StatLab Articles

When it comes to confidence intervals and hypothesis testing there are two important limitations to keep in mind.

The significance level,1 \(\alpha\), or the confidence interval coverage, \(1 - \alpha\),

1. only apply to one test or estimate, not to a series of tests or estimates.
2. are only appropriate if the estimate or test was not suggested by the data.

Let’s illustrate both of these limitations via simulation using R.

Note: This version of the article contains static images of maps generated with Leaflet. You can view a version with interactive maps here. 

What are robust standard errors? How do we calculate them? Why use them? Why not use them all the time if they’re so robust? Those are the kinds of questions this post intends to address.

Multinomial logit models allow us to model membership in a group based on known variables. For example, the operating system preferences of a university’s students could be classified as “Windows,” “Mac,” or “Linux.” Perhaps we would like to better understand why students choose one OS versus another. We might want to build a statistical model that allows us to predict the probability of selecting an OS based on information such as sex, major, financial aid, and so on. Multinomial logit modeling allows us to propose and fit such models.

What are empirical cumulative distribution functions and what can we do with them? To answer the first question, let’s first step back and make sure we understand "distributions", or more specifically, "probability distributions".

A Basic Probability Distribution

Imagine a simple event, say flipping a coin 3 times. Here are all the possible outcomes, where H = head and T = tails:

Let’s say we’re interested in modeling the number of auto accidents that occur at various intersections within a city. Upon collecting data after a certain period of time, perhaps we notice two intersections have the same number of accidents, say 25. Is it correct to conclude these two intersections are similar in their propensity for auto accidents?

Regular expressions (or regex) are tools for matching patterns in character strings. These can be useful for finding words or letter patterns in text, parsing filenames for specific information, and interpreting input formatted in a variety of ways (e.g., phone numbers). The syntax of regular expressions is generally recognized across operating systems and programming languages. Although this tutorial will use R for examples, most of the same regex could be used in unix commands or in Python.

Shiny is an R package that facilitates the creation of interactive web apps using R code, which can be hosted locally, on the shinyapps server, or on your own server. Shiny apps can range from extremely simple to incredibly sophisticated. They can be written purely with R code or supplemented with HTML, CSS, or JavaScript. Visit R studio’s shiny gallery to view some examples.

As data scientists, we’re often most excited about the final layer of analysis. Once all the data are cleaned and stored in a format readable by our favorite programming language (Python, R, STATA, etc.), the most fun part of our work is when we’re finding counter-intuitive causations with statistical methods. If you can prove that the mutual presence of McDonalds really does prevent wars between countries or that an increase in diversity really does boost business profitability, that is a good day.

One of the basic assumptions of linear modeling is constant, or homogeneous, variance. What does that mean exactly? Let’s simulate some data that satisfies this condition to illustrate the concept.

Below we create a sorted vector of numbers ranging from 1 to 10 called x, and then create a vector of numbers called y that is a function of x. When we plot x vs y, we get a straight line with an intercept of 1.2 and a slope of 2.1.