The University of Montana

Department of Mathematical Sciences

Technical report #7/2005

The Oval Experiment, Measuring Distance

**Rudy Gideon**

University of Montana

Missoula, MT 59812

**Abstract**

An actual experiment in an applied statistics class is beneficial in helping students understand the many complexities of estimation. In a senior- graduate level applied statistics class the following independent two-sample experiment was carried out by the students. An Oval sits in the heart of the University of Montana campus with only grass and sidewalks on the edge and interior of this Oval. Bordering on this Oval is the mathematics building in which the classes are held. The distance around this Oval is taken as an unknown parameter and many people walk it every day. There are two classes of students and each class was assigned a different way to estimate the distance. The questions of interest are; (1) are the two methods equally valid (an independent two-sample question), and (2) what statistic best estimates the distance around; a robust estimation procedure or a classical one. The main emphasis is the introduction to robust estimation through rank based correlation coefficients, in particular the Greatest Deviation correlation. A general method of estimation with any correlation coefficient is demonstrated with a rank based correlation. Location, scale, and simple linear regression parameters are estimated and compared to the classical estimators. The simplicity and usefulness of the new method is apparent.

**Keywords:** two-sample problem, scale estimation, robust
estimation, Greatest Deviation Correlation, robust location estimation

**AMS Subject Classification:** 62

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