Statistics How To

Estimators > Sufficient Statistic Contents: Sufficient Statistic Example Formal Definition and Factorization Theorem Complement of sufficiency Are sufficient statistics unbiased? Do sufficient statistics always exist? How do you prove something is not sufficient statistic? Sufficient statistic vs MLE Sufficiency Principle What is a sufficient statistic? A sufficient statistic summarizes all of the information in a … Read more

Hypothesis Testing > Uniformly Most Powerful (UMP) Test What is a Uniformly Most Powerful Test? Uniformly Most Powerful tests (UMP tests) have the highest power among all possible alternate hypotheses of the same alpha level. The existence of UMP is not guaranteed, particularly when the test involves nuisance variables that are irrelevant to your study. … Read more

Probability and Statistics >Basic Statistics > What is a Statistic? Contents: What is a Statistic? What is the Difference Between Inferential and Descriptive Statistics? Notation Data & Variables Vital Statistics & Estimators What is a Statistic? Statistics are everywhere. From the news to the classroom, we are constantly surrounded by data that can help us … Read more

Probability Distributions > Tukey Lambda Distribution What is the Tukey Lambda Distribution?   The Tukey lambda distribution, also called the symmetric lambda distribution, is a family of symmetric distributions with truncated tails. Typically, it aids in identification of an appropriate distribution and is not directly used in statistical modeling. This is because it lacks a … Read more

Hypothesis Testing > Bartlett’s Test Contents: Bartlett’s test for homogeneity of variances. Bartlett’s test for sphericity. What is Bartlett’s test for homogeneity of variances? Bartlett’s test of homogeneity of variances tests the equality of variances among different samples. It checks whether the assumption of equal variances is true before certain statistical tests, such as the … Read more

Probability Distribution List > Muth distribution The Muth distribution, a model for non-negative continuous random variables, was introduced by Muth in 1977 [1]. The distribution has largely been overlooked in the statistical literature [2]; the distribution isn’t usually encountered in introductory probability and statistics courses. However, you’ll come across it in reliability theory, which deals … Read more

Statistics Definitions > Population variance What is population variance? Population variance tells us how data points in a population are spread out. It is the average of the distances from each data point in the population to the mean, squared. The square root of the population variance is called the population standard deviation, which represents the … Read more

Statistics Definitions > Inverse Normal Distribution What is an Inverse Normal Distribution? An inverse normal distribution is a way to work backwards from a known probability to find an x-value. It is an informal term and doesn’t refer to a particular probability distribution. There is also a generalized inverse normal  family, proposed by Robert in … Read more

Probability distributions > Beta prime distribution What is the beta prime distribution? The Beta Prime Distribution is a continuous probability distribution defined on the interval [0, ∞). The distribution has polynomially decreasing fat tails; this tells us that that the probability of observing an extreme value decreases as a polynomial function of the distance from … Read more

Probability Distributions > Hyperbolic Secant Distribution What is the hyperbolic secant distribution? The Hyperbolic secant distribution (also known as the inverse-cosh distribution or sech distribution) is a bell-shaped, symmetric  probability distribution with a mean of 0 and variance of 1. It is a continuous distribution that is tractable (computationally efficient to work with), which means computer … Read more