Test Competing Output Interpretations
Use matched rates and an alternative mechanism to evaluate two interpretations.
Supplied materials
- Original fictional workshop records, same counted product and method: before schedule change, 100 units per day and 50 total labor-hours per day; after, 120 units and 60 labor-hours. A manager interpretation says “Our new schedule raised measured labor productivity.” A second interpretation says “Daily output rose through more total hours, while units per labor-hour stayed constant.” A tool replacement occurred simultaneously; no separate comparison is supplied.
Learn the idea
An interpretation depends on the measure used. Daily output counts units, while labor productivity here is defined as units per total labor-hour. Calculate both before choosing which explanation matches the data. A daily increase of twenty units can coexist with unchanged measured productivity when labor-hours rise proportionally.
Matching a descriptive pattern is different from proving a cause. The second interpretation matches the supplied output and hour figures better, but the records do not isolate why more hours were worked or what the tool replacement contributed. Productivity per labor-hour also does not measure pay, safety, quality, or each worker’s experience. Keep these distinct rather than treating one ratio as a complete social assessment.
- Compute the daily-output change and percent increase.
- Compute units per labor-hour before and after.
- Evaluate each interpretation against the stated measure.
- Identify the simultaneous tool change and two outcomes not established by the ratio.
See the method in action
“Output rose 20 units, or 20%. Before 100/50=2 units per labor-hour; after 120/60=2. The second interpretation fits unchanged measured productivity. The data cannot isolate schedule versus tool contributions or determine worker pay and experiences.”
Check your reasoning
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See the answer and explanation
Units per labor-hour stayed at two despite higher daily output.
Both ratios equal two. Higher total output alone does not establish higher output per labor-hour or any particular tool effect.
Take it further
Changed after figures: 150 units in 60 labor-hours. Model reasoning: “After productivity is 150/60=2.5 versus two before, a 25% rise in this measure. That changes the descriptive productivity conclusion, but simultaneous tool replacement still prevents isolating the schedule’s causal contribution.”
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