JSM 2004 - Toronto

Abstract #301489

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Activity Number: 218
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Graphics
Abstract - #301489
Title: Repeated Use of the Pythagorean Theorem for Plots of Common Statistics
Author(s): Frank J. Matejcik*+
Companies: South Dakota School of Mines & Technology
Address: 501 E. St. Joseph St., Rapid City, SD, 57701-3901,
Keywords: graphics ; plots ; regression ; ANOVA ; contingency tables ; ancient tools
Abstract:

Sums of squares occur in many common statistics. The square root of the sum of squares can be computed graphically using by repeating the Pythagorean theorem. Accordingly, repeating the Pythagorean theorem can be used for plots related to many common statistics and related calculations: the empirical standard deviation, the standard deviation of a probability mass function, the correlation coefficient in regression, the F-test in ANOVA, chi-squared goodness-of-fit test, and chi-squared tests for contingency tables. Plots for each of these calculations are displayed and a brief discussion of their potential value of as diagnostic and instructional aids.

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Revised March 2004