Spearman's Rank correlation

Question (6 marks): A student calculated a Spearman's Rank Correlation Coefficient of rₛ = +0.78 between distance downstream and hydraulic radius across 10 sites (critical value at 95% confidence = 0.564). Explain what this result tells the student about their hypothesis.

Mark scheme (Level-marked, 6 marks):

• Level 1 (1–2): Identifies positive correlation; vague link to hypothesis.
• Level 2 (3–4): States rₛ = +0.78 indicates a strong positive correlation — as distance downstream increases, hydraulic radius increases. Mentions hypothesis can be accepted.
• Level 3 (5–6): Full grade-9 response:
  • +0.78 exceeds the 0.564 critical value at 95% confidence, so the correlation is statistically significant — there is less than a 5% probability the result is due to chance.
  • Hypothesis is accepted: hydraulic radius does increase downstream, consistent with the Bradshaw Model (1978).
  • Acknowledges correlation ≠ causation; other variables (channel geology, tributaries) may contribute.
  • Recognises limits: 10 sites is a small n; repeat with larger sample for greater reliability.