Statistical planning/analysis of null model for PACS experiment. Suppose k guides per g genes (the set of guides is denoted G), n cells measured, threshold set so that a fraction q of cells are gated under no perturbation.Model:$n_i$ cells are sampled from the ith guide with $\sum_{guides}n_i=n$. $x_i$ of each guide appears in the gated population with probability $p_i$ and conditional on the random $n_i$, is binomial with parameters $n_i$ and $p_i$.$n_i$ is itself binomial with parameters $n$ and $n/|G|$.under the null, each $p_i=q$.The null sampling distribution of $\frac{x_i}{n_i}-q$, conditioned on $n_i$ is approximately $N(0, \frac{q(1-q)}{n_i})$; if $q=1/2$ and $n=25$, this sd is approximately 1/10; if $q=.1$, the sd is approximately $0.06$.