Head-tail versus head-head: A counterintuitive property of coin tosses

I saw an interesting mathematical result in Wired magazine. The original article was about mathematical research into prime numbers, but the article included the following tantalizing fact: If Alice tosses a [fair] coin until she sees a head followed by a tail, and Bob tosses a coin until he sees […]
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Monte Carlo estimates of pi and an important statistical lesson

Today is March 14th, which is annually celebrated as Pi Day. Today's date, written as 3/14/16, represents the best five-digit approximation of pi. On Pi Day, many people blog about how to approximate pi. This article uses a Monte Carlo simulation to estimate pi, in spite of the fact that […]
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Why doesn't PROC UNIVARIATE support certain common distributions?

A SAS customer asked: Why isn't the chi-square distribution supported in PROC UNIVARIATE? That is an excellent question. I remember asking a similar question when I first started learning SAS. In addition to the chi-square distribution, I wondered why the UNIVARIATE procedure does not support the F distribution. These are […]
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Guessing games, ensemble averages, and the wisdom of the crowd

How much does this big pumpkin weigh? One of the cafeterias at SAS invited patrons to post their guesses on an internal social network at SAS. There was no prize for the correct guess; it was just a fun Halloween-week activity. I recognized this as an opportunity to apply the […]
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Models and simulation for 2x2 contingency tables

When modeling and simulating data, it is important to be able to articulate the real-life statistical process that generates the data. Suppose a friend says to you, "I want to simulate two random correlated variables, X and Y." Usually this means that he wants data generated from a multivariate distribution, […]
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Balls and urns Part 2: Multi-colored balls

In a previous post I described how to simulate random samples from an urn that contains colored balls. The previous article described the case where the balls can be either of two colors. In that csae, all the distributions are univariate. In this article I examine the case where the […]
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Balls and urns: Discrete probability functions in SAS

If not for probability theory, urns would appear only in funeral homes and anthologies of British poetry. But in probability and statistics, urns are ever present and contain colored balls. The removal and inspection of colored balls from an urn is a classic way to demonstrate probability, sampling, variation, and […]
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Error distributions and exponential regression models

Last week I discussed ordinary least squares (OLS) regression models and showed how to illustrate the assumptions about the conditional distribution of the response variable. For a single continuous explanatory variable, the illustration is a scatter plot with a regression line and several normal probability distributions along the line. The […]
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Plot the conditional distribution of the response in a linear regression model

A friend who teaches courses about statistical regression asked me how to create a graph in SAS that illustrates an important concept: the conditional distribution of the response variable. The basic idea is to draw a scatter plot with a regression line, then overlay several probability distributions along the line, […]
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No major hurricanes have hit the US coast recently. Lucky us!

Perhaps you saw the headlines earlier this week about the fact that it has been nine years since the last major hurricane (category 3, 4, or 5) hit the US coast. According to a post on the GeoSpace blog, which is published by the American Geophysical Union (AGU), researchers ran […]
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