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We assess the effect of magnification bias on the $E_G$ statistic for probinggravity. $E_G$, a statistic constructed from power spectrum estimates of bothweak lensing and redshift space distortions (RSD), directly tests generalrelativity (GR) while in principle being independent of clustering bias. Thisproperty has motivated its recent use in multiple tests of GR. Recent work hassuggested that the magnification bias of galaxies due to foreground matterperturbations breaks the bias-independence of the $E_G$ statistic. Themagnitude of this effect is very sensitive to the clustering and magnificationbiases of the galaxy sample. We show that for realistic values of theclustering and magnification biases, the effect for magnification bias is smallrelative to statistical errors for most spectroscopic galaxy surveys but largefor photometric galaxy surveys. For the cases with significant magnificationbias, we propose a method to calibrate magnification bias using measurements ofthe lensing auto-power spectrum. We test this calibration method usingsimulations, finding that our calibration method can calibrate $E_G$ from 2-4times the simulation error to well within the errors, although its accuracy issensitive to the precision of the measured redshift distribution andmagnification bias, but not the clustering bias. This work gives strongevidence that this method will work increasingly well in future CMB lensingsurveys.

Calibrating magnification bias for the $E_G$ statistic to test general relativity