Search Results for: weighted mean

Objective In Confidence Intervals for Order Statistics, Medians and Percentiles, and Confidence Intervals for Quartiles and Percentiles we show how to estimate confidence intervals for order statistics, the median, quartiles, and percentiles using a binomial distribution approach. We now show how to modify this approach by using the fact that the normal distribution can be used … Read More

LAD Regression is based on minimizing the absolute value of the residuals; i.e. the least absolute deviation, which uses the Lp norm where p = 1, as described in Lp Norm. Ordinary least squares regression is based on minimizing the mean squared error (MSE) statistic, which is based on the Lp norm where p = … Read More

Given a collection of points in r-space, i.e. 1 × r row vectors, we can find a minimum spanning tree for the fully-connected graph whose nodes are the points in the collection and whose edges are all the pairwise connections between these points. The weight for each edge is the distance between the points that … Read More

Basic Concepts The Friedman-Rafsky test is a multivariate version of the Wald-Wolfowitz runs test. Assume that we have two sets of k-tuples X and Y of sizes n1 and n2 drawn from populations with cumulative distribution functions FX and FY. We test the null hypothesis that FX = FY. Univariate Runs Test The univariate test … Read More

Basic Concepts The Real Statistic data analysis tool and cluster analysis functions described in Real Statistics Support for Cluster Analysis are based on using Euclidean distance; i.e. the Minkowski distance where p = 2. Cluster analysis can also be performed using Minkowski distances for p ≠ 2. Also, weighted distances can be employed (see Weighted … Read More

Basic Concepts We now explore another measure of central tendency that is robust to outliers. This measure is based on the Lp norm, which for a vector X = (x1, …, xn) is defined by The Minkowski distance between vectors X and Y is defined as ||X–Y||p. When p = 2 this is the usual Euclidean … Read More

Worksheet Functions Real Statistics Functions: The Real Statistics Resource Pack contains the following functions: UCON(R1,  head): returns output similar to that shown in Figure 5 of Building a Polytomous Model based on the data in R1. UCONFIT(R1,  head): returns output similar to that shown in Figure 2 of Polytomous Model Fit based on the data … Read More

Basic Concepts Just as we do for the dichotomous model (see Building a Rasch Model), we need to evaluate the fit of a polytomous UCON model. As before, this is done by using the infit and outfit measures. Outfit (outlier-sensitive fit statistic): This statistic is more sensitive to more extreme observations (e.g. by subjects on … Read More