METHODOLOGY
Comparing a single observation with a larger sample through Levene's test
Rui Cerqueira
Departamento de Ecologia, Laboratório de Vertebrados, Universidade Federal do Rio de Janeiro, Caixa Postal 68020, 21941-590 Rio de Janeiro, RJ, Brasil, Fax: +5521-290-3308, E-mail: labvert@acd.ufrj.br
It has been stated that most statistics used by biologists are in error (Van Valen, 1978). This author suggested several ways to circumvent the commonly found restrictions to the use of comparison tests.
Another problem facing us is to contrast a single observation with a larger sample. One test for that is derived from the Student t-test. The formula given to compute the test (Sokal and Rohlf, 1969) is:
(1)
where: ts = value of the Student t; X1 = single observation; 
= mean of the larger sample; µ1,2 = means of the two populations; S2 = standard deviation of the larger sample; n2 = number of items in sample 2.
One of the tests suggested by Van Valen (op. cit.) is the Levene test, a test for the mean deviation. For that, after computing the mean (or the median) we calculate the deviation of every observation: = . The test consists in computing the y's of the samples and comparing them using the analysis of variance or the t-test.
Intuitively we may use equation 1 substituting X1and by yiand , then comparing the single observation with a larger sample through Levene's test.
(Received March 10, 1997)
- Sokal, R.R. and Rohlf, F.J. (1969). Biometry. W.H. Freeman, San Francisco.
- Van Valen, L. (1978). The statistics of variation. Evol. Theory4: 33-43.
Publication Dates
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Publication in this collection
06 Jan 1999 -
Date of issue
June 1998
History
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Received
10 Mar 1997
