Table 4.

High gene variance is not a good indicator of cell type heterogeneity under the alternative hypothesis of zero-inflated negative binomial, because the variance can be lower under the alternative hypothesis

Alternative hypothesis	Variance under H0	Variance under HA
Mixture of Poisson	$\lambda =\sum _k{\pi }_k{\lambda }_k$	$\sum _k{\pi }_k({\lambda }_k+{\lambda }_k^2)-{\left(\sum _k{\pi }_k{\lambda }_k\right)}^2$
Negative Binomial	λ	$\frac{{\lambda }^2}{r}+\lambda$
Zero-inflated negative binomial	λ	${(1-{\pi }_0)}^2\left(\frac{{\lambda }^2}{r}+\lambda \right)$