#03 Count variables normalization

Explanation

For discrete counts (words, recordings, sentences): ratio to target, capped at 1 so over-documentation does not inflate the score.

Data & measurement

v_i counts Kifuliiru material (words, recordings, annotated sentences). v_i^target is the policy goal for that Kifuliiru variable. The min(·,1) cap prevents over-achievement from inflating LIS when a Kifuliiru corpus already exceeds targets. Targets should be revised rarely and with migration notes.

Solution & proof

For v_i ≥ 0 and v_i^target > 0, the ratio v_i/v_i^target is nonnegative for Kifuliiru documentation metrics. Taking min(1, ·) yields a value in [0,1]. If v_i ≥ v_i^target, norm_i = 1; otherwise norm_i is the linear fraction of progress toward the Kifuliiru target—standard capped ratio normalization.

Examples

1. 1. Lemma count below target

   Word problem

   The Kifuliiru documentation goal for lemmas is 1,000. The team has 400 validated Kifuliiru entries. What is norm_i?

   Kifuliiru count normalization

   	Value
   Documented lemmas v_i	400
   Target v_i^target	1000

   Solution

   Step 1 — Compute the ratio v_i / v_i^target = 400/1000 = 0.4 for the Kifuliiru lemma count.

   Step 2 — Since 0.4 < 1, min(1, 0.4) = 0.4. So norm_i = 0.4.

   ${\mathrm{norm}}_i=\min \left(1,\frac{v_i}{v_i^{\mathrm{target}}}\right)=\min \left(1,\frac{400}{1000}\right)=0.4$

2. 2. At and above target

   Word problem

   When v_i = 1,000 exactly, what is norm_i? When v_i = 1,500, what is norm_i?

   Same target, different counts

   v_i	v_i / target	norm_i
   1000	1.0	min(1,1)=1
   1500	1.5	min(1,1.5)=1

   Solution

   Step 1 — At the Kifuliiru target, the ratio is 1, so norm_i = 1.

   Step 2 — Above the target, the ratio exceeds 1 but the cap forces norm_i = 1 so extra Kifuliiru documentation does not increase the score.

   $${\mathrm{norm}}_i=\min (1,1)=1,{\mathrm{norm}}_i=\min (1,1.5)=1$$

Source

Impact measurement framework — Normalization Rules

Tags