  We use type Ia supernovae (SNe Ia) data obtained by the Sloan Digital Sky
Survey-II Supernova Survey (SDSS-II/SNe) in combination with the publicly
available SDSS DR16 fiber spectroscopy of their host galaxies to correlate SNe
Ia light-curve parameters and Hubble residuals to several host galaxy
properties. Fixed-aperture fiber spectroscopy suffers from aperture effects:
the fraction of the galaxy covered by the fiber varies depending on its
projected size on the sky, thus measured properties are not representative of
the whole galaxy. The advent of Integral Field Spectroscopy has provided a way
for correcting the missing light, by studying how these galaxy parameters
change with the aperture size. Here we study how the standard SN host galaxy
relations change once global host galaxy parameters are corrected for aperture
effects. We recover previous trends on SN Hubble residuals with host galaxy
properties, but we find that discarding objects with poor fiber coverage
instead of correcting for aperture loss introduces biases in the sample that
affect SN host galaxy relations. The net effect of applying the commonly used
$g$-band fraction criterion is discarding intrinsically faint \mbox{SNe~Ia} in
high-mass galaxies, thus artificially increasing the height of the mass step by
0.02 mag and its significance. Current and next generation of fixed-aperture
fiber spectroscopy surveys, such as DES, DESI or TiDES in 4MOST, that aim at
study SN and galaxy correlations must consider, and correct for, these effects.
