Manuscript Psy03-D@1 · Psy03-D-v1.tex · section · 3e18951d

Ratios of population means

Sequence-level statistical certificates › Ratios of population means · lines 1090–1107

Psy03-D@1#eq:ratiotarget

For disjoint windows, define sequence summaries

p_{i} = \frac{1}{T} t \sum P_{i t}, n_{i} = \frac{1}{T} t \sum I_{i t} .

They satisfy $0 \leq p_{i} \leq n_{i} \leq 1$ . The population estimand is

Π_{old} = \frac{μ _{p}}{μ _{n}}, μ_{p} = E p_{i}, μ_{n} = E n_{i} > 0.

Its plug-in estimate is the pooled count ratio. It is not generally the average of per-sequence ratios.

Displayed formulas in this passage

unlabeled · line 1093
$p_{i} = \frac{1}{T} t \sum P_{i t}, n_{i} = \frac{1}{T} t \sum I_{i t} .$
Psy03-D@1#eq:ratiotarget · line 1099
$Π_{old} = \frac{μ _{p}}{μ _{n}}, μ_{p} = E p_{i}, μ_{n} = E n_{i} > 0.$