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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]

Most of the earliest new churches built in Andalusia (southern Spain) following the thirteenth-century Christian Reconquista occupied the sites of former mosques. In some cases, these churches incorporated pre-existing architectonic elements - particularly minarets, which were converted into bell towers - or took some inspiration from Islamic architecture, creating a combination of Gothic style and elements from Muslim architecture known as Gothic-Mudéjar. This paper analyses the orientation pattern of a group of 68 Gothic-Mudéjar churches built in the cities of re-conquered Andalusia up to the early fifteenth century, and the normalised frequency distribution of azimuths is compared with published data for the qibla (the direction toward which Muslims turn to pray) observed at a group of 82 Andalusian mosques. Results confirm that a large number of churches were oriented via a 90° anticlockwise rotation from orientation to the qibla after placing the apse in the former eastern wall of the mosque. It is further argued, based on the histogram and a distinctive peak around 84°, that the architects aligned these churches to sunrise over the local horizon for 25th March according to the Julian calendar, the date of the canonical equinox. This practice reflects Church teaching and a medieval foundation-stone rite involving a dawn vigil, and the built structures reflect the limited technical capacity of the church builders. The method of orientation would also have created a precedent for the alignment of some later churches in southern Spain dedicated to the Virgin of the Assumption to sunrise on 15th August, the Feast of the Assumption. [ABSTRACT FROM AUTHOR]