Statistics How To

Sampling > Markov Chain Monte Carlo What is Markov Chain Monte Carlo? Markov Chain Monte Carlo is a way to sample from a complicated distribution. What is a “complicated distribution”? One that’s difficult, or near impossible to find probabilities for. These types of problems are called “high-dimensional” problems. One example of a high-dimensional problem is … Read more

Probability Distributions > Degenerate Distribution What is a Degenerate Distribution? A degenerate distribution (sometimes called a constant distribution) is a probability distribution of a degenerate random variable — a constant with probability of 1. In other words, a random variable X has a single possible value, with all of the mass concentrated at a single … Read more

Probability Distributions > Continuous Probability Distribution It’s important to understand the difference between a continuous distribution and a discrete distribution if you’re going to be working with data. These two types of distributions have different characteristics, but they are both important when it comes to making decisions. Let’s take a closer look at what makes … Read more

Statistics Basics > Center of a Distribution What is the Center of a Distribution? The center of a distribution is the middle of a distribution. For example, the center of 1 2 3 4 5 is the number 3. If you’re asked to find the center of a distribution in statistics, you generally have three … Read more

Hypothesis Tests > Hotelling’s T-Squared What Is Hotelling’s t-squared? Hotelling’s T-Squared, sometimes written as T2, is the multivariate counterpart of the T-test [1]. “Multivariate” means that you have data for more than one parameter for each sample. For example, let’s say you wanted to compare how well two different sets of students performed in school. You … Read more

Probability > Complementary events What are Complementary Events? Complementary events happen when there are only two outcomes, like getting a job, or not getting a job. In other words, the complement of an event happening is the exact opposite: the probability of it not happening. Venn diagrams are sometimes used to show complementary events. In … Read more

Probability Distributions > Contents: What is a Factorial? What is a Factorial Distribution? See also: Superfactorial: Definition (Sloane, Pickover’s) What is a Factorial? Factorials (!) are products of every whole number from 1 to n. In other words, take the number and multiply through to 1. For example: If n is 3, then 3! is … Read more

Probability Distributions > Lindley Distribution What is a Lindley Distribution? The Lindley distribution is an important tool for describing the lifetime of processes and devices across a range of fields such as biology, engineering, and medicine. In fact, it’s proven to be particularly effective in modeling mortality studies. This distribution is characterized by a shape … Read more

Logistic Regression > Log Odds Log odds play a central role in logistic regression. Every probability can be converted to log odds by finding the odds ratio and taking the logarithm. Despite the relatively simple conversion, log odds can be a little esoteric. Jaccard [1] calls them “…counterintuitive and challenging to interpret,” especially if you … Read more

Probability > Disjoint Events What are Disjoint Events? Disjoint events cannot happen at the same time. In other words, they are mutually exclusive. Disjoint events are disjointed, or not connected. Another way of looking at disjoint events are that they have no outcomes in common. This definition can be easier to wrap your head around … Read more