Minimum change for detecting a significant difference in point estimates of the parameters Sample Clauses

Minimum change for detecting a significant difference in point estimates of the parameters. For the following we use the point estimates for the parameters f(0), encounter rate 100*n/L (100 * number of detected schools / total line length) and expected school size E(s) from the STAR06 survey presented by Xxxxxxxxxx et al. (2008) as the point estimates from the research vessel 𝑃�𝐸𝑟 and estimate the minimum change required to detect a difference in the point estimates for the tuna vessel 𝑃�𝐸𝑡. As we have no information on precision of these estimates from tuna vessels, we assume the same CVs for the research and tuna vessel. As we expect the size of the CV to change for, e.g. a short trial period compared to the STAR06 survey, we need to consider the following. In general, the standard error 𝑠𝑒(𝑃�𝐸) of the point estimate of a sample mean is defined as 𝑠𝑒(𝑃�𝐸) = 𝑠𝑑⁄√𝑛 where 𝑠𝑑 is the sample standard deviation and �� is the sample size (Xxxxxxx 2003). It follows that if the sample size doubles, the standard error decreases by a factor of 1/√2 or if the sample size halves the standard error increases by a factor of √2. Hence, we can only use the same standard errors as presented in Gerrodette et al. (2008) for calculations where the sample size is the same or, if not, adjust the standard error accordingly. For parameters pertaining to the detection function f(0) and to the expected school size E(s), the number of samples is the number of detected schools used to estimate the parameters. For the encounter rate 100*n/L the expected variance is proportional to the inverse of total line length 1/L (Fewster et al. 2005) and, similarly, if the total line length halves, we expect the standard error to increase by a factor of √2. The same applies to the coefficient of variation (CV).
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