A reader asked whether it is possible to find a bootstrap sample that has some desirable properties. I am using the term "bootstrap sample" to refer to the result of randomly resampling with replacement from a data set. Specifically, he wanted to find a bootstrap sample that has a specific
People love rankings. You've probably seen articles about the best places to live, the best colleges to attend, the best pizza to order, and so on. Each of these is an example of a ranking that is based on multiple characteristics. For example, a list of the best places to
This article uses simulation to demonstrate the fact that any continuous distribution can be transformed into the uniform distribution on (0,1). The function that performs this transformation is a familiar one: it is the cumulative distribution function (CDF). A continuous CDF is defined as an integral, so the transformation is
The skewness of a distribution indicates whether a distribution is symmetric or not. The Wikipedia article about skewness discusses two common definitions for the sample skewness, including the definition used by SAS. In the middle of the article, you will discover the following sentence: In general, the [estimators]are both biased
A previous article about standardizing data in groups shows how to simulate data from two groups. One sample (with n1=20 observations) is simulated from an N(15, 5) distribution whereas a second (with n2=30 observations) is simulated from an N(16, 5) distribution. The sample means of the two groups are close
Testing people for coronavirus is a public health measure that reduces the spread of coronavirus. Dr. Anthony Fauci, a US infectious disease expert, recently mentioned the concept of "pool testing." The verb "to pool" means "to combine from different sources." In a USA Today article, Dr. Deborah Birx, the coordinator
The first time I saw a formula for the pooled variance, I was quite confused. It looked like Frankenstein's monster, assembled from bits and pieces of other quantities and brought to life by a madman. However, the pooled variance does not have to be a confusing monstrosity. The verb "to
Every day we face risks. If we drive to work, we risk a fatal auto accident. If we eat red meat and fatty foods, we risk a heart attack. If we go out in public during a pandemic, we risk contracting a disease. A logical response to risk is to
During an outbreak of a disease, such as the coronavirus (COVID-19) pandemic, the media shows daily graphs that convey the spread of the disease. The following two graphs appear frequently: New cases for each day (or week). This information is usually shown as a histogram or needle plot. The graph
Books about statistics and machine learning often discuss the tradeoff between bias and variance for an estimator. These discussions are often motivated by a sophisticated predictive model such as a regression or a decision tree. But the basic idea can be seen in much simpler situations. This article presents a
