Previous studies using large datasets of spiral galaxies suggest that asymmetry between the number of galaxies that spin clockwise and the number of galaxies that spin counterclockwise exhibits possible patterns of cosmological scale. The asymmetry was observed by several different instruments, including SDSS, Pan-STARRS, and HST. The detected patterns change with the direction of observation and the redshift, and can also exhibit photometric asymmetry between galaxies with opposite spin directions. Different statistical and computational methods are needed to analyze these potential large-scale patterns. These methods include the identification of the existence of possible asymmetry, and profile the differences in different parts of the sky and different redshift ranges. Identification of a possible dipole alignment or multipole alignment of the asymmetry of the spin directions of the galaxies can be done by fitting the entire galaxy population into cosine dependence. Redshift dependence can be identified by correlating the asymmetry with the redshift of the galaxies in small but densely populated regions of the sky. Identification of the links between the redshift dependence and the direction of observation can be done by repeating the analysis with data separated into different redshift ranges. Analysis with real and simulated data shows that the presence of duplicate objects in the dataset or inaccuracy of the galaxy annotation cannot not practically lead to false identification of large-scale patterns. However, if the annotation error is consistently biased towards a certain type of galaxies, even a small bias can lead to statistically significant dipole alignment centered around the celestial pole. That reinforce the use of model-driven annotation algorithms with clear symmetric rules.