Posts Tagged ‘ Statistical Thinking ’

Goodness-of-fit tests: A cautionary tale for large and small samples

November 28, 2016
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Goodness-of-fit tests: A cautionary tale for large and small samples

In the classic textbook by Johnson and Wichern (Applied Multivariate Statistical Analysis, Third Edition, 1992, p. 164), it says: All measures of goodness-of-fit suffer the same serious drawback. When the sample size is small, only the most aberrant behaviors will be identified as lack of fit. On the other hand,

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Sampling variation in small random samples

November 23, 2016
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Sampling variation in small random samples

Somewhere in my past I encountered a panel of histograms for small random samples of normal data. I can't remember the source, but it might have been from John Tukey or William Cleveland. The point of the panel was to emphasize that (because of sampling variation) a small random sample

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What is loess regression?

October 17, 2016
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What is loess regression?

Loess regression is a nonparametric technique that uses local weighted regression to fit a smooth curve through points in a scatter plot. Loess curves are can reveal trends and cycles in data that might be difficult to model with a parametric curve. Loess regression is one of several algorithms in

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Coverage probability of confidence intervals: A simulation approach

September 8, 2016
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Coverage probability of confidence intervals: A simulation approach

The article uses the SAS DATA step and Base SAS procedures to estimate the coverage probability of the confidence interval for the mean of normally distributed data. This discussion is based on Section 5.2 (p. 74–77) of Simulating Data with SAS. What is a confidence interval? Recall that a confidence

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Weighted percentiles

August 29, 2016
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Weighted percentiles

Many univariate descriptive statistics are intuitive. However, weighted statistic are less intuitive. A weight variable changes the computation of a statistic by giving more weight to some observations than to others. This article shows how to compute and visualize weighted percentiles, also known as a weighted quantiles, as computed by

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In praise of simple graphics

June 27, 2016
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'Tis a gift to be simple. -- Shaker hymn In June 2015 I published a short article for Significance, a magazine that features statistical and data-related articles that are of general interest to a wide a range of scientists. The title of my article is "In Praise of Simple Graphics."

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

April 13, 2016
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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 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

March 14, 2016
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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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