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Astron. Astrophys. 318, 729-740 (1997)

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7. An investigation of the errors in the results

To assess whether there exists any observed excess or deficiency in the number of galaxies of one type in the vicinity of galaxies of another, it is necessary to understand the error in the number of galaxy-galaxy separations in the 10 to 60 arcsec range. A na"ive estimate of the error in the number of separations might be as the square root of the number. However, individual separation results will be highly correlated and such a simplistic approach may provide an incorrect error estimate, leading to inappropriate statistical conclusions.

Detailed numerical simulations have been performed of the statistics of galaxy distributions. Randomly distributed galaxies were placed in four simulated data frames corresponding to the samples of Table 4, having the numbers of the observed data. The galaxy-galaxy separations were determined and the number in the 10 to 60 arcsec range calculated. This process was performed repeatedly a total of 200 times for each pair of galaxy samples. The statistics of the number of separations in the 10 to 60 arcsec range provided estimates of the errors in the individual results of Tables 2 and 6; these are the errors quoted in these tables.

The Monte Carlo estimates of the error are larger than a simplistic [FORMULA] estimate, particularly for the bright-faint, the faint blue-faint red, and especially the faint blue-faint blue cases. Indeed had the na"ive estimate been used, it would have given a false anticorrelation between faint blue galaxies at a 2.6-sigma confidence level.

The results obtained using the detailed error assessments are presented in Table 7.


Table 7. Statistical conclusions. The excess densities over random distributions of galaxies are presented for each pair of samples considered. Simulation sets (a) and (b) are as in Table 6 for the faint blue-faint red and faint blue-faint blue studies

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998