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, […]
Post a Comment

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 […]
Post a Comment

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 […]
Post a Comment

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 […]
Post a Comment

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 […]
Post a Comment

In praise of simple graphics

'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." […]
Post a Comment

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 […]
Post a Comment

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 […]
Post a Comment

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 […]
Post a Comment

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 […]
Post a Comment