| # Appendix D Power Analysis of Sponging Success | |
| There is some debate over whether sponging provides a reproductive benefit to spongers. The evidence is mixed. Mann et al. 2008 observed that sponging bottlenose dolphins had 18% greater calving success than nonspongers, though due to small sample size this finding was not statistically significant (at *p* = 0.05). To examine this issue further, I conducted a power analysis to determine how small of a reproductive benefit could be reliably detected by Mann et al. 2008. The power analysis, shown in the R code below, indicates that the smallest difference in calving success that could be reliably detected (at 1 – *β* = 0.8) was a 43% (one-sided) or 48% (two-sided) greater calving success for spongers over nonspongers. Importantly, this minimally detectable reproductive advantage is much larger than is required by my models. In fact, it is well above even the largest reproductive advantage (25%) that I considered in my simulations and it is also much larger than the reproductive advantage (18%) found in the empirical data. | |
| From Mann et al. 2008, the number of non-spongers in the power analysis is 116 with a mean calving success of 0.132 and a standard error of 0.008. The number of spongers is 16 with a mean calving success of 0.15 with a standard error of 0.018. |