Ecological surveys risk incurring false negative and false positive detections of the target species. With indirect survey methods, such as environmental DNA, such error can occur at two stages: sample collection and laboratory analysis. Here we analyse a large qPCR based eDNA data set using two occupancy models, one of which accounts for false positive error by Griffin et al. (J R Stat Soc Ser C Appl Stat 69: 377-392, 2020), and a second that assumes no false positive error by Stratton et al. (Methods Ecol Evol 11: 1113-1120, 2020). Additionally, we apply the Griffin et al. (2020) model to simulated data to determine optimal levels of replication at both sampling stages. The Stratton et al. (2020) model, which assumes no false positive results, consistently overestimated both overall and individual site occupancy compared to both the Griffin et al. (2020) model and to previous estimates of pond occupancy for the target species. The inclusion of replication at both stages of eDNA analysis (sample collection and in the laboratory) reduces both bias and credible interval width in estimates of both occupancy and detectability. Even the collection of > 1 sample from a site can improve parameter estimates more than having a high number of replicates only within the laboratory analysis.