklinMarch 15, 2023 2

Fitting a distribution to an expert's opinion: An application of the metalog distribution

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,

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Analytics | Learn SAS | Programming Tips

Rick WicklinMarch 13, 2023 1

Use the metalog distribution in SAS

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

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Learn SAS | Programming Tips

Rick WicklinMarch 8, 2023 6

How Newton calculated pi to 16 decimal places

Happy Pi Day! Every year on March 14th (written 3/14 in the US), people in the mathematical sciences celebrate "all things pi-related" because 3.14 is the three-decimal approximation to π ≈ 3.14159265358979.... Modern computer methods and algorithms enable us to calculate 100 trillion digits of π. However, I think it

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Learn SAS | Programming Tips

Rick WicklinMarch 6, 2023 0

The variance of the sums of variables

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

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Analytics | Programming Tips

Rick WicklinMarch 1, 2023 0

The distribution of the difference between two beta random variables

A SAS programmer wanted to compute the distribution of X-Y, where X and Y are two beta-distributed random variables. Pham-Gia and Turkkan (1993) derive a formula for the PDF of this distribution. Unfortunately, the PDF involves evaluating a two-dimensional generalized hypergeometric function, which is not available in all programming languages.

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Analytics | Programming Tips

Rick WicklinFebruary 27, 2023 0

Compute hypergeometric functions in SAS

In applied mathematics, there is a large collection of "special functions." These function appera in certain applications, often as the solution to a differential equation, but also in the definition of probability distributions. For example, I have written about Bessel functions, the complete and incomplete gamma function, and the complete

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