19. Code-Switching

Data & measurement

Continuity metrics emphasize intergenerational transmission, corpus completeness, and structural stability. Keep cohort definitions fixed across measurement waves. Symbols: f_cs (Code-switching frequency (0 to 1)); S_mixed (Sentences mixing Kifuliiru with other languages); S_total (Total sentences analyzed). Log instrument versions, sample frames, and cleaning rules whenever estimates are refreshed so longitudinal comparisons stay valid.

Solution & proof

Conceptual summary: How often speakers mix Kifuliiru with French, Swahili, or other languages within the same sentence or conversation. Treat this as a measurement recipe: map each symbol to an empirical quantity, substitute estimates, and simplify with ordinary algebra (including logarithms, min/max caps, or piecewise branches where shown). Where limits or integrals appear, approximate with discrete sums on cohorts or time steps when closed forms are impractical. Interpret the result against thresholds in the cited source and report uncertainty on inputs.

Examples

1. 1. Word problem — field log

   Word problem

   A measurement round produced the table below. Each symbol matches the Variables section for “Code-Switching”. Find the computed value using the formula above.

   Illustrative inputs—replace with your field numbers

   Quantity	Symbol	Value
   Code-switching frequency (0 to 1)	f_cs	0.52
   Sentences mixing Kifuliiru with other languages	S_mixed	0.63
   Total sentences analyzed	S_total	0.74

   Solution

   Step 1 — From the table, assign f_cs = 0.52; S_mixed = 0.63; S_total = 0.74.

   Step 2 — Substitute into the definition of “Code-Switching” at the top of the page (same structure as the source formula).

   Step 3 — After arithmetic, the illustrative output rounds to 0.851. Replace with numbers from your own community logs before publishing or sharing.

   $$\text{Given: }{f}_{c}s=0.52,S_{m}ixed=0.63,S_{t}otal=0.74$$

   $$f_{cs}=\frac{S_{mixed}}{S_{total}}$$

   $$\text{Illustrative numeric result: }\approx 0.851$$

2. 2. Second scenario — adjusted inputs

   Word problem

   The same measure applies with corrected inputs for the next report (see table). Recompute using the same formula.

   Revised values for the next report (illustrative)

   Quantity	Symbol	Value
   Code-switching frequency (0 to 1)	f_cs	0.59
   Sentences mixing Kifuliiru with other languages	S_mixed	0.63
   Total sentences analyzed	S_total	0.74

   Solution

   Step 1 — From the table, assign f_cs = 0.59; S_mixed = 0.63; S_total = 0.74.

   Step 2 — Substitute into the definition of “Code-Switching” at the top of the page (same structure as the source formula).

   Step 3 — After arithmetic, the illustrative output rounds to 0.851. Replace with numbers from your own community logs before publishing or sharing.

   $$\text{Given: }{f}_{c}s=0.59,S_{m}ixed=0.63,S_{t}otal=0.74$$

   $$f_{cs}=\frac{S_{mixed}}{S_{total}}$$

   $$\text{Illustrative numeric result: }\approx 0.851$$

Variables

Source

ALL_FORMULAS.md — Continuity

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