JSM 2005 - Toronto

Abstract #304585

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 27
Type: Contributed
Date/Time: Sunday, August 7, 2005 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistical Education
Abstract - #304585
Title: The Consequences of Nonrandom Sampling for Confidence Intervals
Author(s): Michael Mosier*+
Companies: Washburn University
Address: 1700 SW College Ave, Topeka, KS, 66621, United States
Keywords: Confidence intervals ; teaching ; random sampling ; coverage probability ; classroom exercise ; data collection

An important topic, which most statisticians fully understand, is that in order for many statistical inference procedures to be valid, the data must come from a random sample. Most introductory statistics textbooks make this point clearly, usually stated in a list of necessary assumptions. However, the consequences of not meeting this assumption are rarely discussed and seldom demonstrated. Without a firm understanding of this concept, our students from other scientific disciplines are at risk for performing "bad research" in the future. In this paper, we discuss how heart rate data collected by students may be used to demonstrate this concept. When asked to collect data from a sample of five people, the students will never follow true random selection to select the subjects. This data then gives the instructor a large number of samples of size n=5, ready-made for estimating the coverage probability of confidence intervals for the mean heart rate. This coverage probability has never failed to be far below the stated confidence level.

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Revised March 2005