1. Survival Equation

Data & measurement

For Kifuliiru intergenerational health, collect V_y and V_e from the same fluency instrument and scoring rubric for Kifuliiru; mixing tasks breaks comparability. T normalizes the comparison window (use 1.0 for a single cross-section). Stratify by region if sample sizes allow, then aggregate with documented weights. Store raw counts and exclusion reasons next to each rate.

Solution & proof

By definition S = (V_y/V_e) × T for Kifuliiru youth versus elder proficiency on a shared task. Algebraically this is a ratio of two rates scaled by T. If V_y = V_e, then S = T (usually 1.0). Values below 1 indicate youth fluency lags elders on the chosen measure; values above 1 indicate the reverse. Uncertainty in S combines relative errors in V_y and V_e; prefer reporting confidence intervals on the inputs and propagating them to S when publishing Kifuliiru outcomes.

Examples

1. 1. School district cohort

   Word problem

   In Uvira district, the same Kifuliiru oral proficiency task was given to youth (ages 5–25) and elders (60+). The rubric scores each cohort on [0, 1]. Youth averaged 0.72; elders averaged 0.80. The wave uses T = 1 (single cross-section). What is the survival score S for Kifuliiru?

   Kifuliiru cohort fluency rates

   Cohort	Symbol	Value
   Youth fluency rate	V_y	0.72
   Elder fluency rate	V_e	0.80
   Time normalization	T	1

   Solution

   Step 1 — Identify the model S = (V_y / V_e) × T for Kifuliiru.

   Step 2 — Substitute the table values.

   Step 3 — Divide and multiply: 0.72 / 0.80 = 0.90, times T = 1 gives S = 0.90. Interpretation: on this Kifuliiru task, youth are at 90% of elder proficiency; track across waves to see whether the gap closes.

   $$S=\frac{V_y}{V_e}\times T$$

   $$S=\frac{0.72}{0.80}\times 1=0.90$$

2. 2. After-school program site

   Word problem

   A second Kifuliiru program site shows stronger youth performance on the same task: V_y = 0.85, V_e = 0.68, T = 1. What is S?

   Second Kifuliiru site

   Cohort	Symbol	Value
   Youth fluency rate	V_y	0.85
   Elder fluency rate	V_e	0.68
   Time normalization	T	1

   Solution

   Step 1 — Same Kifuliiru survival formula.

   Step 2 — Substitute.

   Step 3 — S = 0.85 / 0.68 ≈ 1.25. Values above 1 mean youth outperform elders on this Kifuliiru measure—note possible task bias or schooling effects in the report.

   $$S=\frac{0.85}{0.68}\times 1\approx 1.25$$

Variables

Source

ALL_FORMULAS.md — Continuity

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