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I Remember You: Independence and the Binomial Model
Author(s) -
Levine Douglas W.,
Rockhill Beverly
Publication year - 2006
Publication title -
teaching statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.425
H-Index - 13
eISSN - 1467-9639
pISSN - 0141-982X
DOI - 10.1111/j.1467-9639.2006.00239.x
Subject(s) - independence (probability theory) , binomial distribution , econometrics , variance (accounting) , statistics , negative binomial distribution , null hypothesis , matching (statistics) , mathematics , conditional independence , type i and type ii errors , binomial (polynomial) , economics , accounting , poisson distribution
Summary We focus on the problem of ignoring statistical independence. A binomial experiment is used to determine whether judges could match, based on looks alone, dogs to their owners. The experimental design introduces dependencies such that the probability of a given judge correctly matching a dog and an owner changes from trial to trial. We show how this dependence alters the probability of a successful match of dog to owner, and thus alters the expected number of successful matches and the variance of this expected quantity. Finally, we show that a false assumption of independence that results in incorrect probability calculations changes the probability of incorrectly rejecting the null hypothesis (i.e. the Type I error).