Statistics How To

Statistical Process Control > A c chart is a type of control chart that shows how many defects or nonconformities are in samples of constant size, taken from a process (Misra, 2008). Formulas The c chart formulas are (Doty, 1996): Number of defects per unit c = Σc / Σn = Σc / m Upper … Read more

Descriptive Statistics > An area chart is an extension of a line graph, where the area under the line is filled in. The “lines” are actually a series of points, connected by line segments. As well as looking slightly different from the run-of-the-mill line graph, area charts have different connotations; While a line graph measures … Read more

Statistics Definitions > Key Takeaways: The Bertrand Paradox, which concerns probabilities, isn’t actually a paradox at all. The problem is with wording, not with actual situations. An example can be illustrated with the “equilateral triangle drawn within a circle” problem. What is the Bertrand Paradox? The Bertrand Paradox shows that if you don’t define probabilities … Read more

Statistics Definitions > A complete statistic T “… is a complete statistic if the family of probability densities {g(t; θ) is complete” (Voinov & Nikulin, 1996, p. 51). The concept is perhaps best understood in terms of the Lehmann-Scheffé theorem “…if a sufficient statistic is boundedly complete it is minimal sufficient. The converse is false” … Read more

Statistics Definitions > Prevalence in statistics Prevalence is the number of disease cases in a population; incidence is number of new cases that develop. Contents: What is Incidence in statistics? What is Prevalence in statistics? 1. Incidence Definition Incidence is the number of newly diagnosed cases of disease at a specified time. For example, let’s … Read more

Time Series > The GARCH model, or Generalized Autoregressive Conditionally Heteroscedastic model, was developed by doctoral student Tim Bollerslev in 1986. The goal of GARCH is to provide volatility measures for heteoscedastic time series data, much in the same way standard deviations are interpreted in simpler models. The simplest GARCH model is the ARCH(1) model, … Read more

RCT > Pre-test and post-test probability refers to the probability of having a disease before a diagnostic test is performed (pre-test probability) and after a test is performed (post test probability). How to Determine Pre-Test and Post-Test Probability There are many different ways to calculate pre-test and post-test probability. The pre-test probability is simply the … Read more

Statistics Definitions > Residual Variance (also called unexplained variance or error variance) is the variance of any error (residual). The exact definition depends on what type of analysis you’re performing. For example, in regression analysis, random fluctuations cause variation around the “true” regression line (Rethemeyer, n.d.). The total variance of a regression line is made … Read more

Probability Distribution: List of Statistical Distributions A severity distribution (or loss severity distribution) is a probability distribution of the amount of losses incurred per operational loss event. As it is a distribution (rather than a single figure or set of numbers), it doesn’t put a dollar amount on the loss. Rather, it shows the variability, … Read more

Cointegration > The Engle Granger test is a test for cointegration. It constructs residuals (errors) based on the static regression. The test uses the residuals to see if unit roots are present, using Augmented Dickey-Fuller test or another, similar test. The residuals will be practically stationary if the time series is cointegrated. Engle Granger Test … Read more