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- Title
Statistical Properties of the Relative Weight (W[subr]) Index and an Alternative Procedure for Testing W[subr] Differences between Groups.
- Authors
Brenden, Travis O.; Murphy, Brian R.; Birch, Jeffrey B.
- Abstract
Fishery managers commonly test for differences in relative weight (W[subr]) between or within populations using standard parametric or nonparametric statistical tests. However, the statistical properties of the W[subr] index have not been studied; consequently, we cannot be certain that W[subr] data satisfy the theoretical assumptions upon which many standard tests are based. In particular, we do not know if W[subr] data are independent and identically distributed (i.i.d.), which is an assumption made by most standard statistical tests and which can increase the type I error rate of a statistical test when it is violated. We derived approximations to the expectation, variance, and covariance of the W[subr] index using the Delta method and estimated these parameters with sample data for muskellunge Esox masquinongy, largemouth bass Micropterus salmoides, and black crappie Pomoxis nigromaculatus. Additionally, we devised a likelihood ratio test (R-test) that tests for differences in W[subr] between groups and that does not assume i.i.d, data. We applied the R-test to the sample data and compared the results with those obtained from traditional statistical tests. The statistical properties of the W[subr] index were conditionally dependent on fish length. This conditionality prevents the covariance from equaling zero across an entire fish sample, so that W[subr] data will be inherently correlated. For the sample data, parameter estimates increased with fish length and typically were above realistic W[subr] values. This bias was attributed to variability in sample length-weight data. Traditional statistical tests were more liberal than the R-test in declaring statistical significance when testing for differences in W[subr] between groups. Based on our derivations, we conclude that W[subr] data will violate an i.i.d, assumption to some extent. To avoid falsely declaring statistical significance when testing group differences, we recommend that the R-test be used with...
- Subjects
FISH populations; FISHERY management; FISH habitat improvement; STATISTICS; MARINE biology; MARINE sciences
- Publication
North American Journal of Fisheries Management, 2003, Vol 23, Issue 4, p1136
- ISSN
0275-5947
- Publication type
Article
- DOI
10.1577/M02-126