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Rick WicklinJune 14, 2021 5

Simulate correlated variables by using the Iman-Conover transformation

Simulating univariate data is relatively easy. Simulating multivariate data is much harder. The main difficulty is to generate variables that have given univariate distributions but also are correlated with each other according to a specified correlation matrix. However, Iman and Conover (1982, "A distribution-free approach to inducing rank correlation among

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Analytics | Programming Tips

Rick WicklinJune 7, 2021 1

Permutation tests and independent sorting of data

For many univariate statistics (mean, median, standard deviation, etc.), the order of the data is unimportant. If you sort univariate data, the mean and standard deviation do not change. However, you cannot sort an individual variable (independently) if you want to preserve its relationship with other variables. This statement is

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Analytics | Programming Tips

Rick WicklinJune 1, 2021 10

The Hampel identifier: Robust outlier detection in a time series

It is well known that classical estimates of location and scale (for example, the mean and standard deviation) are influenced by outliers. In the 1960s, '70s, and '80s, researchers such as Tukey, Huber, Hampel, and Rousseeuw advocated analyzing data by using robust statistical estimates such as the median and the

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Analytics | Programming Tips

Rick WicklinMay 26, 2021 1

The running median as a time series smoother

When data contain outliers, medians estimate the center of the data better than means do. In general, robust estimates of location and sale are preferred over classical moment-based estimates when the data contain outliers or are from a heavy-tailed distribution. Thus, instead of using the mean and standard deviation of

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Learn SAS | Programming Tips

Rick WicklinMay 19, 2021 0

Implement a product function in SAS

A SAS programmer noticed that there is not a built-in function in the SAS DATA step that computes the product for each row across a specified set of variables. There are built-in functions for various statistics such as the SUM, MAX, MIN, MEAN, and MEDIAN functions. But no DATA step

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Analytics | Learn SAS | Programming Tips

Rick WicklinMay 12, 2021 2

Nonstandard ways to standardize variables

You can standardize a numerical variable by subtracting a location parameter from each observation and then dividing by a scale parameter. Often, the parameters depend on the data that you are standardizing. For example, the most common way to standardize a variable is to subtract the sample mean and divide

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Learn SAS | Programming Tips $Odani's truism for fractions that are near each other$

Rick WicklinMay 10, 2021 1

Odani's truism for fractions that are near each other

Odani's truism is a mathematical result that says that if you want to compare the fractions a/b and c/d, it often is sufficient to compare the sums (a+d) and (b+c) rather than the products a*d and b*c. (All of the integers a, b, c, and d are positive.) If you

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Learn SAS | Programming Tips $Odani's truism: A probabilistic way to compare fractions$

Rick WicklinMay 5, 2021 1

Odani's truism: A probabilistic way to compare fractions

Quick! Which fraction is bigger, 40/83 or 27/56? It's not always easy to mentally compare two fractions to determine which is larger. For this example, you can easily see that both fractions are a little less than 1/2, but to compare the numbers you need to compare the products 40*56

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Analytics | Programming Tips

Rick WicklinApril 28, 2021 1

Compute the Hoeffding D statistic in SAS

There are many statistics that measure whether two continuous random variables are independent or whether they are related to each other in some way. The most well-known statistic is Pearson's correlation, which is a parametric measure of the linear relationship between two variables. A related measure is Spearman's rank correlation,

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Learn SAS | Programming Tips

Rick WicklinApril 26, 2021 1

On passing a list to a SAS/IML module

SAS/IML programmers often create and call user-defined modules. Recall that a module is a user-defined subroutine or function. A function returns a value; a subroutine can change one or more of its input arguments. I have written a complete guide to understanding SAS/IML modules, which contains many tips for working

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