Statistics How To

Outliers > The generalized ESD test, or generalized extreme studentized deviate test, is a statistical test for outliers. It is used on univariate data which follows an approximately normal distribution, and can be used to detect one or more outliers. It is especially useful in situations where the number of outliers is not known: in … Read more

Statistics Definitions > Mathematical statistics is the application of mathematics to study statistics using probability theory, linear algebra, measure theory, and stochastic analysis. Topics in Mathematical Statistics Typical topics covered in a course [1]: Bivariate distributions Combinatorics and basic set theory notation Discrete distributions and continuous distributions Conditional probability Confidence Intervals: definitions, duality with hypothesis … Read more

Statistics Definitions > Cross covariance of x and y, in statistics, is a measure of the similarity between x and shifted versions of y, as a function of the shift (lag). The cross covariance is given by the equation where E is the expectation operator, and the processes have mean functions vt=E[Yt] and μt=E[Xt] In … Read more

Probability Distributions > Kent distribution The Kent distribution, also known as the 5-parameter Fisher-Bingham distribution, is a probability distribution in ℜ3, the real three dimensional coordinate space, of a two-dimensional unit sphere. Kent Distribution PDF The Kent distribution’s probability density function, f(x), is given by the equation: Here, x is a three dimensional unit value. … Read more

Probability > The memoryless property (also called the forgetfulness property) means that a given probability distribution is independent of its history. Any time may be marked down as time zero. If a probability distribution has the memoryless property the likelihood of something happening in the future has no relation to whether or not it has … Read more

Finding Sample Sizes > In many cases, finding an appropriate sample size results in a sample size that’s too large. You may not have the resources to conduct a large study, or ethical reasons may prevent testing on a large scale. Reducing sample size usually involves some compromise, like accepting a small loss in power … Read more

Regression Analysis > What is the Gauss-Newton Method? The Gauss-Newton method is an iterative algorithm to solve nonlinear least squares problems. “Iterative” means it uses a series of calculations (based on guesses for x-values) to find the solution. It is a modification of Newton’s method, which finds x-intercepts (minimums) in calculus. The Gauss-Newton is usually … Read more

Sampling > Importance sampling is a way to predict the probability of a rare event. Along with Markov Chain Monte Carlo, it is the primary simulation tool for generating models of hard-to-define probability distributions. Rare events can usually be found on the tails of probability distributions. For example, on a bell curve for IQ, the … Read more

Sampling > Experience Sampling What is Experience Sampling? Experience sampling is a way to find out more about an experience while the event is actually happening. Participants stop what they are doing and take time to note their experiences over a period of days, weeks, or even years — which can result in hundreds of … Read more

Nonparametric data and tests > The gamma coefficient (also called the gamma statistic, or Goodman and Kruskal’s gamma) tells us how closely two pairs of data points “match”. Gamma tests for an association between points and also tells us the strength of association. The goal of the test is to be able to predict where … Read more