Data from a cross-sectional study of caries rates across various US states is plotted, showing average DMFT score against the percentage of cities with water fluoridation. What conclusion can be drawn from the graph?

Correct answer: B. Water fluoridation and DMFT scores have a moderate negative correlation

• A. The direction is right but the strength is overstated. The vertical scatter at any given fluoridation percentage is substantial — states near 50% coverage show DMFT values ranging from about 6 to 10. That dispersion is the signature of a moderate, not a strong, relationship.
• B. CORRECT on both counts. The direction is NEGATIVE — the trend line slopes downward, so as fluoridation coverage rises, DMFT falls. The strength is MODERATE, not strong: the points are widely scattered around the trend line rather than hugging it, which is what a correlation coefficient of roughly −0.5 to −0.6 looks like. A strong correlation would show points tightly clustered along the line.
• C. The direction is wrong. A positive correlation would slope upward, meaning more fluoridation accompanied MORE caries. The trend line here clearly descends.
• D. This is the causation trap, and it is the single most tested error in this topic. The study is CROSS-SECTIONAL — an observational snapshot measuring exposure and outcome at the same moment. It cannot establish temporal sequence and cannot exclude confounding by income, access to care, or dental workforce density. Correlation is not causation; only a controlled experimental design supports a causal claim.

Note: Rules of thumb for the correlation coefficient r: 0.0–0.3 weak · 0.3–0.7 moderate · 0.7–1.0 strong; the sign gives direction only, never strength. Ecological studies like this one compare populations rather than individuals and are additionally vulnerable to the ECOLOGICAL FALLACY — a group-level association need not hold for any individual.