Figure 5.

Effect of reduced sample size on false negative and positive results. Quantification of the loss in statistical power in 3D tracking as a function of the reduction in sample size. The analysis was conducted by progressively and randomly (100 repetitions) reducing the population size available to 3D tracking from its full size (average, solid line; standard deviation, shaded area) of n = 90 to 30. First, the 70-dimensional binary vector aggregating pairwise differences from the first column in Fig. 3 was assembled. Then, the sample size was reduced and an equivalent vector was generated. The number of false results due to the random and progressive reduction was quantified through the Hamming distance between the two vectors. Our results show that the Hamming distance increases monotonically, with a new false result being generated on average every sixth removed fish (computed from the start and endpoint of the black line). Dashed lines represent the number of false results obtained in 2D front (blue) and top (red) tracking with full sample size (n = 90). These numbers (as reported in Fig. 3) are equal to 12 for 2D top and 9 to 2D front, respectively, whereby 2D top view yields 4 false negative and 8 false positive results and 2D front view 5 false negative and 4 false positive results. Our findings show that the statistical power of 2D tracking on a dataset comprising 90 individuals is comparable to that possessed by 3D tracking over a population comprised of half the subjects.