Interpreting a Sparse Data Table
A student reads a report on urban tree cover. The report includes this sentence: "Cities that planted more street trees saw larger drops in summer surface temperature." The student also finds a small table: City A planted 400 trees and recorded a 1.2°C drop; City B planted 900 trees and recorded a 2.1°C drop; City C planted 150 trees and recorded a 1.9°C drop. City C is described in a footnote as having "an unusually dense canopy of mature trees predating the program." The student writes: "The data prove that planting trees cools cities, and City C shows the effect is not linear."
1. Evaluate the student's two conclusions against the report sentence and the table.
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First conclusion - "the data prove planting trees cools cities" - overstates. Three cities cannot establish proof; the report's own language ("saw larger drops") describes an association, not a controlled causal test. City C is a direct counterexample to a clean dose-response story: it planted the fewest trees (150) yet had a nearly as large a drop (1.9°C) as City B (900 trees, 2.1°C). Second conclusion - "City C shows the effect is not linear" - is better supported as an observation but misattributes the cause. The footnote says City C already had a dense mature canopy, which plausibly drives its temperature drop independent of new planting. So City C is a confounded data point, not evidence about the shape of the planting-temperature relationship. The student should either exclude City C or treat it as a case where a pre-existing variable, not new planting, explains the result.
2. If the student wanted to test the report's claim more rigorously, what would the table need to show, and what does the current table fail to control for?
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The table would need more cities (a sample large enough to distinguish signal from noise), a consistent measure of baseline canopy so that new planting is separated from pre-existing trees, and ideally a comparison group of cities that did not plant. The current table fails to control for baseline canopy - City C's footnote reveals exactly the variable that could explain its outlier result. It also lacks any measure of other confounds (city size, climate, measurement method, timing). With three rows and one documented confound, the table can illustrate a hypothesis but cannot test it. A rigorous version would report baseline canopy, new plantings, and temperature change for many cities, then ask whether new plantings predict temperature change after accounting for baseline canopy.