Unit U3.4 · embed after: the error table / fire-alarm analogy

Hypothesis Testing - Type I / Type II errors and power (with counters and bars)

Data Science & Big Data Analytics • ITec4121 • Wolkite University • Online-First

Fire-alarm / court analogy with live counters and a bar chart: reality (H₀ false?) against your decision (reject H₀?). Three scenario presets (fire alarm, quality control, judicial) set α and power; record trials manually, run fixed batches, or use the batch-size selector up to 500. Watch TP/FP/TN/FN counts, expected-vs-observed totals, empirical P(Type I) and empirical power.

Concept - fire alarm (or court verdict)

	H₀ false fire / guilty	H₀ true no fire / innocent
Alarm rings / convicted reject H₀	TP - correct rejection	FP - Type I error (α)
No alarm / acquitted retain H₀	FN - Type II error (β)	TN - correct

H₀ = “no fire”. Rejecting H₀ when fire is absent = Type I (false positive). Keeping H₀ when fire is present = Type II (missed fire). Power = probability a real fire is detected = 1 − β.

Scenario & probabilities

Scenario:

P(H₀ true) power P(alarm|fire) α P(alarm|no fire)

Run trials

Reality Decision
batch

Bars = observed counts; the same-colour dashed boxes = the counts expected from your α, power and P(H₀ true) after the trials run so far.