Statistics How To

Reliability & Validity > Sampling Validity What is Sampling Validity? Validity is how well a test measures what it is supposed to measure; Sampling validity (sometimes called logical validity) is how well the test covers all of the areas you want it to cover. For example, if you’re doing an assessment of effectiveness of math … Read more

Inter-rater reliability > Krippendorff’s alpha (also called Krippendorff’s Coefficient) is an alternative to Cohen’s Kappa for determining inter-rater reliability. Krippendorff’s alpha: Ignores missing data entirely. Can handle various sample sizes, categories, and numbers of raters. Applies to any measurement level (i.e. (nominal, ordinal, interval, ratio). Commonly used in content analysis to quantify the extent of … Read more

Design of Experiments > Inter-rater Reliability What is Inter-rater Reliability? Inter-rater reliability is the level of agreement between raters or judges. If everyone agrees, IRR is 1 (or 100%) and if everyone disagrees, IRR is 0 (0%). Several methods exist for calculating IRR, from the simple (e.g. percent agreement) to the more complex (e.g. Cohen’s … Read more

Probability > Benford’s Law (The First Digit Law) What is Benford’s Law? Benford’s law (also called the first digit law) states that the leading digits in a collection of data sets are probably going to be small. For example, most numbers in a set (about 30%) will have a leading digit of 1, when the … Read more

Probability Distributions > Trapezoidal Distribution What is a Trapezoidal Distribution? Trapezoidal distributions are in the shape of a trapezoid— a quadrilateral with two parallel and two non-parallel sides. They tend to be a good fit for data that shows fairly rapid growth, a leveling out period, and then fairly rapid decay. All three stages are … Read more

Descriptive Statistics > Seven Number Summary What is a Seven Number Summary? A seven number summary is a set of seven facts about a normally distributed data set. It can be a simple check for the assumption of normality, which is required by many statistical tests. The summary is usually made up of: The 2nd … Read more

Statistics Definitions > Power Law What is the Power Law? The power law (also called the scaling law) states that a relative change in one quantity results in a proportional relative change in another. The simplest example of the law in action is a square; if you double the length of a side (say, from … Read more

Probability Distributions > Zeta Distribution (Zipf Distribution) What is the Zeta Distribution? The Zeta Distribution (also called the Zipf distribution, after American linguist George Zipf) is a member of the family of general exponential distributions, used to model the size or ranks of randomly chosen objects from certain population types. In general, it’s used to … Read more

Regression Analysis > Cook’s Distance What is Cook’s Distance? Cook’s distance, Di, is used in Regression Analysis to find influential outliers in a set of predictor variables. In other words, it’s a way to identify points that negatively affect your regression model. The measurement is a combination of each observation’s leverage and residual values; the … Read more

Probability Distributions > Inverse Gaussian Distribution What is the Inverse Gaussian Distribution? The Inverse Gaussian Distribution, also called the Wald or normal-inverse Gaussian, is an exponential distribution with a single mode and long tail. The distribution is used to model non-negative, positively skewed data and has a wide variety of applications in business, survival analysis, … Read more