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

Flexibility ratios

Sequence-level statistical certificates › Flexibility ratios · lines 1152–1181

One possible predeclared definition uses, on each sequence, nonempty early and stable windows with mean accuracies $e_{i}, s_{i} \in [0, 1]$ . Define

F = \frac{E e _{i}}{E s _{i}} .

Theorem thm:ratio applies without upper truncation at one:

F \in [\frac{e _{L}}{s _{U}}, \frac{e _{U}}{s _{L}}], s_{L} > 0.

The ratio can exceed one.

A pooled-trial definition is a different estimand. If its early and stable correctness and exposure summaries have means $μ_{ce}, μ_{n e}, μ_{cs}, μ_{n s}$ , then

F_{pooled} = \frac{μ _{ce} μ _{n s}}{μ _{n e} μ _{cs}} .

Certify all four means and the required denominator positivity before forming that ratio.

Adding $1 0^{- 8}$ to a denominator produces a regularized statistic, not a proof that the original ratio exists.

Displayed formulas in this passage

unlabeled · line 1158
$F = \frac{E e _{i}}{E s _{i}} .$
unlabeled · line 1162
$F \in [\frac{e _{L}}{s _{U}}, \frac{e _{U}}{s _{L}}], s_{L} > 0.$
unlabeled · line 1172
$F_{pooled} = \frac{μ _{ce} μ _{n s}}{μ _{n e} μ _{cs}} .$