1.3.3.1.1 95 % CI for total loss

Because total loss is a proportion, theoretically its confidence interval can be calculated using equation 1.1.2.c. This approach is valid when calculating a 95% CI for losses within one operation. However, if all the colonies in an operation are measured, one’s sample is the whole population, there is no need to calculate the CI. When total losses are calculated for a region, the losses of several operations are being combined, using the previously mentioned equation to calculate the 95% CI is inappropriate because the assumption of independence is not meet. Across operations the chances that a colony will die is not the same for every colony. In such cases the quasi-binomial family is introduced to take into account the increased standard error introduced by dependence within the data (vanEngelsdorp et al., 2011). An R script example which calculates both the corrected CI from the quasi-binomial model and the uncorrected CI from the Wald model (equation 1.1.2.c.) are given in Box 3.

Box 3