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We further analyzed the implications of introducing the concept of degree of confidence, based on the estimated point variances, into the estimates of some of the indices.
Point variances are the sums of variance components in the x and y dimensions.
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However after critical point (Variance = 10−2) method 1 shows minimum T M index because the dynamic phasor concept is more sensitive to noise due to its flat gain around fundamental frequency.
Variance components for the x and y coordinates of each point were summed to obtain the point variance estimates shown in Table 1.
This extensive sampling procedure allowed us to ascertain at which point variance component estimates became most stable, and at which point the inclusion of additional animals into training yielded diminishing returns.
The average of the set of point-by-point variances around the mean path provides a measure of the bird's fidelity to its habitual path.
As a trade-off of improving point estimation, variances of the proposed estimators are bigger than those of the naive estimators, which has also been observed in other problems concerning measurement error or misclassification (e.g., Carroll et al. 2006; Yi 2017).
Student's t-test was used for comparisons between time points and for comparisons between groups at a particular time point; equal variances were not assumed.
Detailed descriptive statistics and measures of association were computed using the SUDAAN system (Version 9.0, Research Triangle Institute, Research Triangle Park, NC), to take into account the complex survey design and design effect in producing point and variance estimates using Taylor series linearization for variance estimation [ 21].
For the first measurement point, the variance was satisfactory and reached an acceptable level at the second measurement point with a value of 1.26.
According to Fig. 17, there is a stable trend for least square based methods (method 1, 2 and 3) before critical point with variance about 10−2.
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