Statistics How To

Statistics Definitions > Non Centrality Parameter (NCP) What is the Non Centrality Parameter (NCP)? The non centrality parameter (λ) is a measure of “…the degree to which a null hypothesis is false” (Kirk, 2012). In other words, it tells you something about the statistical power of a test. For example, an F-distribution with an NCP … Read more

Reliability & Validity in Research> Formative Validity & Summative Validity What is Formative Validity? In a broad sense, formative validity shows that a measure that improves a program, assessment or theory. The idea is that a measuring tool (e.g. a test or procedure) should give you some useful, formative information about the direction you want … Read more

Statistics Definitions > Morisita Index What is the Morisita Index? The Morisita Index of Dispersion (or Morisita overlap index) is a measure of how similar or different two sets of data are. The index ranges from 0 (no similarity) to 1 (complete similarity). It can, however, give values larger or smaller than 1, which may … Read more

Measures of Dispersion > Index of dispersion (Variance to Mean Ratio) What is the Index of dispersion? The index of dispersion is a measure of dispersion for nominal variables and partially ordered nominal variables. It is usually defined as the ratio of the variance to the mean. As a formula, that’s: D = σ2 / … Read more

Statistics Definitions > Relative Variance What is the Relative Variance? The relative variance (RV) is a measure of error, or how much the “noise” of a data point or set of data points can vary. RV doesn’t have a universal definition, and it isn’t used very often in statistics except in very informal terms. Different … Read more

Measures of Dispersion > Coefficient of Dispersion What is a Coefficient of Dispersion (COD)? The term “coefficient of dispersion” can mean a few different things in statistics. There isn’t one formula or definition that is universal. Everything depends on the context of where you’re using the coefficient and what you want to do with it: … Read more

Deciles > Interdecile Range What is the Interdecile Range? The interdecile range (IDR) is the distance between the 9th decile and the 1st decile (or the 10th and 90th percentiles). It is a measure of dispersion or spread; Cutting off the top and bottom 10% of scores eliminates the very high scores and very low … Read more

Statistics Definitions > The term “U statistic” can have several meanings: Unbiased (U) statistics. Mann Whitney U Statistic. U statistic in L-estimators. Theil’s U. 1. Unbiased (U) statistics Unbiased “U” statistics are a way to construct unbiased estimators to study large sample behavior; the “U” in U-statistics stands for “unbiased”. Constructing U-statistics involves use of … Read more

Statistics Definitions > L-Estimator What is an L-Estimator? An L-estimator is a linear combination of statistics based on order statistics, or sample quantiles. L-estimators were first outlined by Daniel (1920) and were revived in robustness studies thirty years later. They have the advantage of being robust and simple to use, but tend to have problems … Read more

Descriptive Statistics > Upper and Lower Fence What are upper and lower fences? Upper and lower fences cordon off outliers from the bulk of data in a set. Fences are usually found with the following formulas: Upper fence = Q3 + (1.5 * IQR) Lower fence = Q1 – (1.5 * IQR). Where IQR is … Read more