Statistics How To

Statistics Definitions > Graph Theory is the study of lines and points. It is a sub-field of mathematics which deals with graphs: diagrams that involve points and lines and which often pictorially represent mathematical truths. Graph theory is the study of the relationship between edges and vertices. Formally, a graph is a pair (V, E), … Read more

Normal Distributions > A Gaussian mixture model is a distribution assembled from weighted multivariate Gaussian* distributions. Weighting factors assign each distribution different levels of importance. The resulting model is a super-position (i.e. an overlapping) of bell-shaped curves. Gaussian mixture models are semi-parametric. Parametric implies that the model comes from a known distribution (which is in … Read more

Statistics Definitions > An error term in statistics is a value which represents how observed data differs from actual population data. It can also be a variable which represents how a given statistical model differs from reality. The error term is often written ε. Examples of the Error Term in Statistics In econometric theory, the … Read more

Statistics Definitions > The Hidden Markov Model (HMM) is a relatively simple way to model sequential data. A hidden Markov model implies that the Markov Model underlying the data is hidden or unknown to you. More specifically, you only know observational data and not information about the states. In other words, there’s a specific type … Read more

Statistics Definitions > A fractile is the cut off point for a certain fraction of a sample. If your distribution is known, then the fractile is just the cut-off point where the distribution reaches a certain probability. In visual terms, a fractile is the point on a probability density curve (PDF) so that the area … Read more

Statistics Definitions > Slutsky’s theorem is used to explore convergence in probability distributions. It tells us that if a sequence of random vectors converges in distribution and another sequence converges in probability to a constant (not to be confused with a constant sequence), those sequences are jointly convergent in distribution. Basically, it allows you to … Read more

Statistics Definitions > A non negative integer is an integer that that is either positive or zero. It’s the union of the natural numbers and the number zero. Sometimes it is referred to as Z*, and it can be defined as the as the set {0,1,2,3,…,}. Z, the set of integers, is defined as {…,-3,-2,-1,0,1,2,3,…}. … Read more

Statistics Definitions > Contents: Definition Absolute Value Integer Programming Definition An integer includes whole numbers and negative whole numbers. Integers can be positive, negative, or zero. For example: 1, -1, 0, 101 and -101. The set of integers is often given the symbol Z, and Z is defined as {…, -3, -2,-1, 0, 1, 2, … Read more

Types of Bias > Self-selection bias is a bias that is introduced into a research project when participants choose whether or not to participate in the project, and the group that chooses to participate is not equivalent (in terms of the research criteria) to the group that opts out. Examples of Self-Selection Bias Suppose you … Read more

Regression Analysis > Ridge regression is a way to create a parsimonious model when the number of predictor variables in a set exceeds the number of observations, or when a data set has multicollinearity (correlations between predictor variables). Tikhivov’s method is basically the same as ridge regression, except that Tikhonov’s has a larger set. It … Read more