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For refcode 1993ApJ...402..141V:
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1993ApJ...402..141V EFFECT OF MALMQUIST BIAS ON CORRELATION STUDIES WITH THE IRAS DATA BASE FRANCES VERTER NASA/Goddard Space Flight Center, MC 685, Greenbelt, MD 20771 Received 1992 February 25; accepted 1992 June 30 ABSTRACT This paper aims to cover four points: First, we reiterate the observation that Malmquist bias is a serious effect in optical galaxy catalogs (e.g., Tammann et al. 1979) and is even more severe in the deeper IRAS survey (e.g., Strauss et al. 1992). Second, we demonstrate that the removal of Malmquist bias in correlation and regression studies of global galaxy luminosities alters their results significantly. Third, we have developed a new procedure for removing Malmquist bias in linear regression statistics that is presented in an appendix. Fourth, we argue that detailed interpretation of the results from statistical studies with the IRAS data base must await improved treatment of bias in the galaxy samples and improved models of emission regions in individual galaxies. The data presented here are log-log plots of the global galaxy luminosities L_FIR_, L_H{alpha}_, and L_B_, as well as ratios of galaxy emission at these wavelengths, for galaxies drawn from the H{alpha} survey of Kennicutt & Kent (1983). These same galaxy properties have been studied before, using subsets of the same survey, by both Lonsdale Persson & Helou (1987) and Trinchieri, Fabbiano, & Bandiera (1989). These previous two studies disagreed slightly in the strength of the correlation results, and disagreed drastically in their physical interpretation of the galaxy emission. The statistical tests presented here are linear regressions that have been corrected for Malmquist bias. Our treatment of the Malmquist bias in linear regressions is the first to appear in the astronomical literature. Error bars are derived for both the correlation and regression results by bootstrap resampling. We find that the removal of Malmquist bias significantly alters the results of the statistical tests, in general lowering the correlation confidence and lowering the best-fit slope. The effect of the bias differs from case to case, so that once it is removed the relative strength of the results is also reordered. All the luminosity-luminosity plots are now consistent, to within 2 {sigma}, with slope unity, as would be expected for a pure luminosity increase with galaxy size. Subject headings: galaxies: photometry - infrared: galaxies
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