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Since data meet the criteria for applying Equation B-3, this last has been used for estimating the propagated errors in declinations assuming flat local horizons in the direction of the azimuth, as summarised in Table A1. Figure B3 shows the empirical SPD for declinations of subsample S2* (n = 111), which excludes from S2 those azimuths > 180°, to avoid ambiguity in orientations. As in the case of the azimuths, this Normal distribution has been used as the limiting probability distribution for generating numerically simulated SPDs with the same sample size and with [sub ] values randomly sampled from S2**. A-1: Quantitative Assessment of the Null Hypothesis A by the Method of the Confidence Envelope Curve using the Azimuth SPD A-2: Dataset for the Empirical Sample S2 (Churches of the Assumption in Southern Spain) A-3: Analysis of a Multiplet in the Azimuth SPD of Sample S2 A-4: Approximate Fast Assessment of Peaks from the Raw Dataset B: Adaptation of Methods and Application to SPDs of Declinations B-1: Coordinate Transformation and Propagated Errors in the Estimation of Declinations B-2: SPD of Declinations for the Empirical Sample S2 (Churches of the Assumption in Southern Spain) B-3: Statistical Assessment of Peaks in the SPD of Declinations for S2* A: Complementary Methods, Dataset and Computations A-1: Quantitative Assessment of the Null Hypothesis A by the Method of the Confidence Envelope Curve using the Azimuth SPD The method was first presented by Silva (2020) for the declination histograms. [Extracted from the article]

The study of structures' orientations in archaeoastronomy often involves the analysis of the empirical sum of probability densities (SPD) for azimuths and declinations. A first logical step is to test the null hypothesis A of a random distribution of azimuths. This paper applies two methods: (1) the confidence envelope method with the azimuth SPD; and (2) binomial distribution with a probability parameter found from geometric estimates. Some empirical SPDs for which A is rejected can be composed of several subpopulations of structures with different grouping criteria. To assess the statistical significance of peaks or attractors potentially targeted to specific azimuths or declinations, a null hypothesis B is formulated. In its strong version, this hypothesis negates the existence of any attractor, while its weak version focuses on the local region of the peak without hypothesising about the rest of the SPD. This paper presents two methodologies for assessing B: (1) the method of the confidence envelope, applied to the strong version of B; and (2) a geometric method with the binomial distribution and a probability parameter estimated from the normalised frequency around the peak in the SPD (for the weak version of B). The methodology is illustrated with a case study of churches dedicated to the Virgin of the Assumption in southern Spain. [ABSTRACT FROM AUTHOR]