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Broken stick problem: What is the probability that three randomly chosen points will break a segment into a triangle?

Rick WicklinJuly 26, 2017 1

A classical problem in elementary probability asks for the expected lengths of line segments that result from randomly selecting k points along a segment of unit length. It is both fun and instructive to simulate such problems. This article uses simulation in the SAS/IML language to estimate solutions to the

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Programming Tips

Rick WicklinJuly 24, 2017 1

Difference operators as matrices

For a time series { y1, y2, ..., yN }, the difference operator computes the difference between two observations. The kth-order difference is the series { yk+1 - y1, ..., yN - yN-k }. In SAS, the DIF function in the DATA step computes differences between observations. The DIF function

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Advanced Analytics | Programming Tips

Rick WicklinJuly 12, 2017 36

The bias-corrected and accelerated (BCa) bootstrap interval

I recently showed how to compute a bootstrap percentile confidence interval in SAS. The percentile interval is a simple "first-order" interval that is formed from quantiles of the bootstrap distribution. However, it has two limitations. First, it does not use the estimate for the original data; it is based only

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Programming Tips

Rick WicklinJuly 10, 2017 10

Bootstrap estimates in SAS/IML

I previously wrote about how to compute a bootstrap confidence interval in Base SAS. As a reminder, the bootstrap method consists of the following steps: Compute the statistic of interest for the original data Resample B times from the data to form B bootstrap samples. B is usually a large

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Analytics | Programming Tips

Rick WicklinJuly 5, 2017 7

Test for the equality of two proportions in SAS

A SAS customer asked how to use SAS to conduct a Z test for the equality of two proportions. He was directed to the SAS Usage Note "Testing the equality of two or more proportions from independent samples." The note says to "specify the CHISQ option in the TABLES statement

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Programming Tips

t test for difference between group means in SAS

Rick WicklinJuly 3, 2017 6

Summary statistics and t tests in SAS

Students in introductory statistics courses often use summary statistics (such as sample size, mean, and standard deviation) to test hypotheses and to compute confidence intervals. Did you know that you can provide summary statistics (rather than raw data) to PROC TTEST in SAS and obtain hypothesis tests and confidence intervals?

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Programming Tips

Rick WicklinJune 28, 2017 0

The average bootstrap sample omits 36.8% of the data

Suppose you roll six identical six-sided dice. Chance are that you will see at least one repeated number. The probability that you will see six unique numbers is very small: only 6! / 6^6 ≈ 0.015. This example can be generalized. If you draw a random sample with replacement from

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Programming Tips

Rick WicklinJune 26, 2017 0

Video: Create and use lists and tables in SAS/IML

My presentation at SAS Global Forum 2017 was "More Than Matrices: SAS/IML Software Supports New Data Structures." The paper was published in the conference proceedings several months ago, but I recently recorded a short video that gives an overview of using the new data structures in SAS/IML 14.2: If your

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Advanced Analytics | Learn SAS | Programming Tips

Rick WicklinJune 21, 2017 11

Jackknife estimates in SAS

One way to assess the precision of a statistic (a point estimate) is to compute the standard error, which is the standard deviation of the statistic's sampling distribution. A relatively large standard error indicates that the point estimate should be viewed with skepticism, either because the sample size is small

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Analytics | Programming Tips

Rick WicklinJune 14, 2017 21

Two ways to compute maximum likelihood estimates in SAS

In a previous article, I showed two ways to define a log-likelihood function in SAS. This article shows two ways to compute maximum likelihood estimates (MLEs) in SAS: the nonlinear optimization subroutines in SAS/IML and the NLMIXED procedure in SAS/STAT. To illustrate these methods, I will use the same data

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