John M. Hoenig

The abuse of power : The pervasive fallacy of power calculations for data analysis

It is well known that statistical power calculations can be valuable in planning an experiment. There is also a large literature advocating that power calculations be made whenever one performs a statistical test of a hypothesis and one obtains a statistically nonsignificant result. Advocates of such post-experiment power calculations claim the calculations should be used to aid in the interpretation of the experimental results. This approach, which appears in various forms, is fundamentally flawed. We document that the problem is extensive and present arguments to demonstrate the flaw in the logic.

Tag Reporting Rate Estimation: 1. An Evaluation of the High-Reward Tagging Method

Abstract Tag-return models can be used to estimate survival rates and tag recovery rates. The additional knowledge of an estimated tag reporting rate allows one to separate total mortality into fishing and natural mortality rates. This paper examines the use of high-reward tags in tagging studies. We find that many of the problems encountered in tagging studies can be avoided if tagged animals are released in small batches in as many locations as possible rather than in large batches at a few locations. Often, the use of substantial monetary rewards for the return of standard tags may be justified as cost effective because of the higher tag return rates they induce. The high-reward tagging method is an important method for estimating the tag reporting rate for standard tags. For this method it is assumed that high-reward tags are reported 100% of the time. This assumption is investigated. Other assumptions of the method are also considered, and particular attention is paid to whether the reporting rate of...

Catch Rate Estimation for Roving and Access Point Surveys

Abstract Optimal designs of recreational angler surveys may require complemented surveys, in which different contact methods are used to estimate effort and catch. All common methods of estimating catch involve on-site interviews that may either be based on access (complete trip) or roving (incomplete trip) interviews. In roving surveys, anglers to be interviewed on a given day are intercepted with a probability proportional to the length of their completed fishing trip, whereas in access surveys, anglers are intercepted as they leave the fishery and are intercepted with the same probability regardless of the length of their completed fishing trip. There are four complemented survey designs which use interviews at access points (mail–access, telephone–access, aerial–access, and roving–access); there are four corresponding designs which use roving interviews (mail–roving. telephone–roving, aerial–roving, and roving–roving). For all of these surveys, total catch is estimated as the product of total effort a...

Survival of Juvenile Lemon Sharks at Bimini, Bahamas, Estimated by Mark–Depletion Experiments

Abstract The survival rate of juvenile lemon sharks Negaprion brevirostris in North Sound, Bimini, Bahamas, was estimated by marking a cohort of small sharks (≤53 cm precaudal length) each spring from 1995 to 1999 and by estimating the number of survivors 1 year later by using a depletion method on the marked population. Annual survival rate estimates varied between 38% and 65%, which was somewhat higher than the 39% steady-state survival predicted from a life cycle (Leslie matrix) model. These are the first direct estimates of the survival rate of a juvenile elasmobranch, and the results support modeling efforts that have been used in determining limits to sustainable exploitation of elasmobranchs. Estimates of survival rates in the present study were negatively correlated with estimated initial abundance and are consistent with strong, density-dependent survival.

CALCULATION OF CATCH RATE AND TOTAL CATCH IN ROVING SURVEYS OF ANGLERS

SUMMARY To estimate the total catch in a sport fishery sampled by a roving creel survey, we multiply an estimate of the total fishing effort by the estimated catch rate (i.e., catch per unit of fishing effort). While the statistical theory for estimating the fishing effort from instantaneous or progressive counts is well established, there is much confusion about the appropriate way to estimate the catch rate. Most studies have used the ratio of means or the mean of the ratios of individual catches and efforts. We analyzed the properties of these estimators of catch rate under the assumption that fishing is a stationary Poisson process. The ratio of means estimator has a finite second moment, while the mean ratio estimator has infinite variance. Simulation studies showed that the mean of ratios estimator tends to have high and unstable mean squared error relative to the ratio of means estimator and this is in accordance with empirical observations. We also studied the properties of the mean of ratios estimator when all interviews with people fishing for less than e minutes duration were disregarded for values of e up to 60 minutes. There was typically a marked reduction in mean squared error when the shorter trips were not included. We recommend that the mean of ratios estimator, with all trips less than 30 minutes disregarded, be used to estimate catch rate and hence total catch under the roving creel survey design. It has the correct expectation (at least approximately after the truncation) and almost always had smaller mean squared error than the ratio of means estimates in our simulations.

Using Demographic Models to Determine Intrinsic Rate of Increase and Sustainable Fishing for Elasmobranchs: Pitfalls, Advances, and Applications

Abstract Leslie matrices and life tables are demographic models commonly used to evaluate the ability of specific elasmobranch life history strategies to sustain given levels and patterns of fishing pressure. These models are generally density independent and provide an instantaneous rate of population growth for a specified set of life history traits that correspond to a specific population size. Many investigators are using these models to compute rates of population growth that they claim are estimates of the maximum population growth rate (r intrinsic); they then use these estimates to compute purported estimates of maximum sustainable fishing mortality. However, neither a Leslie matrix nor a life table can be used to estimate r intrinsic without additional information, except in the special case where a severely depleted population is modeled. Only in a severely depleted population will competition for resources be at a minimum and both density-dependent compensation and the rate of population growth...

Testing and Viewing Symmetry in Contingency Tables, with Application to Readers of Fish Ages

SUMMARY If there are several methods for assigning an integer score to something and the true value is unknown (or even nonexistent), then one can compare the methods only with each other. We develop a new approach to detecting nonrandom differences among methods based on subtracting the smallest reading from all the readings on a specimen before combining counts into a contingency table. When there are three methods, the approach projects the cube of possible triples of scores into a regular hexagon. It conceals some information, but patterns that survive projection can become easier to detect both formally and visually. Summarizing data by projection may be necessary for achieving sufficient power to detect that methods are not equivalent. We illustrate with data on age determination of scallops from shell markings.

Superposed Epoch Analysis: A Randomization Test of Environmental Effects on Recruitment with Application to Chub Mackerel

Abstract Superposed epoch analysis, a nonparametric technique, can be used to test the statistical significance of associations between extreme environmental events and recruitment success. A test statistic, similar to a paired t-statistic, is used to compare recruitment in years with extreme events to recruitment in the immediately surrounding years. Because statistical significance is determined by a randomization test, superposed epoch analysis does not rely on the usual assumptions (random sampling, normality, homogeneity of variance, independence of observations) of parametric testing. Thus, the method can be used when regression analysis, correlation, or a t-test would be inappropriate. As an example, we tested the association between elevated sea level (often associated with El Nino events) and high recruitment success of chub mackerel Scomber japonicus off the coast of southern California. The association was statistically significant (P < 0.01) for the period preceding the collapse of the chub ma...

Estimating mortality from mean length data in nonequilibrium situations, with application to the assessment of goosefish

Abstract The Beverton–Holt length-based mortality estimator has received widespread use primarily due to its applicability in data-limited situations. The mean length of animals that are fully vulnerable to the sampling gear can be used to estimate total mortality from basic growth parameters and a known length at first capture. This method requires equilibrium conditions because the mean length of a population will change only gradually after a change in mortality. In this study, we derive the transitional behavior of the mean length statistic for use in nonequilibrium conditions. We investigate conditions affecting the reliability of the Beverton–Holt results and then develop a new procedure that allows a series of mortality rates to be estimated from mean length data representing nonequilibrium conditions in multiple years. We then examine an assessment of goosefish Lophius americanus that was criticized for its use of the Beverton–Holt estimator under nonequilibrium conditions. Using data from the 196...

Direct and Indirect Estimates of Natural Mortality for Chesapeake Bay Blue Crab

Analyses of the population dynamics of blue crab Callinectes sapidus have been complicated by a lack of estimates of the instantaneous natural mortality rate (M). We developed the first direct estimates of M for this species by solving Baranovs catch equation for M given estimates of annual survival rate and exploitation rate. Annual survival rates were estimated from a tagging study on adult female blue crabs in Chesapeake Bay, and female-specific exploitation rates for the same stock were estimated by comparing commercial catches with abundances estimated from a dredge survey. We also used eight published methods based on life history parameters to calculate indirect estimates of M for blue crab. Direct estimates of M for adult females in Chesapeake Bay for the years 2002-2004 ranged from 0.42 to 0.87 per year and averaged 0.71 per year. Indirect estimates of M varied considerably depending on life history parameter inputs and the method used. All eight methods yielded values for M between 0.99 and 1.08 per year, and six of the eight methods yielded values between 0.82 and 1.35 per year. Our results indicate that natural mortality of blue crab is higher than previously believed, and we consider M values between 0.7 and 1.1 per year to be reasonable for the exploitable stock in Chesapeake Bay. Remaining uncertainty about M makes it necessary to evaluate a range of estimates in assessment models.